gah, I hate tierney with the blazing force of a million O-class stars. oh look, he's soooo brave! who would have ever dared to imagine talking about the deadly issue that cost st. larry summers (patron saint of douches) so dearly, and eventually caused him to be living in a gutter in his own urine-stained pants running the fucking government.
living in a gutter in his own urine-stained pants running the fucking government
No strikethrough necessary, really.
Trying to investigate sounds great. The article also mentions "interactive discussions or other activities that increase the awareness of the existence of gender bias." As 'other activities' are cheaper, this means another web-based 30 minute bore I have to sit through to get a piece of paper required so I can keep working.
go back to slate, douchey mcassholestein! get this motherfucking contrarian out of my motherfucking science times!
We need more women editors and publishers.
Yeah, Tierney pretty consistently sucks, and I don't know why he gets paid to write his inane columns. I suppose he sucks slightly less than Greg Easterbrook.
talk about damning with faint praise...
Plato, for heaven's sake, pointed out why this argument was flawed.
Short version: it's possible, indeed highly likely, that women are intellectually inferior to men in general. However, there's probably some overlap - ie the brightest women will be brighter than the stupidest men. Therefore it's foolish to bar women from any profession or discriminate against them, because you'll be missing out on the top 1% of women who might actually be able to compete on a level playing field against men.
If you're more sexist than Plato you have problems.
If you're more sexist than Plato you...
must be living in a cave.
Yeah, poor Larry.
And what a feat of derring-do on the part of Tierney (who is absolutely awful, btw, though admittedly he may be slightly less awful than some other awful writer-dude).
Hey, I learned a relevant word just now! Neuroessentialism!
though admittedly he may be slightly less awful than some other awful writer-dude
The awfulness of awful writer-dudes is not zero sum.
sucks slightly less than Greg Easterbrook
Who, in turn, sucks slightly less than Saletan. There's probably some serious scholarly work to be done on the taxonomy of pseudoscience writers, but I guess they are neither as appealing nor as interesting as, say, beetles or cockroaches.
Leaving aside just how utterly stupid and fucked-up this whole proposition is (I mean, ferchrissakes, at least in the 50s people said things like "I'm sure as soon as there are qualified Negroes applying for those positions they'll be given jobs"), it would be interesting to see how this all plays out over the next 20 years. Because walking around any reasonably selective campus these days, it's hard not to notice that there's a lot of very bright young women studying the sciences, carrying around the biggest backpacks and getting the best grades. Much more so even than 15 years ago when I was first in college. So what are we going to see down the road? Will these young women take their rightful places as the top researchers, teachers and sciency professionals? Or will libertarian meritocracy fail them for some mystifying reason? I suspect only Tierney and his cohort of Yale old boys know for sure.
Will these young women take their rightful places as the top researchers, teachers and sciency professionals?
Will they build illicit labs in dormant volcanoes and hire legions of bejumpsuited minions? Or will they waste time on curing diseases and shit?
Yeah, poor Larry.
This is sort of on-topic, given that we are talking about crappy thinking that passes in some circles for scholarship, and the persecution of the fabulously wealthy in the US.
Noted scholar Thomas Sowell manages to cite the existence of the Internet and the widespread availability of running water as examples of how government doesn't help the advancement of public welfare.
Of course, the taxonomy of nitwits puts Sowell on a different branch of the evolutionary tree from his journalistic cousins.
11: Sifu Tweety and I read the same mind-sci blogs, apparently.
5: We need more women editors and publishers.
But Bob, Tierney pointed out that women are overrepresented among those who excel at standardized tests of verbal ability. Which means that they must be overrepresented among editors and publishers. Right?
18: everybody should read mind hacks! I actually don't keep up with it as much as I should, because every time I get to one of those link dump posts (that he posts something like daily) I feel compelled to read all of the papers he links to, and it takes me fucking forever to get through them.
17: Thomas Sowell should get on his knees and thank his lucky stars that Jonah Goldberg exists, because otherwise the Goldberg Rule would almost certainly be known as the Sowell Rule. Jesus H. Christ.
Which means that they must be overrepresented among editors and publishers. Right?
Sadly, they lack sufficient testosterone for this sort of gladiatorial activity, and are thus forced to teach grade school English instead because, you know, kids.
22: On the plus side, they get to keep their heads.
I knew a woman in math grad school who was obviously the brightest student in her year. A crotchety old guy had just read some similar article mused to her "I guess women really are worse than men at math." The woman said that it wasn't even like he said it triumphantly -- he was just musing aloud, and there was a woman in math in the room, so the subject of "women in math" came naturally to his mind.
You may be surprised to learn that this woman is no longer in math...
America has Superman. Britain has Milkman.
I think Britain won this round.
there's no proof out there that the pool of innate mathematical/scientific talent among women is identical to that among men.
Here's my belief: male/female brains are probably different, but not necessarily better/worse at math and science. However, dominating the rhetoric and shaping the approaches and perspective for 2000 years will favor the brain that is most similar to the historical brains. In other words, 2000 years of women dominating math would have a different presentation, even if the actual nature of the theorems discovered was identical, and that presentation would lend itself to girls and women making sense of the material more immediately.
Someone should dig out Tierney's old column in which he complained about the heavy hand of Woman on our public discourse via the prevalence of gossip in the news media. I think the peg for the complaint was the seven or eight front pages that the New York Post gave some poor girl who had been stood up at the altar ("I tried to tell her").
Not to mention Bicycle Repair Man.
Most Monty Python is quite abysmal when translated into German, but Fahrradrepariermann is an exception, solely due to how funny that word sounds in German.
19:Right
No
28:Closet Lamarckist. Not really. Cultural Lamarckist?
No. But...
In other words, 2000 years of women dominating math would have a different presentation
This needs consideration. Mimetics.
and, in fact, the more gay male friends that a woman had, the more sexually attractive she felt, although conversely, longer friendships with the closest gay friend predicted lower self-perceived attractiveness.
Alongside biases against various objectively-identifiable protected classes, there are a bunch of others-- biases for people from the same educational institution, of the same ethnicity, pro- or anti-Bourbaki people....
In my mind, the clearest refutations to claims that there's no need for protection are the particular obstacles that women who did succeed had to overcome-- Barbara McClintock, Emmy Noether, and Sophie Germain all come to mind.
Math is pretty unusual in that the size of a working group remains small-- almost all other fields are tending to work based on more and more complex apparatus for sample preparation and for detection, which leads to engineering and administro-political skills being more important than hypothesis generation and experimental design chops for most projects, though not necessarily for actual progress.
Math attracts the socially inept (because you can do productive work alone). Also bloviating by essentialist imbeciles, who haven't themselves worked at anything long enough to notice that some tasks get easier as you do them more often, even though the end result looks like pure brainpower.
Does anyone under 40 read op-ed columnists? I read Pomfret and Krugman pretty often, but that's about it.
Not science, but I've always liked Heather Havrilesky's writing, and really liked
Whoops, this link.
http://www.salon.com/entertainment/tv/heather_havrilesky/2010/04/10/am_i_a_hoarder/index.html
Also, seriously?
The Duke researchers report in Intelligence, "Our data clearly show that there are sex differences in cognitive abilities in the extreme right tail, with some favoring males and some favoring females."
Because it's not as if any social factors could overwhelm innate cognitive abilities in 12- and 13-year olds. They're practically blank slates!
That's a bit harsh for getting a link wrong.
28: You could be a pioneer in the study of Womynist Math!
The Price nonsense (Jung?) on Old Kingdom Egypt was written to explore the questions about how and why culture changes, how and why culture affects individuals.
Imhotep made an entire civilization monarchical in one generation? Like, how?
As someone apparently pretty resistant to culture(s), "The Patriarchy made them this way" seems to me to assume a mechanism not in evidence. At least it is not evident to me.
Now maybe y'all understand the means by which culture is imprinted, but I see too many exceptions to have a scientific confidence that I can predict outcomes. And without being able to explain why the one Mormon kid out of a dozen in a family took off for Manhattan at 18, we don't have science, but hand-waving, superstition, and religion.
And without being able to explain why the one Mormon kid out of a dozen in a family took off for Manhattan at 18, we don't have science, but hand-waving, superstition, and religion.
I don't think you understand how science works, Bob.
I think that the experience of concert musicians --where blind auditions led relatively rapidly to gender parity in a previously male-dominated field-- means that the burden of proof should be on people who claim that real-life differences are caused by inherent factors.
Furthermore, so long as the number of women in a field is increasing it is very difficult to argue that we've already reached the point where the difference is explained by inherent factors.
For example, I would not actually be very surprised if men are inherently more inclined/able to become top chess players (though as explained above I think the default assumption should be that men and women are equally capable of being top chess players), however, I think it's abundantly clear that the current situation with one woman in the top 100 is *not* explained solely by inherent factors. As evidence, 4 years ago Fischer could reasonably say that he could spot any woman a knight. Now, the world champion can't assume they wouldn't lose to Polgar at even odds (indeed Kasparov did lose to Polgar while he was the champion). Since there's been significant change in the past 30 years, it's idiotic to expect that there won't be more change in the next 30. So once things stabilize for 30 years then come back and make the argument.
36:Piaget
The formal operational period is the fourth and final of the periods of cognitive development in Piaget's theory.[9] This stage, which follows the Concrete Operational stage, commences at around 11 years of age (puberty) and continues into adulthood.[9] In this stage, individuals move beyond concrete experiences and begin to think abstractly, reason logically and draw conclusions from the information available, as well as apply all these processes to hypothetical situations.
40:Probably not.
why the one Mormon kid out of a dozen in a family took off for Manhattan at 18
That would be because he was "sensitive."
Here's the only take on this I've seen so far at any of the science blogs I usually read.
39.last: That strikes me as a strange example since portions of Manhattan have been densely populated, diverse, and urban since before Mormonism existed.
As evidence, 4 years ago Fischer could reasonably say that he could spot any woman a knight.
Is that "4' supposed to be "40"?
Not even Hari Seldon could have predicted the Mormon kid's relocation.
You can know either the location or the velocity of a Mormon, but not both. If you give me $1.65 million over three years, I'll see if this finding is applicable to Methodists and Sunni Muslims.
Does anyone under 40 read op-ed columnists?
Maybe not. But they do read blog posts and tweets and etc, based on op-ed columns (or on someone's opinion of someone else's reading of the column, and so on). No doubt Tierney's insinuation that workshops on gender equity represent a new form of Soviet-style re-education camp will circulate broadly.
I really like FSP, linked in 44. It's rare to find a blog that focuses on the practice of being a research professor (as opposed to blogs that focus on scientific content) that's written by someone who's actually a very successful academic. Usually the people who want to blog about academia as a profession are people who aren't as successful (as people blog more when they're unhappy with their jobs, cf. Breath, Lizard).
46, yup, not sure how that happened. Meant 40 years. Before he went nuts.
I agree with this from the link in 44
On one point I reluctantly sort of agree with him: i.e., workshops to "enhance gender equality", mandated if certain legislation becomes law, could be kind of grim. In all likelihood, these would be yet another sounds-good-in-theory administrative requirement that PIs and others would have to sit through to be allowed to run our research groups.
workshops on gender equity represent a new form of Soviet-style re-education camp
I have been meaning to simplify my life.
yup, not sure how that happened
It's 4 years in girl math.
It's 4 years in girl math
The g-word! How offensive!
It's called Womynist Math, apo!
50: Yeah, it's become one of my favorite blogs to read. And unlike a lot of academic blogs I mostly recognize the culture it talks about.
Just did a quick count -- at the workshop I'm currently attending, about 12 of about 85 participants are women. It's hard to see how anyone would think a number like that doesn't need to be improved.
58: Workshop. OTB parlor. Whichever.
You can know either the location or the velocity of a Mormon, but not both.
You can know either the exact location or the exact velocity of a classic 1930s automobile, but not both. This is known as the Duesenberg Uncertainty Principle.
Apparently, Pittsburgh doesn't have any OTB parlors. Lots of public libraries, but nothing except the casino to help kids learn math.
60: I like this one, and will be finding strained excuses to work it into conversation. This comment constitutes a preemptive apology to anyone present when this takes place.
62: But there is one in Harmarville, a few miles outside of town.
See, my question about the stuff in the link is: what on earth is the ostensible motivation of studies about whether Barbie or Ken is better at math? What do those grant proposals look like? Even supposing one of these proved, in some way I can't fully imagine because I'm apparently part girl, that Men Math Better, women are demonstrably able to function at the highest levels in at least some cases, so the rest seems just to be about desperate rooting for an objective-looking pretext not to have to do anything about obvious inequities. Am I missing something?
"Why would a reviewer make the point of saying someone's not a genius?" -Eli Cash.
desperate rooting [about] for an objective-looking pretext not to have to do anything about obvious inequities. Am I missing something?
Nope.
Heebie's comment in 28 reminded me of this really wonderful 18th-century publication: The Ladies' Diary: or Woman's Almanack. One of its most popular features: the journal would publish a math problem, and then solicit solutions from readers (some of which would then be published in the next edition). It had a really long print run (began around 1704 and was still being published well into the 19th century, I think).
64: That's on the other side of the river.
68: I'm on the "other" side of that river right now, and I'm in Pittsburgh.
And also: 'Daring to Discuss Women in Science,' indeed.
I'm going to link one more time to the classic illustration of journalism's paradigm. Scroll down to see three concentric circles, labeled:
- The sphere of consensus
- The sphere of legitimate debate
- The sphere of deviance
Phooey on Tierney and all his ilk for dancing on the border of consensus and pretending they're anywhere near deviance. They ought to be ashamed.
69: It will always be Allegheny City to me.
sphere of deviance
Great idea. Now I can get back to my Star Trek fan fiction.
I know; that's why I incessantly link it.
sphere of deviance
Great idea. Now I can get back to my Star Trek Divina Commedia fan fiction.
Presumably somewhere around the Sphere of Venus.
And also: 'Daring to Discuss Women in Science,' indeed.
Yeah, it's ridiculous. He's probably disappointed that the legislation is so tame: a couple of years ago, he was fretting about the possibility of a quota system "that could seriously harm scientific research and do more harm than good for women."
Am I missing something?
THE QUEST FOR TRUTH!
Instapundit had a link to a story yesterday about some under the table affirmative action for men, especially at let's call them second tier schools. Supposedly when the mix of male to female gets out of whack the institution loses "prestige". This is at the undergrad level. COnsidering it is a bunch of 18 year olds making the decision whether to apply and then matriculate, maybe it is not that strange, but still.
80: I thought that had been going on fairly openly at lots of schools for a while now -- seems as if I started hearing about it ten years ago or so.
This is an interesting theory:
Two parrots cannot occupy the same space at the same time. This is known as the Polly Exclusion Principle.
I would have thought we were well past "Where the Boys Are". http://www.imdb.com/title/tt0054469/
Perhaps there should be a college that didn't have a football team and would admit only the smartest students, not ones looking for future mates or networking opportunities for future Chets. But that would be silly.
There's "affirmative action" (that is, preferential admission despite test scores lower than those of foreign applicants) for the US-educated in grad programs in the exact sciences-- Physics, EE, and CS for sure.
in the exact sciences-- Physics, EE, and CS for sure.
Like everybody else is 'inexact' for working on harder problems.
Since when are EE and CS "exact sciences"?
76: I had a very good high school English teacher named Kenn.
84.2: American higher education has a bit of a Stein's Law issue at the moment that arguably ought to be addressed by schools' focusing on what they're good at (or could be good at) rather than gaming the Useless News rankings, but prediction, future, yada yada.
Since when is physics an "exact science"?
Inventorying exact sciences is not an exact science.
86: I had a psych prof in undergrad who divided the sciences into hard sciences where control of all variables is difficult or impossible, and easy sciences where you can control all your variables and run lots of trials.
Hard sciences: economics, boxing, cosmology.
Cosmetology is the hardest science because of the nipple concerns.
The number of residential four year colleges is bound to go down. In this day of podcast and videoconferencing there is simply no need to be in the same room. Thousands could listen to the same lecture all over the world.
But you, know, tradition. Well, most "traditions" are less than 150 years old.
The next bubble to burst is higher education. My condolences to those in Academia, or struggling to get in the Ivory Tower.
Boxing is both hard and sweet, like peppermints.
96.1 The desire of late teens to get out of mom and dad's house hasn't changed and you can't get a scholarship, grant or loan to move across town and listen to video conferences.
My dad constantly makes the argument in 96, but I think it's totally wrong. The attraction of the university to undergrads is, roughly, 85% credentialing and socialization, and 15% information supposedly transmitted in the lecture hall, so I think expensive 4 year colleges will be with us for a long time.
The number of residential four year colleges is bound to go down. In this day of podcast and videoconferencing there is simply no need to be in the same room. Thousands could listen to the same lecture all over the world.
Every time I hear people say something along these lines I think that by conflating "college education" with "going to classes", they missed the point. Or I wonder if I did.
Huh, I guess that's not really English-- точные науки gets many more google hits than does the english phrase.
Population biology has many useful exact results, but biology isn't a hard science.
Actually saying hard and sweet aloud should be worth some kind of prize.
96.3 is, unfortunately, probably right.
Have you dropped by your local boxing gym, Halford?
"Exact science" is an English phrase. See?
"Next"? If you've seen the academic job market in the past two years, you'd argue it has already.
No, but I did sign up with Crossfit, based largely on your advice that they weren't that scary. You were right! They aren't! Thank you! My legs are awfully sore, though, and holy shit do I need to work on getting more flexible.
If you've seen the academic job market in the past two years, you'd argue it has already.
I should hope you keep your moods in better order in German, young lady.
In the humanities, anyway. See the t-t stats for German, for instance.
Well, most "traditions" are less than 150 years old.
There was a gag in Britain when I was a kid about an announcement on some unspecified Ivy campus: "It is traditional that undergraduates other than seniors do not walk on the grass in the quadrangle. This tradition will come into effect from next Monday."
I think expensive 4 year colleges will be with us for a long time
I think that's right at the high end, but the middling private schools have a problem, as do a whole lot of the publics.
||
71: It will always be Allegheny City to me.
I'm having a bad day with a bad headache at a bad all-day business meeting, but am buoyed by the fact that from certain places in the room I can see this Shepherd Fairey "OBEY" wall mural.
|>
Also, this is a very wrong thing:
In this day of podcast and videoconferencing there is simply no need to be in the same room.
We're not going to get over the social primate thing any time soon.
111 -- I guess, but on that theory the mid-range and lower-end expensive private colleges should have been crowded out by the public universities a long time ago. It turns out that "I'm likely rich and expensively educated" is a signal that a lot of people will pay quite a bit of money for, even if they could signal "I'm smart" much more cheaply.
The desire of late teens to get out of mom and dad's house hasn't changed and you can't get a scholarship, grant or loan to move across town and listen to video conferences.
The attraction of the university to undergrads is, roughly, 85% credentialing and socialization, and 15% information supposedly transmitted in the lecture hall, so I think expensive 4 year colleges will be with us for a long time.
I am sympathetic to the arguments above, as soon as the employers catch on to the fact that a college degree has been so devalued as to be meaningless as credentialing it won't matter that Johnnie wants to get out of the house, 'cuz Daddy ain't paying for 4 years of drunken "socialization" without some sort of payoff.
even if they could signal "I'm smart" much more cheaply
I pay an undocumented immigrant to walk in front of me saying "He's smart."
115: What on God's green earth makes you think employers' interest in credentials rests on the assumption that they're an indicator of ability?
social
Well, that certainly explains why there aren't deferential crowds of youngsters here hoping to find morsels of free knowledge.
What fraction of marriages are to partners met in college, and is this dropping? My college girlfriend moved to the city where I went to grad school, and we married so that she could get insurance.
Johnnie
is a scotch.
@108
It's striking that the pattern in that chart follows the real estate bubble closely.
106: Ooh, I'm glad they turned out to be a good group. I've seen people get a lot out of Crossfit.
Sore muscles: Do a few of the exercises that made them sore to get blood to the area (lightly). Ice and Vitamin I.
I will say that, from a consumer perspective, there doesn't seem to be much reason to spend four years in college anymore -- two years at a good CC to get decent instruction in the basic courses, then a transfer and two years at a 4 year institution to get the upper-level courses, credentialing, and jobs. Plus, with a two year and then transfer plan, you are far less likely to end up drunk for four years in a fraternity/sorority or high for four years in a co-op.
I will admit that this is probably not the course of action I would recommend to my own kid, but I can't really think of a good reason for that, other than that I am probably captured by the prestigo-industrial complex.
Thanks, Megan. I will try that.
121: I'm really puzzled by this one. Something like what you say seems clearly right. OTOH, I can't quite see advising Sally and Newt to head for anything other than Ivy/Stanford/MIT/UofC, regardless of the fact that it'll be brutally expensive for us, with very little clear payoff.
I'm sort of hoping that tertiary education changes drastically in the next 5-10 years, enough to clarify choices.
124: Me too. It was simple, but there really wasn't a clear best strategy.
123: For very bright kids, there's some advantage to being in a place where most of the other kids are also very bright. Faster-placed classes, more interesting drunken bull sessions, etc.
126: A strange game. The only winning move is to pretend not to play.
captured by the prestigo-industrial complex
That's a great phrase.
With the caveat that my own experiences are probably totally unrepresentative, but the counter-caveat that I would guess they're more representative among the Mineshaft than the general public:
121 I will say that, from a consumer perspective, there doesn't seem to be much reason to spend four years in college anymore -- two years at a good CC to get decent instruction in the basic courses, then a transfer and two years at a 4 year institution to get the upper-level courses, credentialing, and jobs. Plus, with a two year and then transfer plan, you are far less likely to end up drunk for four years in a fraternity/sorority or high for four years in a co-op.
If your only goal is to get a credential, then yes. But if your goal is to really get a good education, I think you can't underrate the opportunity of being really immersed in an academic environment and talking to people who know their field backwards and forwards. There's a lot of oral tradition and folklore and jargon one has to absorb to become an expert in something, and it isn't easy to pick up from books or from people outside the culture of the field.
Even looking only at coursework, my first-year math class at the UofC was more advanced than anything outside of grad classes at the local 4-year university where I grew up, much less anything CCs teach.
123 121: I'm really puzzled by this one. Something like what you say seems clearly right. OTOH, I can't quite see advising Sally and Newt to head for anything other than Ivy/Stanford/MIT/UofC, regardless of the fact that it'll be brutally expensive for us, with very little clear payoff.
Not necessarily brutally expensive. Even working under the assumption that they'll get no financial aid, the UofC offers a lot of merit scholarships, and some of the other schools of similar quality offer a few.
Well, if you're a super-genius going into theoretical physics and advanced mathematics, and can get a merit scholarship to the University of Chicago, things probably look a little different.
But most folks aren't particularly interested in learning a "field" in undergrad education; they're going to get the degree and use it to a stepping stone in something else, either grad school or in the marketplace, and not stick it out in academia. And even then, it seems like a pretty poor investment of, what, $100K for two years?
Thousands could listen to the same lecture all over the world.
Even putting the social and out-of-class aspects aside, listening to lectures does not an education make.
135: I KNOW! STOP LECTURING ME!
134: I don't think there's much argument with that. LB's kids are not "most folks", and for a lot of students you're right that CC + State U is as good a route as going straight to State U or a mediocre private.
135 is right. And D2 isn't here any more to argue that all professors do is make PowerPoint presentations.
138: and drink schmancy beer and overpriced scotch.
137: And, of course, they're eight and ten. Plenty of time yet to lose all interest in academics and end up on a completely different trajectory. (Newt is fascinated by the Food Channel, and keeps on asking about how culinary school works. Given that he still doesn't like any actual food beyond bread, meat, and pickles, I don't know that this is a realistic plan.)
134.1: That wasn't really my point, and I wouldn't characterize myself that way. I agree with you that for most people a CC and a university to get a credential is a good plan, if they need that credential. But for people whose goal really is to learn -- and I think this is a far-wider class than "genius", whatever the hell that means -- a good university can make a huge difference.
141: And of course, it's hard to tell going in. I've always had a lousy relationship with academics, and got much less out of college than I should have -- I might well have been better off with the CC + 2 years at a state school than I was at the excellent schools I went to, which I got through by doing the minimum work necessary to get pretty good grades. But there wouldn't be any easy way of sorting me into a group of people who shouldn't bother; what held me back from getting more out of it was some kind of emotional/psychological screwiness, not any sort of incapacity or disinterest in academic subjects.
140: By the time Newt is college age there will, God willing, be a very nice culinary school on the slopes of Diamond Head. But I'm betting he'll end up at Elite U instead.
142 strengthens my suspicion that LB is my long-lost sister. But I was even more unprepared for elite education and bailed out to State U rather than another elite school.
Given that he still doesn't like any actual food beyond bread, meat, and pickles,
Sounds like he's ready to open the hottest new restaurant on the Lower East Side.
I'm not really arguing that a good university makes no difference. Of course it does, particularly at the upper levels. But it's a little hard for me to see why even very smart kids would get a huge benefit in purely educational terms [I'm not talking about social connections, or the old boys network] from (just to compare) spending two years at a CC in LA and then transferring to UCSB versus spending four years at even a very good liberal arts college. And I believe that we're talking about a 75% or more difference in cost between the two plans.
Arguably, there's a level of confidence that comes from knowing that you're in the "better" or more expensive school, and a degree of socialization with smart people that can be critical. On the other hand, there's also the fact that about 1/2 of the student body even at very good colleges are basically spending their time partying, and the ability to transfer up and work on your own can be confidence-building as well.
Again, I probably wouldn't select plan (2) in practice, but I'm not really sure I've got good reasons.
Maybe a trendy sausage maker? I swear half of the boy's bodyweight is various forms of dry salami, sopressata, pepperoni... at some point in his adolescence, we're going to have to get him a meat grinder, a spice shelf, and half a pig and see what happens.
I mean, I went to a very good and expensive school for four years, and my writing sucks.
The best plan depends on the kid-- different kids have different personalities. CC in its current form seems counterindicated for bright but passive kids.
Private U costs $35 per year, though, that's a lot to pay for peer motivation.
I mean, I went to a very good and expensive school for four years, and my writing sucks.
And yet you charge $800 per hour.
146.1: IME there was a pretty significant difference in sophistication of course content between Elite U and (pretty good) State U.
153/154: They're using the razor cartridge refill model of pricing.
154: $34,065 is the price for mathematicians. For the arithmeticians, it's $34,965.
After I graduated, and before graduate school, I went to the local, very highly regarded CC. (I made it through a summer and then I had to be back in school - really, this is embarrassing.) While I felt that I got a very good education in the four classes I took, the dedication or lack thereof of my fellow students really caught me by surprise. I had already come from a school where most were not all that interested in academics, but at the CC, this seemed to quadruple (or more, it was a lot, ok?). I think it would be very hard to be in that environment - temptation abounded to slack and there was definite peer pressure to not sound smart.
Two of my best friends did the CC + 4 year college route, and they both got great educations, but it never, ever just takes 4 years (arguably, it doesn't at many four year institutions too). Both were highly dedicated and very smart, and both took much longer to finish. Transferring just isn't that easy and you end up having to repeat a number of things.
Orly Taitz might win the Republican nomination for California Secretary of State?
Oops, pretend 158 is in Stanley's primary thread.
158: Does that mean she gets to certify Obama's eligibility to run for president in CA? Because that would be interesting. If she's not in a position to pull a Katherine Harris I hope she wins. Let the tea partiers hang that millstone around the neck of the GOP and it will most certainly hurt them.
OTOH, I can't quite see advising Sally and Newt to head for anything other than Ivy/Stanford/MIT/UofC, regardless of the fact that it'll be brutally expensive for us, with very little clear payoff.
I'm shocked by this statement but I don't know why.
It may just be an East Coast/West Coast thing, with much less emphasis being placed on college status on the West Coast. I don't know that any of my peers in HS were being advised to look at just "Ivy/Stanford/MIT/UofC" and certainly the only advice that I got was, "look for a college that appeals to you and seems like a good fit" not "go the the best school that you can get into."
The high status of the University of California has got to make West Coast perceptions very different from East Coast -- I think of state school and elite school as disjoint sets, but of course that doesn't work in California.
I also generally think of things like 'good fit' as, while nice if you can get it, really impossible to achieve in any educated fashion, barring the occasional really unusual school.
The first time I heard the dollar amount that we should ideally be saving for college, I was truly shocked. It is brutally expensive.
Yeah, it is strange to me that your default wouldn't automatically be your excellent state university, unless there were a particular reason to go somewhere else.
But when I look at how the Cal state system has been damaged in the budget cuts (and presumably the UC's as well), I don't know if I can still recommend the schools that were the default for my whole life.
We're just not saving anything like what we need to be. I'm sort of figuring that the apartment will be paid off by then, and remortgaging it will cover us.
There are many examples of colleges and universities reputations getting better, but how many have lost market share by reputations going down? Does it happen?
And the SUNY's are fine, respectable schools where you can get a perfectly decent education, but they're teaching a broad spectrum including a lot of poorly prepared kids.
It may be a midwestern thing too, but is probably a social class thing more generally. I got into the U of Chi, but no one told me I was a fool for turning them down and going to the SLAC that I liked better and that offered me better funding.
In my case it wasn't so much parent driven, as that the public high school I went to was very competitively college admissions focused, so everyone had a clear sense of relative status, and the assumption was that you were going to the highest status school you could make it into, unless you had a clear sense of why your choice was better for you.
Part of my whole lack of cultural capital thing was just assuming that the next step after taking AP classes and such was to trundle off to the best school that would have me (for certain poorly-defined values of "best").
172: The siblinghood continues!
It is somewhat frightening that my son at 13 has more of a clue than I attained until probably some time in my 30's.
The high status of the University of California has got to make West Coast perceptions very different from East Coast -- I think of state school and elite school as disjoint sets, but of course that doesn't work in California.
You do have Rutgers within 50 miles. Maybe I only think of it as an "elite school" for field-dependent reasons.
I can't quite see advising Sally and Newt to head for anything other than Ivy/Stanford/MIT/UofC
Why no love for brutally expensive private universities in the Alleghenies?
It is somewhat frightening that my son at 13 has more of a clue than I attained until probably some time in my 30's.
Is he a writer for kid's tv shows? The dad is always clueless in those shows.
171: My hippie school was like that. They sat me down in 9th grade and earnestly explained that it was up to me to choose how to make the world a better place, but with PSAT scores like that, I could pick my Ivy League school if only I'd turn in homework once in a while, and what the hell was wrong with me anyway.
174: Didn't you once comment that your parenting goal was to raise your children to get a clue at a younger age than yourself?
Congratulations! You're done!
I gave frighteningly little thought to my school choice. Berkeley did OK by me, but in retrospect I wonder whether I would have had a better experience in a place where they notice you.
I didn't learn though, and gave equally little thought to the question of whether I should go to superfluous law school. Apparently, I'll go to any school on any day if it flirts with me.
The high status of the University of California has got to make West Coast perceptions very different from East Coast -- I think of state school and elite school as disjoint sets, but of course that doesn't work in California.
I'm in Washington, so I don't know if that's the explanation.
It's that, on the West coast, there are more social circles and, crucially, employers that just don't care that much where you went to school. At least compared to what I've heard about the East Coast.
In my case it wasn't so much parent driven, as that the public high school I went to was very competitively college admissions focused, so everyone had a clear sense of relative status, and the assumption was that you were going to the highest status school you could make it into, unless you had a clear sense of why your choice was better for you.
Yeah, I sometimes wish that I had spent at least some time in an environment that pushed people to focus on college admissions, but nothing in my HS experience did.
Of course, my family background is part of it. My parents went to Antioch college, and were mildly hostile to high status universities (only mildly, they didn't say anything negative, but I never got the impression from either of them that the Ivy's were anything to aspire to).
Mine as well. Both parents did lots of school, and neither ever gave me the sense that the Ivy's had anything special to offer me. CalTech, on the other hand...
Yeah, my public school had decent counselors, but a poor trudling service.
There were certain high-achieving kids at my school who applied mostly to Ivies (and could tell you what the Ivies were, which I certainly couldn't have), but most of my (very smart) friends applied to a wide range of schools, likely selected through an elaborate process of shuffling brochures performed on their bedroom floors.
179: That's probably not far from the truth. I could walk in front of a bus tomorrow and the kid would probably be fine.
181: UW isn't doing so badly these days either.
All well and good to talk about Ivies, but I mean, really, Cornell?
It's the best of both worlds: an Ivy with an Ag school!
What 185.2 said. UW Seattle is definitely pretty high up in my personal taxonomy of good schools. Plus, it's gorgeous there, so I don't understand why anyone would ever leave.
All well and good to talk about Ivies, but I mean, really, Cornell?
You better be careful with that one around these parts.
It's certainly seems to be the case in California that more strong students go to state schools relative to what happens on the east coast. Furthermore, because of this it seems to me that the CC+State School approach is more normal and viable in California. The top math undergrad at Berkeley last year was a CC transfer student, and although that's rare it's not the first time it's happened.
It will be interesting to see how this develops with the ongoing collapse of the California government and the resulting huge detrimental affect on the Cal State and UC systems. It's now much less affordable to go to a UC, and it's unclear whether the UCs will be able to retain their prestige given their lack of resources to hire and retain professors.
Plus, it's gorgeous there, so I don't understand why anyone would ever leave.
I can't argue with that.
Personally I wanted a smaller school, and I think that was the right choice (I ended up going to Willamette which offered my a nice scholarship), but just being a couple hundred miles south felt like a noticeably different environment, and I missed the area in which I grew up.
I am very attached to this part of the country.
It's that, on the West coast, there are more social circles and, crucially, employers that just don't care that much where you went to school. At least compared to what I've heard about the East Coast.
That is very true, and really is a big difference between the coasts. Or at least between the West Coast and the Northeast Corridor. It can be shocking for some Ivy League northeastern transplants here to find out just how little people care about college as a marker of identity.
[Not that a Harvard degree isn't helpful, but it doesn't have remotely the same social or professional impact that it would back east]
The top math undergrad at Berkeley last year was a CC transfer student, and although that's rare it's not the first time it's happened.
It makes me happy to know that.
No, I am afraid I do NOT know Coach Paterno.
I went to four state schools and one community college, and I can read and write like a champ!
I'm somewhat skeptical of the point in 181 about employers. My impression was that the top bay area employers are all cabals of Stanford alums.
Plus, it's gorgeous there, so I don't understand why anyone would ever leave.
Possibly the total absence of sun for weeks on end.
All this nostalgia made me Google up this guy, whose introductory economics section was one of the best classes I ever took. Nice to see he's done OK for himself since getting the Ph.D.
It can be shocking for some Ivy League northeastern transplants here to find out just how little people care about college as a marker of identity.
It is true. The important marker of identity is your tan. That's how we know if you're important.
193: In his valedictory speech he said that the first math class he took in college was the equivalent of a highschool Algebra 1 class. Somehow he got from there to taking all grad classes at Berkeley.
195: You misspelled "chimp".
200: like I don't know how to spell own name.
You're not one of those face eating chimps, are you, Tweety? 'Cuz that's really gross.
Is it wrong that I'm contemplating not voting because doing so would cut into watching the Lakers game?
Long lines at the polling place? Doubtful.
203: Isn't there one proposition that it is important to vote against? Or is it sure to lose anyway?
198: Do freckles count as a partial tan?
My impression was that the top bay area employers are all cabals of Stanford alums.
Yeah, that's about how things seem to me, as well. Admittedly quite second-hand, but my roommate's old classmates from Stanford certainly seem uniformly successful without too much regards to brilliance/charisma/whathaveyou in ways that a comparably bright group of, say, UCLA students would not be.
Also, U of C has a lot of merit-based scholarships? What sort of qualifications did they offer those scholarships for? I don't remember hearing of any schools offering merit-based as opposed to needs-based when I was going into college (2002ish), aside from some minor breaks for people who topped the Intel Talent Search or finished in top 20-30 on USAMO multiple times through high school. So, well, damn. I remember being really disappointed, too, since I'd always heard such things existed before starting to look at colleges.
I don't remember hearing of any schools offering merit-based as opposed to needs-based when I was going into college (2002ish)
There are some examples.
Whitman Achievement-based Scholarships: Whitman awards renewable, four-year merit-based scholarships, ranging from $8000 to $12,000 to entering students who have excelled academically.
I remember that they had significantly better merit-based scholarships than Willamette did, but they all used HS GPA as a cutoff, and my GPA was just pretty good so I didn't qualify, though my test scores were great.
This is a bit of a fraught issue for me. All I got in terms of college choice advice from my parents was a strong expectation that I would get a scholarship to BYU. My high school had only a few kids in any given year who could get into elite schools (most were lucky not to drop out), and there was basically no one to say, "hey, think about these options." I applied to two schools, BYU and one Ivy, and only got in to BYU. Which was an okay school but lacked (among other things) the kind of robust intellectual culture that I imagined better schools had. I got a decent education, but I felt the classes weren't challenging enough and most of my fellow students weren't smart enough.
For Chicago, you just check a box on the application if you want to be considered. Other schools that offer merit scholarships in moderately large numbers: Wash U, Rice, CWRU, UVa. (This is how I decided where to apply when I was in high school. In retrospect, this was kind of dumb, but it worked out okay in the end.)
Hey, it's late to the party bad joke time!
You can know exact position and velocity of an iceberg. This is known as the Eigen Berg Principle
Emmy Noether was fucking rad.
Or at least between the West Coast and the Northeast Corridor.
Yeah, it's more specific than East/West, says this representative of the UNC-UVa axis.
Oh, NYU also has merit scholarships. And apparently pretty much anywhere does if they want you enough; someone I knew got a full scholarship to Caltech, which IIRC at the time claimed not to give any merit scholarships. But he was one of those olympiad-winner types and I guess they somehow bend the rules.
213: Not as rad as Marie Curie!
Groan.
Is it wrong that I'm contemplating not voting because doing so would cut into watching the Lakers game?
Aren't you gonna get out and vote for Mickey Kaus? THINK OF THE BLOGGING!
Apparently, going to a prestigious school pays off. Going to an expensive school pays off too.
http://www.halfsigma.com/2006/08/attending_an_iv.html
I had seen that study cited for the opposite conclusion.
211: "awarded to applicants on the basis of outstanding academic and extracurricular achievement, demonstrated leadership, and commitment to their communities"
Ah, never mind, now I understand why I never even heard about any of these. Gotta admit, I probably should have played the extracurriculars game a bit more in high school if I had really intended to be wanted by these schools.
But he was one of those olympiad-winner types and I guess they somehow bend the rules.
Yeah, I knew a few of those guys at my high school, but they were pretty much the only people I knew who got merit-based without going to state schools or places like Olin College. "I'm gonna represent my nation at the math olympiad" doesn't exactly seem like a good way to plan for a scholarship, though.
Hmm... I guess I should start worrying about this sort of thing if I'm only going to have kids in... 3-10 years, right? How much am I supposed to be saving?
Washington University has used merit scholarships to impressively increase the schools prestige:
I had never heard of the school when I went to college.
I recall an op-ed from the author of that study making exactly the opposite point (i.e., claiming that an expensive college does not provide a good financial payoff) so I am skeptical of the linked blogger's summary.
From the link in 221:
''there's no reason why America can't have more than one No. 1 institution.''
Math is hard! Let's go shopping!
Everyone at my high school knew about WashU, presumably because it ranked high in some combination of proximity and prestige. A few of my high school friends and acquaintances went there.
222 to 219.
Also, anyone who subtitles their blog "The new politics of common sense. Neither Republican, Democratic, nor Libertarian" can blow me.
I like to have someone buy me dinner first.
210: pfff. That ain't fraught!
Having many, many people to say "hey, think about these options!" but lacking the desire to attend or particularly pay attention to the requirements of high school, I applied to nine schools, including my father's alma mater, and got into one of them, State School No. 1. Hating the fact that it was in the sticks -- and that it was full of drunken morons -- I transferred to State School No. 2, an urban commuter campus which lacked competitive admissions. Opting to spend more time on my bong-wrangling and being-depressed, I dropped out halfway through my first semester there.
[ cut to TEN YEARS LATER ]
Going back to school, I opted for Community College No. 1, which was surprisingly even more humiliating than either of the first two schools. Making it out of there, I started taking classes at State School No. 3, until [ CRAPPY LIFE EVENTS OMITTED ], then eventually landed at State School No. 4, which I almost dropped out of while I chatted with a bunch of over-educated high-scholastic-achievin' ivy-league types on the internet, but which I finally, gaspingly, finished. And now I'm looking to attend even more school! HAH! I know. I assume deep down it's all one long attempt to stick it to the HS math teacher who had the gall to tell me that I'd passed his class (and would therefore graduate) (something I hadn't realized was likely to be a problem, actually) at the prom. I'll show him!
What I don't like about the post linked in 219 is its explicit assumption that the only possible benefit of going to college is more money.
You ever have one of those comments where by the end of it you forget who you were talking to and why?
Everyone at my high school knew about WashU, presumably because it ranked high in some combination of proximity and prestige.
Where'd you grow up, essear? I don't remember WashU being mentioned much when people were considering undergrad from my Illinois high school, but I've had a few friends go there for law since.
226: My conscious mind is fully reconciled to the choices I made and the way they've played out over the years, but I still have the occasional dream where I've gone back to Elite U to finish a bachelor's degree there.
Wash U. had one of the best (perhaps the best) early open EFnet servers.
It can be shocking for some Ivy League northeastern transplants here to find out just how little people care about college as a marker of identity.
This could not be farther from my experience. I went to an LB-approved grad school, then moved west to postdoc. My grad school affiliation was a matter of course on the East Coast; out here, whenever anyone asks where I went to school (which they do, surprisingly often), they look at me like I suddenly sprouted an extra brain. Nope! Still the same person you were interacting with a second ago, back before things got awkward! It'd be nice if search committees cared enough that they give me a second look, when the time comes; everyone else should please be indifferent.
I remember being vaguely aware that Wash U was a really good school when I was looking at colleges, and I was 1000s of miles away and this was well before (I think) Po-Mo or SER were looking at schools, so, data point.
I omitted my name on 232 so that no one would start looking at me funny.
232 -- Well, I'm sure people IN ACADEMIA care about where you went to school.
Sorry, that wasn't meant to be yelling. But yeah, it's not surprising that folks in academia are more school conscious than those outside of it. And I don't think it's that Ivy League schools aren't prestigious (they are); it's just that no one much assumes that there's a recognizable class of people who went to such schools whom one should aspire to imitate or hire or whatever. It's more of an interesting novelty, like a funny accent.
It's more of an interesting novelty, like a funny accent.
Being British really helps get jobs on the west coast, too. Unless you're Geordie, because then no one can even understand that you're speaking english.
The lecturing has started. I didn't think it would be youtube, but hey, whatevs.
http://chronicle.com/article/A-Self-Appointed-Teacher-Runs/65793/
219: That blogger seems none too bright, so I wouldn't have much confidence in his analysis.
But it probably is true that it pays off to go to a very elite, prestigious school. The problem is with the 4-year non-elite liberal arts degree, which, while less expensive than the fancy degree, is still pretty expensive (not only in tuition and living expenses but also in opportunity costs). Does it make sense to spend the money on that sort of degree? I used to think so, but I increasingly suspect it does not.
I recall an op-ed from the author of that study making exactly the opposite point (i.e., claiming that an expensive college does not provide a good financial payoff) so I am skeptical of the linked blogger's summary.
They found that if a student went to a school with a lower average SAT score than another school that they got admitted to, they didn't make less money. They did make less money if they went to a less prestigious (based on Barrons) or cheaper school than another one they got into.
They also found that the benefits to the high tuition are greatest for those with disadvantaged backgrounds.
http://www.irs.princeton.edu/pubs/pdfs/409.pdf
In economic terms, my take is that elite education mostly pays off for people who want to pursue very elite career paths and for relatively weak students who squeeze into elite schools through some combination of family background, hard work, and luck. For folks who want to be at the very top of the pyramid, it's useful to have gone to school with the Barry O's of the world. Weaker students profit from the way that colleagues and prospective employers will trust Harvard as evidence of smarts over what they see with their own eyes. For very good students who don't have exalted career aspirations, doing very well at State U will set you up just fine, so elite education is mostly only worthwhile if you care about the education itself. Which you should!
For very good students who don't have exalted career aspirations, doing very well at State U will set you up just fine, so elite education is mostly only worthwhile if you care about the education itself.
I was a good student (I'm not posting my transcript) who went to State U and I think the education was very good, at least in those parts where I wanted it to be*. As anybody looking for an academdic job will tell you, there is no shortage of good teachers. You do have to work to find them, but it isn't hard. And State U will have some kind of honors program to shove you together with motivated peers.
*When it wasn't something that I felt was important, I took the easy class.
I still say that Half Sigma can blow me, but this:
They also found that the benefits to the high tuition are greatest for those with disadvantaged backgrounds.
makes good sense to me. The main benefit of a high-tuition school, in general, is that there's more of a safety net and it's harder to fail out/go completely under the radar. It seems sensible to assume that this would provide the most benefit to folks who have farthest to fall if they fail.
I don't disagree with anything in 243.
For very good students who don't have exalted career aspirations, doing very well at State U will set you up just fine, so elite education is mostly only worthwhile if you care about the education itself.
Just because you got into an elite school doesn't mean that you will do very well at state university. If you got into an elite school, you probably are not as smart as your SAT score says you are.
For folks who want to be at the very top of the pyramid, it's useful to have gone to school with the Barry O's of the world.
This is very, very true. I have no doubt that my current job came from my graduate school as much or more than it came from my brilliance (I'd like to think that the latter has contributed to keeping my job, but it was only a possibility due to the old boy's network).
The informal connections of the top schools are a bit staggering, along with the college recruitment programs for top employers, the incessant offers for interesting research projects, and all the other benefits that make it so much easier to glide through and somehow just find yourself in the right place with the right friends at the end of it all.
Where'd you grow up, essear? I don't remember WashU being mentioned much when people were considering undergrad from my Illinois high school, but I've had a few friends go there for law since.
I grew up in Louisville, so WashU was one of the closest well-regarded private universities. (A half-hour closer than Chicago, although now that I think about it probably Vanderbilt is a bit closer than either one of those.)
245: Why won't anybody argue with me?
246: I was using "very good student" to mean "very good student", not "student who got into Elite U".
249: Well, I will say that I'm not sure the Econ 101-equivalent I referred to upthread could have been taught at the State U I attended. You can do more cool things when even the dumb kids are reasonably smart.
239: But it probably is true that it pays off to go to a very elite, prestigious school.
If you actually make the concerted effort to turn it to your advantage, by availing yourself of the old boys network, it does. To the extent that elite, prestigious schools also tend to produce intelligent, articulate graduates, it pays off there as well; but I'm not sure that a 4-year non-elite but still high-quality school can't do the latter also.
250.last: I suppose you can. Except for calc, I took my 101 classes in large lecture halls. The upper level classes in my major were mostly honors classes. Frequently the honors classes were just graduate seminars where we had a one less paper to write or something.
252: See, that's pretty much what I should have been doing at State U. Instead I just took a random assortment of classes that seemed interesting and got the hell out as soon as they'd give me a diploma. And I'm not sure that the honors program was as well-developed then as it is now, but I never took the time to figure that out (or maybe I was ineligible as a transfer student?).
253: Probably better that you didn't. I enjoyed it so much I went to graduate school and prevented myself from getting a real job.
254: On the other hand, you didn't go to law school.
but I'm not sure that a 4-year non-elite but still high-quality school can't do the latter also.
Agreed.
However, my question has to do with the middling- to lower-ranked schools, which are not high-quality. The vast majority of American college students attend these middling-to-lower ranked institutions. Does it make sense for them to do so? Or would many of them be better off working or apprenticing to a trade or something like that?
Or, in any case, what I suspect is that enrollment for these places (at least for the general liberal arts degree) will decline, not because of podcasts but for economic reasons: a mediocre 4-year liberal arts degree is not a good investment.
226 is interesting.
There is a huge difference between elite institutions and others for the very top level of student who reaches to get the most out of the experience -- the really brilliant types who will likely go into research careers, the inventor-class engineers at a place like MIT, etc. For such students elite vs. other schools can be like night and day. But for the average or even the ordinarily good student there is not necessarily such a big difference.
The informal connections of the top schools are a bit staggering, along with the college recruitment programs for top employers, the incessant offers for interesting research projects, and all the other benefits that make it so much easier to glide through and somehow just find yourself in the right place with the right friends at the end of it all.
Exactly, this puts it even better.
However, my question has to do with the middling- to lower-ranked schools, which are not high-quality.
Depends on how low of a rank we are talking about and what you want to study. Majoring in criminal justice or elementary education at East Dakota State College & School of Ranching makes sense if you want to teach or be a cop in East Dakota. Going to the same school in Econ is likely not the thing you should be doing.
There are definitely a lot of people for whom college is probably not the right choice. My cousin, in her fourth or fifth year of trying to get a college degree while also working a full-time job, was re-taking for the third time a math class roughly equivalent to my seventh-grade algebra class, hoping to finally pass. I don't think anyone had the heart to tell her she was wasting her time and money.
I don't think anyone had the heart to tell her she was wasting her time and money.
Haven't any of you heard of an anonymous e-mail account?
Or yard signs. Sure, when I put out a sign saying "Gary is making more than breakfast in the backroom of IHOP," it caused some problems. But, in the end, it prevent a bad marriage, none of the bullets went into vital organs, and nobody knew it was me anyway.
260: You seem to think you have provided enough evidence to support your premise. I don't think you have.
261, 262: Or just email SEK and let him take care of it for you.
263: Yeah, I feel sort of bad about dredging up a real person as an example. But when someone can't even complete required remedial coursework that doesn't count toward their degree after multiple tries, I think the odds of ever finishing the degree are pretty long.
I grew up in Louisville, so WashU was one of the closest well-regarded private universities.
I knew a whole lot of people from Louisville at WashU ('99). I don't know where the people at WashU come from now; it's pretty clearly a different school than when I was there.
But yeah, it's not surprising that folks in academia are more school conscious than those outside of it.
But Halford, I get this response when I'm introduced to people at church, friends of friends, etc.; educated people, but by no means all academics. I get the same thing when I visit my (western) hometown. I presume grad school is coming up in these conversations now because I'm new in town, and it'll get better soon. Right now, the progression goes like this: How long have you been in New Town [Not very], Where were you before [Grad Town], What were you doing there [Working on my doctorate, and please can we talk about something else], Oh really at which school [Grad School], Ohhhh you must be really smart, I could never have done that [facepalm].
It would all be fine if they just didn't ask about the damn school.
(What really gets me about this sort of interaction is how people rush to devalue their own abilities. Give yourselves some credit, people. I do, and I've only just met you.)
If you'd been to school where I've been to school, most people shift the conversation to football.
Aaaand for evidence that a degree from my grad school does not guarantee intelligence, I've just managed to stick my finger in my eye. Ow.
Right now, the progression goes like this: How long have you been in New Town [Not very], Where were you before [Grad Town], What were you doing there [Working on my doctorate, and please can we talk about something else], Oh really at which school [Grad School], Ohhhh you must be really smart, I could never have done that [facepalm].
I realize you weren't asking for suggestions, but IME one way to head off conversations that you can predict this well is to set up pre-planned detours.
How long have you been in New Town?
-Not very, but I really like the parks. Are there any good ones you would recommend? Or: I'm excited about having the chance to take up Ultimate Frisee/contra dancing/stamp collecting/ATV-ing....do you know any groups?
If one detour doesn't work, just try again:
-Where were you before?
(back East/out West/in the mountains -- Gee, I just love it here, it's so different! I'm really enjoying the ____.)
It's my experience that most people don't have a lot of practiced topics for chitchat. If you lack a child or other prop as an obvious topic of conversation, they will fall back on a handful of predictable questions. Luckily, most people are also not very interested in these questions or attached to their plan of asking them, so it's very nearly effortless to detour them into more interesting topics.
(Exceptions made for people whose lifeblood is gossip, but those people will go far beyond grad school and into your romantic attachments, fertility, plans for homeownership, etc. with no encouragement whatsoever.)
I definitely was at WU because of generous aid. Great place for undergrad, I was very happy there and with the education I got, but other private schools were financially impossible for my folks and me.
Seems to be leaning republican now, no surprise due to the Danforth connection.
-Where were you before?
(back East
And then you get pilloried for telling people you went to school "near Boston". Really, you can't win in a conversation like that.
Thanks, Witt. I've had some luck recently with the boy-I'm-feeling-lucky-to-be-in-New-Town diversion (it helps that this is quite true), but I would do well to remind myself of the script ahead of time.
Where were you before?
"They said I don't need to register, so that's none of your business."
What really gets me about this sort of interaction is how people rush to devalue their own abilities.
Is this ever the truth. I kind of hate telling people what I do.
248 Wash U was also a popular choice among smart kids in Lexington, not too surprisingly. A bunch of my friends went. Oh but Louisville is such a more excellent place to have grow up...
(I went to the University of Texas, not inherently a particularly good choice but it worked out well because of Austin. And it was astonishingly cheap.)
276: Math is a seriously overrated field, which can end up pretty great sometimes. But that's only in industry, where you're not surrounded by other people with PhDs in the field and embarrassed silences after you say your major can lead to higher salaries. It was much more awkward back in college, when it always came up in social settings and resulted in a healthy cushion of empty space.
It was much more awkward back in college, when it always came up in social settings and resulted in a healthy cushion of empty space.
See, if you were female and a math major, then it's not awkward at all because everyone says, "Oh! Do you want to teach high school?"
I went to the University of Texas, not inherently a particularly good choice but it worked out well because of Austin.
Hook 'em!
See, if you were female and a math major, then it's not awkward at all because everyone says, "Oh! Do you want to teach high school?"
I would think it would get very awkward once you punch them in the face.
279: Oh geez, really? Damn, that must've been annoying!
It took me a few minutes to think of why anyone would even major in math if they just wanted to teach it in high school, before realizing that anyone teaching AP Calc, etc. probably would have a major.
Umm... I suppose mild condescension is a form of socializing, at least?
Where were you before?
All of a sudden I'm hearing Bogart and Bergman. "Who are you really, and where were you before? What did you do? What did you think?"
I had more things to say about LB's comment way back whenever, but I've forgotten them.
Suffice it to say, then, that of the top executives at my old job, none of them had gone to anything resembling an Ivy or quasi-Ivy. In fact, only one had gone to what I think most of us here would consider a second-rate university. Most had gone to third-rate or lower schools, and the head of my division had not even completed her BA at a third rate school.
So, you know, money don't get everything it's true, but what it don't get, I can't use.
"Who are you really, and where were you before? What did you do? What did you think?"
They have melted the snows from Erebus, weighed the clouds,
hunted down the white bear, hunted the whale the seal the kangaroo,
they have set private enquiry agents onto Archipiada:
What is your name? Your maiden name?
Go in there to be searched. I suspect it is not your true name.
Distinguishing marks if any? (O anthropometrics!)
Now the thumbprints for filing.
Colour of hair? of eyes? of hands? O Bertillon!
51
46, yup, not sure how that happened. Meant 40 years. Before he went nuts.
Fischer was always nuts. The story goes that when he was a child prodigy some chess patrons considered trying to get him help for his obvious mental problems but dropped the idea for fear this would interfere with his chess playing.
41
I think that the experience of concert musicians --where blind auditions led relatively rapidly to gender parity in a previously male-dominated field-- means that the burden of proof should be on people who claim that real-life differences are caused by inherent factors.
Chess and math already have reasonably objective standards so this sort of bias can not explain the male domination of these fields.
I knew Shearer would be along to bring the crazy.
123
I'm really puzzled by this one. Something like what you say seems clearly right. OTOH, I can't quite see advising Sally and Newt to head for anything other than Ivy/Stanford/MIT/UofC, regardless of the fact that it'll be brutally expensive for us, with very little clear payoff.
You don't think attending an elite university provides clear advantages in later life (in the world as it is)? Not to mention the parental status points.
163
The high status of the University of California has got to make West Coast perceptions very different from East Coast -- I think of state school and elite school as disjoint sets, but of course that doesn't work in California.
I am not convinced it is so different. I am from California and in my family (in my generation and the next) the UC schools were seen as safety schools at best.
I knew Shearer would be along to bring the crazy.
And me without any popcorn.
But I mean, yeah, wouldn't everyone just be so ashamed if they had a math degree from Berkeley?
My parents had something like LB's attitude with a vengeance. Towards the end of my very slackerish first two years of high school they presented me with a list of US institutions they would pay for (Ivies, equivalent private Unis, little Ivies and the five or six top public schools) and said either I get in or I go to Uni de Geneve with its zero tuition and life at home. It wasn't even that the cost was such an issue since two professional salaries and an employer who will pay three quarters of tuition plus travel home made even US college costs bearable with an only child; it was more that they didn't see anything else worth paying for at all.
Here's the thing: You either have it, or you don't. The best young director I know (and based on what I've seen and heard about theater around the country, I would not be surprised to hear that she was one of the top 5 or 10 young directors in the country) had a bog-standard suburban upbringing and education, and graduated without any particular fanfare from a Big State University theatre program that is well-regarded but hardly "prestigious". You're going to do a lot better for your kids reading to them, introducing them to interesting ideas and pursuits, taking them to the library regularly and such like, versus agonizing about whether they're getting into the "best" schools. You know what they have at the "best" schools? Lots of blow. Nose candy. Flake. Girl. That's what you're paying for: access to a better sort of drug dealer.
Where was my nose candy flake girl? No one offered my nose any candy.
I would say if you have it, it'll come out without proper grooming; but if you don't, or if you have some of it but you're kind of lazy, you'll meet the people at the right schools who will help you produce it going forward, and you'll be able to flash a pedigree in lieu of a portfolio half of the time.
you'll be able to flash a pedigree in lieu of a portfolio half of the time
This, definitely. It isn't everything, by any means, but it's something.
My impression was that, while the UCs have always been very good schools (well, most of them), there was a shift towards elite students choosing them in higher numbers during the late 80s/early 90s as the disparity between state tuition "fees" and private university tuition grew.
I think I'd have done better socially at a private school but it's doubtful that I'd have gotten any higher level of classes (of the classes I took) at any other of the schools I have some knowledge and/or experience of. I may have been more motivated to take more advanced classes at another school.
Incidentally, when I did grad school visits, the students who got into big deal Ivy and big deal west coast non-Ivy had noticeably different undergrad backgrounds, with a much higher proportion of elite private school grads in the Ivy cohort.
Allow me to be the first to say: this sort of comment thread depresses.
Ohhhh you must be really smart, I could never have done that [facepalm]
I feel like I've said something along these lines before, but as awkward a conversation as this is, at this point "thank you" gives you more options than [facepalm].
It's more than just polite -- it reframes the person's last remark as a generous compliment rather than an awkward self-deprecation.
A good pivot: a question about them.
A good pivot: a question about them.
That's actually great conversational advice, in general. Ask questions. People love to talk about themselves—if you hit on the right set of topics.
What makes you say that?
(Sorry, but someone had to go down the path of the cliche; why not me?)
298 and 299 are of course true (and I trust it's understood that I don't actually perform the [facepalm] maneuver; good lord). I don't think I could bring myself to say "thank you", though, since that seems to condone a sentiment that I absolutely don't want to condone; the reframing doesn't work for me. I tend to go with something along the lines of "Nonsense; it's really just a question of putting in the time. You know how easy it is to put time into doing what you love. [Introducing friend] mentioned that you do X?"
... Nonetheless, there's plenty of evidence that there is at least some bias against women in the sciences, which is a bad thing regardless of whether or not there are innate gender differences. So is it really so bad to investigate and try to eliminate that bias, regardless of what the distribution of scientists would end up being in a perfectly gender-egalitarian world?
A potential downside is that some women may be pushed onto a science career path when they would actually be happier and more successful doing something else.
Yes, because that happens all the time. Think of all those poor scientists, plugging away at PhDs, postdocs, writing grant applications, spending 20 hours a day in the lab while making $20k a year at 35, sighing, thinking "I wish I had the skills to make this kind of money in some other field".
303: the VC influence is very interesting. An old boss of mine once explained to me that it was far better (as a tech company founder) to have never gone to college than to have not finished, because I guess the VCs thought dropping out showed something about your character?
306 cont'd: I actually don't particularly agree with that typology. If you look at successful entrepreneurs, credentialing might not necessarily be important, but they've very often got the kind of networks you'd acquire as a quote-unquote Mandarin and similarly almost always have the kind of industry experience you would expect in (mostly) Lifers.
304: Won't someone think of the ladies? They may be dazzled by vanity at first, but one day they'll wake up thinking, "If only I hadn't sacrificed my femininity on the altar of that higher learning for which I am so unsuited by nature, I could have been a happy 3rd grade teacher. Or a super model!"
306: A guy I knew in high school who was something of a big nerd is now a fancy pants VC. His FB page is just a succession of pictures of him and a gaggle of 25yo blondes at Sundance or Squaw Valley, etc. That seems fun!
308: it's so easy to drift through life, doing nothing but taking graduate level math and science courses and constructing research programs, without ever realizing that what you really want to do is focus on being beautiful.
310: good work if you can swing it. Which I assume involves having a ton of connections.
305: I so wish I'd thought like that when I graduated college.
304: Women are much more likely to be pushed towards a "practical" field that yields credentials in a reasonable time and promises solid earning potential or into a traditionally feminine one.
287: I completely reject the notion that math has more objective standards than concert music did. In fact, I would argue that it's much easier for conductors/musicians to objectively evaluate musicians who play different instruments than it is for mathematicians to evaluate the research of people outside their subfield.
Chess evaluation is certainly more objective than music or math, but I don't know well enough the process by which young people end up being trained in chess and so don't know whether evaluation of children has a more subjective component.
To be fair, academia is in fact kind of a horrible pit of vipers.
312: Yeah, I have no idea how that works. He immigrated to this country in 9th grade and his family was quite poor. But then he went to MIT and Stanford. I guess that is where one meets people willing to let you play with their money.
A potential downside is that some women may be pushed onto a science career path when they would actually be happier and more successful doing something else.
Oh, Shearer.
Also 314 is right.
314.2: and the chess world is ridiculously, hilariously sexist. What are the chances they're going to objectively evaluate (even if they could!) some six-year-old little girl as a chess prospect (which is really when you have to start looking at these things) if they don't believe (as Shearer does not) that women will ever be competitive in chess? What's the chance anybody's going to teach her in the first place? Chess at the highest levels is as much a matter of strategic and practical knowledge as it is some platonic ability to look ahead X moves and do pattern recognition. If you look at the world of chess-playing computers, the very best ones now integrate large amounts of prior knowledge; what are the chances that same six-year-old is going to have any encouragement to dive into that prior knowledge, given that nobody in the chess world thinks girls can play?
Such a terrible example. I love Shearer!
I am from California and in my family (in my generation and the next) the UC schools were seen as safety schools at best.
Maybe it's a white thing. The Asians sure don't seem to see the UC's as "safety schools at best".
305
Yes, because that happens all the time. Think of all those poor scientists, plugging away at PhDs, postdocs, writing grant applications, spending 20 hours a day in the lab while making $20k a year at 35, sighing, thinking "I wish I had the skills to make this kind of money in some other field".
I believe the dropout rate on the science track is generally higher for women. This is often attributed to prejudice ala 24 but an alternative explanantion is women are more likely to find the work uncongenial.
316: from what I understand of the situation the combination of correct degree + plausible subject knowledge + ability to hang with the boys and look good in a suit are enough to get somebody to say "I bet you could be better than average at evaluating some of these prospects!"
It's more meritocratic (in terms of actually knowing the field) than a lot of finance seems to be, but not a ton more.
319: I think its an imaginary Shearer thing.
Although of course it depends on the UC. Davis is obviously barely one step up from UNLV-Pahrump.
320: Or they find the prejudice uncongenial. Seems reasonable to suppose that reducing or eliminating it would be a good first step, just on the grounds of decency.
313
304: Women are much more likely to be pushed towards a "practical" field that yields credentials in a reasonable time and promises solid earning potential or into a traditionally feminine one.
50 years ago maybe. Not so much today especially among the elite.
I'm not going to continue to engage with Shearer on this point. As I said I think the objective evidence (in particular from concert music --basically the only field where it's possible to completely remove bias from hiring/promotions/evaluations) is that bias is a substantial factor. And so denying that very solid evidence by simply speculating about other possible contributing factors just being obtuse and anti-scienctific.
Chess evaluation is certainly more objective than music or math, but I don't know well enough the process by which young people end up being trained in chess and so don't know whether evaluation of children has a more subjective component.
Well, in my experience the way this works usually is that chess-playing guy thinks, "I can't wait to have a son, so I can teach him to play chess."
And on the other side is Pere Polgar....
"I can't wait to have a son, so I can teach him to play chess."
This is what they mean when they say sexism hurts men.
314
I completely reject the notion that math has more objective standards than concert music did. In fact, I would argue that it's much easier for conductors/musicians to objectively evaluate musicians who play different instruments than it is for mathematicians to evaluate the research of people outside their subfield.
The problem solving component of math ability is reasonably easy to measure objectively by things like the Putnam exam. And personally evaluating work outside your subfield is not necessary as long as you can rely on the evaluations of the people within the subfield. And some evaluation is possible without detailed knowledge. Someone solving long outstanding problems is probably pretty good.
323
320: Or they find the prejudice uncongenial. Seems reasonable to suppose that reducing or eliminating it would be a good first step, just on the grounds of decency.
If the average guy working in a field is unattractive to women does this constitute bias?
326
... And so denying that very solid evidence by simply speculating about other possible contributing factors just being obtuse and anti-scienctific.
I am not denying that concert musicians were a bunch of sexist pigs. But bias has less opportunity to work in fields with more objective standards.
325: I good friend of mine experienced exactly that pressure. She went into Chemical Engineering and later Medicine, but she certainly had the chops for Physics, Math, Chemistry, or Biology. She also had an interest in those fields. She was pressured by family to be practical. Her brother, experiencing no such pressure, went to art school.
The effect that got Larry Summers into hot water may well be real, but it's also obviously swamped by other effects. If it were not, the proportion of women in MEST fields would not be increasing. If the utopian gender balance for the sciences turns out not to be 50/50 that wouldn't be a surprise to most people. That it is so far from 50/50 in the presence of known effects discriminating against women suggests it ought to be a lot closer.
Part of being a successful Talent is building the right network. You might do that painstakingly on your own by dint of sheer effort, or you might shortcut the process by acquiring a Mandarin credential (e.g. Harvard Lampoon). I see the latter phenomenon as Mandarins colonizing the domain of the Talents.
But if this is so, then it has always been thus. I mean, Bill Gates went to Harvard and his dad was rich. Bill Hewlett went to Stanford. Google and Yahoo are products of Stanford PhDs. The original writers on the Simpsons largely knew each other through Harvard. Unless you're talking about the first generation of oil barons or movie moguls or something like that you're often as not talking about people with Mandarin-esque credentials and connections. Unless you're talking about the very, very first into a field where the specialized knowledge doesn't exist yet, I'm not sure that you can really talk about a pre-colonial Talent-driven era in any field.
318
There was (and maybe still is to some extent) a lot of bias against women in chess. But it took the form of restricted opportunities. If a women got the opportunity to play in a male tournament her score was a pretty objective measure of her ability. It didn't depend on the whims of the judges.
The mark of a Lifer is not having industry experience. Lots of Talents and Mandarins acquire some along the way as well. What distinguishes the Lifer is the grueling march through the ranks. An entrepreneur who drops out of that race to start his own gig and "be his own boss" is a different animal. Mind you, there is some degree of lateral movement among the tracks; Meg Whitman comes to mind (Lifer to Talent).
Well, right. Lifer to Talent, or Mandarin to Talent, or Talent to Lifer, or Mandarin to Lifer to Talent (Whitman went to Princeton and Harvard Business School). I don't think the categorizations hold up at all except in very specialized cases.
335: her score was a pretty objective measure of her ability and skill, as acquired through practice and training. The bias comes in to play long before she enters the tournament as an adult (or even as a relatively young child), when people are evaluating her potential and deciding whether to encourage her if she wants to blow off everything else and play chess all day.
There was (and maybe still is to some extent) a lot of bias against women in chess. But it took the form of restricted opportunities.
So? Why should that sort of bias be discounted?
If the average guy working in a field is unattractive to women does this constitute bias?
What if the reason the average guy in the field is unattractive to women is that he's absolutely certain that he is entitled to his job and they are not entitled to theirs? Many women find this quite unattractive.
Also, many potentially excellent female chess players may find the atmosphere of sexism that surrounds the game so repugnant that they choose not to participate in what is, after all, an entirely frivolous activity.
except maybe drug dealing
It's like you never heard of Jeffrey Kindler.
The problem solving component of math ability is reasonably easy to measure objectively by things like the Putnam exam.
The Putnam certainly doesn't measure pure problem-solving ability. Those sort of exams get quite a bit easier with some practice, and they all tend to rely on a few of the same techniques for the people who are really serious about them. So there's a lot of acculturation mixed in with ability when it comes to Putnam scores, and by college, the acculturation is pretty much done.
I don't know about math, it's a pretty hard one to deal with. There's no denying that there are sexist barriers to entry, and we should work on tearing those down and making advanced classes and extracurriculars more welcome to women (this needs a big push by parents as well as kids and teachers). However, I'll also admit that I'm a little pessimistic about this hitting true gender parity relative to, well, virtually any other field where I think gender parity is desirable or women are probably even better at it (see: Finance).
Most of my pessimism does stem from the math competition days from junior high through high school, and seeing the incredible attrition rates even as things didn't seem to be getting all that much harder to me. I mean, heebie (and formerly m. leblanc) can attest to the sexism in the field, and there's a long way to go before we can claim that we've sorted out the effects of "fat-tailed males" or whatever, but I remember the trek from junior high competitions where nearly half the people in the room were girls to state junior high competitions where one girl made the top 10 to national high school competitions where the number of girls in the top hundred or so could be counted on one hand. Parity is... a long way away.
Though I'll also admit that the sort of math "ability" measured by those competitions is only a rough gauge of one aspect necessary for even high-level academic work in the field.
except maybe drug dealing, and I'm not even sure if that's a valid exception
It is not. Some folks like their dealer to have more of a "one! of! us!" feel. Plus, it helps to have parents who will bail you out (literally and figuratively) over and over and over.
My casual empiricism
Ah yes, this is my second favorite "casual _______" activity too!
My five-year-old daughter had a crappy little plastic mitt (a toy for a baby) that I insisted she replace, though she didn't want to. In the store, I was showing her mitts, and how much better she'd be able to catch if she had a nice mitt. She wasn't interested until she saw they had a pink mitt, which she wanted to own at once.
I blame myself.
(But at least the pink mitt was a good-quality mitt.)
345: So you won't be joining Caitlin Flanagan in the battle against casual empiricism?
Yes, because that happens all the time. Think of all those poor scientists, plugging away at PhDs, postdocs, writing grant applications, spending 20 hours a day in the lab while making $20k a year at 35, sighing, thinking "I wish I had the skills to make this kind of money in some other field".
This does actually happen a lot.
Even Silicon Valley is a lot more wedded to credentials than its image would suggest; not because the entrepreneurs have to get their tickets punched at Stanford or Harvard, but because the VC's do
The VC world is weird. They're always giving you the entrepreneur propaganda about how they're the risk-takers who drive the economy. Ummmm....
One thing the Putnam measures (beyond problem solving ability,which is certainly one thing it measures) is whether you got lucky enough on a particular exam in order to qualify for MOP at some point in highschool. (MOP being a summer training program where they teach you how to do well at these types of exams.) A comparison of Putnam scores right above and below the MOP cutoff, or a comparison of people whose best USAMO score came as a senior vs. as a junior (it's very difficult to qualify for MOP as a senior relative to other years) should be able to pretty easily detect this luck factor.
Similarly, some schools offer Putnam training (MIT) while others don't (Harvard) which should also be a pretty easy thing to detect.
And this is all for just one small component of mathematical ability that is among the most objective. Evaluating research (and even worse research potential) is much more subjective, as should be clear to anyone who has ever submitted a paper to a journal that uses multiple referees.
I completely reject the notion that math has more objective standards than concert music did
I think the problem is that Shearer thinks that all mathematics is basically adding up, and so you can tell objectively whether someone is any good by checking the answers in the back of the book.
Shearer thinks that all mathematics is basically adding up
Shearer has a PhD in math from MIT, so probably not.
This does actually happen a lot.
Bwah? In my field, women who are unhappy leave (and promptly start making piles of money). All the time. If you're unhappy and you don't leave, it's because of the years and years of insidious conditioning telling you that every other career path is morally and/or intellectually inferior to academia, and that you are therefore a lesser person and a sellout if you leave.
354: Do you know how to counter that conditioning? Because I'm thinking I could use an income boost so I can stock canned goods and ammo before Peak Oil destroys our interconnected world.
re: 346
A couple of the women that used to come to our kickboxing club had bought 'girly' gloves. Bright pink, or sparkly white. It's a very odd thing.
355: Would that I did.
the Mandarin track has certain attractions. If you are smart, dilletantish, and a little lazy, you're going to prefer a career path that confers a nice standard of living, has some downside protection, gets easier with time, and doesn't necessarily require you to compete vigorously with your immediate peers for a limited number of slots.
You include academia as a career path that doesn't require vigorous competition for a limited number of slots?
She was pressured by family to be practical. Her brother, experiencing no such pressure, went to art school.
My parents did this, since my father'd be damned if his girls ever ended up dependent on some man. They were willing to pay for our college so long as it was in a science. Anything else we could figure out how to do on our own. It worked; he got two engineers out of it.
I might have liked to do something else. The blogging seemed to suggest that I might have been a writer or something. But you know what's awesome? My middle class lifestyle in a very secure field. Affording my house without a second income. I have to think they were right. I'll be curious about whether my Dad puts the screws to my brother.
'girly' gloves. Bright pink, or sparkly white. It's a very odd thing.
One woman at our meets dresses head to toe in pink. Pink tights, pink wristbands, pink pink pink. I called her Powerlifting Barbie. But when I went back to put all our lifts and weights into my spreadsheet, she was fucking strong. (I was deceived by her numbers because she's small-ish.) Strength-to-weight much stronger than me. So now I have to give respect and will try to stop calling her Powerlifting Barbie.
Affording my house without a second income.
That is one of those accomplishments that seems less than amazing once you leave the coasts.
Also, many potentially excellent female chess players may find the atmosphere of sexism that surrounds the game so repugnant that they choose not to participate in what is, after all, an entirely frivolous activity as elaborate a waste of human intelligence as you can find outside an advertising agency. (Raymond Chandler FTFY)
re 359
Yeah. In one case, since she was otherwise not girly in that sense [tattoos, piercings, etc], I presume she'd just gone to the shop and asked for some gloves and they'd given her the Reebok UberFemme, or whatever they were called.
354: exactly. The insidious conditioning you refer to is very compatible with being miserable and complaining all the time.
Also, dunno your field, but some lab sciences don't necessarily develop skills that offer an easy transition to high-paying external opportunities. Many do, of course.
361: Yes, I used to think that women were just too smart to become good chess players, but then I realized that was sexist.
Reebok UberFemme
You have to get them to make those just for the name alone.
Also, if math is objective:
-Which is a better journal, JAMS, Inventiones, or Annals?
-Is it better to have one paper in JAMS or 2 papers in Duke?
-Is it better to have a singly authored paper in Duke, or a coauthored paper in JAMS? Does the answer to this depend on whether the coauthor is someone more senior? Does this depend on the number of coauthors?
-Given two potential postdocs each of which have written two papers, one of whom had both papers accepted by a mediocre journal (say the Journal of Algebra), and the other of whom hasn't had the papers accepted yet but who submitted the papers to a higher caliber journal, which is more qualified?
-Which is better having a Ph.D. from MIT and one paper in a solid journal (say Crelle's), or a Ph.D. from BU and two papers in the same solid journal?
359, 362: Yeah, this harks back to some of the bad old femininity arguments, but sports equipment doesn't get lousy just because it's pink and sparkly -- if you're into being femme, and also into being an athlete, they're not categorically incompatible.
The sucky thing, which happens with kids' stuff a lot, is of course when the pink & sparkly equipment is made lousier because the manufacturer assumes girls aren't really going to be using it.
re: 367
Sure. It just seems unfortunate that that seems to be the default.* And I suspect some of that kit, aimed at 'boxercise' classes probably really isn't as good or well made as the plain ordinary stuff.
* at least I'm assuming this particular person didn't actively choose that colour as it'd be at odds with what little I know of her aesthetic choices. If, otoh, that's what people are into, it's all good.
I kind of feel compelled to jump on Shearer more but I guess Po-mo and Commenter have it covered. The idea that the Putnam measures some sort of raw unadulterated talent just seems absurd to me given how much effort some of those people put into math competitions beginning by age 12 or so. I admit they have a talent I don't, so it's measuring something; I only qualified for the USAMO one year in high school and only solved a couple of problems the one time I tried to take the Putnam, and while I'm sure with some serious preparation I would have done better, I would never have been at the top level. But these tests are very much focused on a particular flavor of discrete-math-y problem-solving that one can learn strategies for, which is only one of many forms of mathematical problem-solving, and not obviously correlated with research ability.
(Shearer could be one of those people with a very narrow view of research ability, I suppose, which might skew how Putnam skill correlates with research skill. A few of the best physicists I know look down their noses at anything that isn't a technical tour-de-force, which is perhaps why they're doing highly mathematical things only tenuously connected to the real world. My cavalier attitude that the important thing is to get the big-picture concepts right and find comprehensible toy examples instead of burying your ideas in a 100-page stack of hypergeometric functions seems dilletantish to them, I think.)
Might as well strike the first sentence of 370 since I decided to go ahead and do it anyway.
368: That really sounds like a stretch.
I don't really buy this division at all, but certainly Talent is a very poorly chosen word for something that's meant to describe Buchanan but not Clinton. It is batshit crazy to think that Bill Clinton of all people was successful because of his being good at school and racking up credentials, rather than that he was good at school because he's good at everything.
Also, I don't see how being a performer is less structured/credentialed than being an academic. If you want to be a comedian you need to spend time doing standup in little clubs in new york until you've adequately impressed the right gatekeepers. Credentials like being in the cast of SNL are incredibly important. Academia involves developing your own research program and goals, is entirely self-organized on a day-to-day basis, etc.
370: I'm not sure people who are very good at math and think that there are diminishing returns to being great at math have a very good perspective on what things are like for the great majority of the population who just aren't that good. I know for me, I hit a very distinct wall somewhere around differential equations that actually did stop me from reaching competence in intensively math-based fields. It felt almost genetic, like not being able to jump high enough.
genetic, like not being able to jump high enough.
It's important to note that jeans can restrict one's jumping ability quite substantially, particularly those tight, hipster jeans so en vogue at present.
376: So hipsterism is ironically-deployed Harrison Bergeronism?
377: How else would the hipsters deploy it?
I felt like the part of the analysis that made the most sense was the "Lifer" section. And yes, most of those executives I was referring to are Lifers, both under this specific rubric and as the term is generally understood. I am also dubious about the Talent/Mandarin distinction. It seems like we're saying really "there are two kinds of exceptionally gifted people -- the ones who stay in school as long as they can and the ones who don't", which might be a useful tautology to express sometimes, but it's still a tautology. My sense in reading popular accounts of the big success stories of Silicon Valley is that there are a lot of organizations where Talents and Mandarins are completely interchangeable. Sure, most start-ups are going to have mostly Talents at the very beginning, especially back in the 70s and 80s, but the Mandarins tend to move in pretty quick right after the company is off the ground. And once there's any real money flowing, the Lifers show up too.
Also, any big totallizing narrative where you're reduced to saying "of course, all X are a little bit Y" in the first page or two of your explanation strikes me as being less than perfectly specific.
I recognized the three big classes KR describes. Seemed like a useful first cut, if not perfectly precise.
It seems like we're saying really "there are two kinds of exceptionally gifted people -- the ones who stay in school as long as they can and the ones who don't"
I'd say the split is closer to taking the difference between those who want to take a career path in a stable, pre-existing organization that offers a higher chance of less strenuous success at the cost of independence and extreme wins (the Mandarins) and those who want to strike out on their own and take on substantial risk for the chance at extreme success and running everything (the Talents). But I think it seems like a clear distinction to me because I'm utterly on the Mandarin side of the split.
Furthermore, I think there's sort of a diction issue here with the term "Lifer" -- colloquially we use that term to describe someone who's not going anywhere, like the fellow at my old job who's been doing the Exact. Same. Report. every day since I first worked there 15 years ago. Clearly, that's not what those executives are doing. Rather, they're people who may be just as good at seeing the main chance and going for it, but happen to do so within larger, more stable organizations where the risks and rewards are more clearly defined. Take out the pejorative connotations of "Lifer" and it sounds like the way to bet.
"Talent" seems to occupy the privileged position in this scheme, unsurprisingly given that it was written while we were still on a dot.com bubble high nationally. And as Lemann points out, the "Talent" ethos is bound up in the national mythology in a way that the other two (plus the Episcopacy) are not.
There was (and maybe still is to some extent) a lot of bias against women in chess. But it took the form of restricted opportunities.
You know, I have had the opportunity for a natural study of this issue. And it turns out that when you put a bunch of high school aged kids in a room at lunchtime with four chess boards, and almost none of them know how to play already, and they are from two dozen different cultural, racial, ethnic and religious groups so there is no overriding narrative of What Chess Means, and they are supervised/taught by a majority-female team that is deliberately paying attention to whether girls are getting the chance to play as often and so forth....
...well, it turns out that when all this happens, some teens are interested and some aren't, and some of both sexes are more persistent in wanting to learn chess than others of both sexes. But very quickly, the majority cultural narrative that Chess Is Male starts to seep in. Without herculean, pushy effort, the lunchtime games start to become more male, and the kibbutzing groups standing around the players start to become almost entirely male, and the social and psychological barriers for any female person who wants to join in get higher and higher.
So, yeah. 'Restricted opportunities,' my left elbow. The world is sexist. Kids are not slow to respond, and to start policing the boundaries themselves.
If Shearer wants to use the Putnam as a measure of talent, it could be countered with the Intel Science Talent Search: in the last 12 years, 8 of the 1st place winners were women and 4 were men. (I go back 12 years so that I can say that I know 3 of the winners, and I'm quite sure that affirmative action played no role in their winning.)
I recognized the three big classes KR describes. Seemed like a useful first cut, if not perfectly precise.
Yes, this.
Increasingly, though, I think undergrad education (as opposed to graduate school or professional school) is increasingly unimportant even in "Mandarin" professions. Going to a good college may help one get into a good professional or graduate school, but a fancy undergrad school functions more like an extremely expensive high school than a credential that turns into a Mandarin job.
Interestingly, that cuts both ways. If I can channel Shearer for a moment, I would guess that his response would be "The Putnam is a much better measure of innate mathematical potential". Whether the Putnam is or isn't a good measure of innate mathematical potential, or instead more of a measure of thoroughly nurtured and supported mathematical potential, the fact that girls are doing well in the Intel Science Talent Search suggests that whatever the Putnam measures isn't the only thing necessary for success in STEM fields. And yet women are still underrepresented in STEM fields other than pure mathematics.
The insidious conditioning you refer to is very compatible with being miserable and complaining all the time.
Sure. But do you think that only girls get targeted for insidious conditioning, or that only girls complain about grad school? Or just that, as Shearer opined, it's an especially big pity that they have to worry their pretty heads about all this silly status business?
If I can channel Shearer for a moment...
I was hoping for a Spinal Tap impersonation.
One last thing, with the caveat that I wish only the best for the kids of everyone here: If you're a Mandarin, don't bet on raising any Mandarin kids. Talents beget Talents all the time, and Lifers beget everybody, just because there are so many more Lifers than anything else, but IME, Mandarins begetting Mandarins is exceedingly rare. Of all of the kids I knew growing up who lived in Mandarin-led households, I can't think of a single one who became a Mandarin. If they're not Talents, then their initial advantages (since most Mandarins are going to be able to provide quite well for their kids educational and cultural opportunities) generally push them toward being fairly successful Lifers. Or they hit a wall of 'tired blood' and just wind up as Nothings.
If you're growing up in a Mandarin household, you're probably seeing your parent/s working long hours, kow-towing to idiotic Lifers and Talents, getting ulcers and never spending enough time with you. Where's the benefit in following a Mandarin path yourself? You're probably going to a decent school no matter what, probably with little debt when you get out, and you feel like you've seen all there is to offer in the Mandarin lifestyle. So why not go for the comfy sinecure, with the help of your folx's connections? Or go live in an artists' colony and throw pots if that's your thing?
[Note: The context where this does not apply is if you come from a very well-established Mandarin dynasty -- the Walkers, the Bushes, the Browns, the Kennedys, the Tafts, and now probably the Clintons and Obamas. If you're in that position, and you can see very tangible rewards for pursuing the Mandarin path, there's a good chance you'll go for it. But if your 'rents are just common or garden Mandarins, friends down at the Statehouse, weekends at the lake, etc., it's not a big inducement.]
tired blood
At last a diagnosis for my condition.
389: I think if I put that much thought into social structure, I might become an anarchist.
//
Here is a logic puzzle I disagree with:
"I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"
To me I think you can ignore the "on tuesday" information. The boy has to be born on a specific day of the week. The man knows the day we don't.
"I have two children. One is a boy born on a June 14th 1999 at 12:02AM he loves star wars, and basketball, but is in the 37% percentile for height. What is the probability I have two boys?"
Is it very close to 1/2? or is it 1/3?
I say 1/3. Parents will tell you anything about their kids.
>
390: Hanno Buddenbrook? Are you going to fall sick and then choose to die?
I think the answer is 1/3, but if it had said "the oldest is a boy", then it would be 1/2.
One last thing, with the caveat that I wish only the best for the kids of everyone here: If you're a Mandarin, don't bet on raising any Mandarin kids.
Wasn't there an earlier comment talking about a stereotype of a trajectory for successful immigrant families (and, obviously, "successful" is doing a lot of work there):
The immigrant generation works long hours in a profitable but low status job and sends their children to good schools.
Their children become lawyers (or some other Mandarin profession) and send their children to good schools.
Their children become artists.
here's the comment I was thinking of:
So my family follows the classic Jewish immigrant pattern:
1) The generation that immigrates makes money doing something legal, but not particularly high prestige (e.g. buying apartment buildings in a ghetto).
2) Their children then make money doing something professional (e.g. medicine or the law).
3) Their children forego money-making in order to do something altruistic or intellectually or artistically ambitious (e.g. legal aid attorney or writing).
4) Their children start out pursuing the third path and then veer off into the second. (That's me, a failed academic now in law school).
So, anyway, here's the relevant part. My grandmother's youngest uncle made his money rescuing sunken cans from the botton of the city harbor and reselling them without the labels during the depression.
392: The probability that the second child is a boy is .50 (or .51 or so). The probability that you have two boys is .33 (or so). The "Tuesday" shit is what happens when a theoretical statistician wants to annoy people with actual data to work with.
The probability that the second child is a boy is .50 (or .51 or so). The probability that you have two boys is .33 (or so).
As I've said here before, I am a math moron, but I don't understand the difference between these two. You already know that there's one boy, right, and that there are two children? So why isn't the probability that the second child is a boy exactly the same as the probability that there are two boys?
400: Equivocation between 'second child' meaning the younger child : probability 1/2; and 'second child' meaning 'not the boy born on a Tuesday who I've already mentioned': probability 1/3 (because there are three possible pairs with at least one boy: Boy then Girl, Girl then Boy, and Boy then Second Boy, and only one of those pairs has two boys in it.
400: Consider the number of ways you can have two kids: (boy,boy), (girl,boy), (boy,girl), (girl,girl). If you know that one's a boy you have three equally likely possibilities, only one of which is (boy,boy). If you know the first is a boy, there is only one way to get (boy,boy). Total number of possibilities is three, 1/3 (boy,boy) and 2/3 not if no information about order is given, or 50/50 if it is.
"The probability that the second child is a boy is .50" means that whatever the first child is, the second is equally likely to be a boy or a girl. The probability that the first child is a boy is also .50. That means that the probability of B then G is .25, G then B is .25, and B then B is .25, so the probability that you have two boys given that you have one is .33.
Pwnage hurts so much less when you have company.
400: So why isn't the probability that the second child is a boy exactly the same as the probability that there are two boys?
Having two boys is two events that are independent (leaving aside identical twins). The probability of each being a boy is .5, so the probability of both being a boy is .25 (or 1 out of 4). However we know that one of those four conditions (girl + girl)*, does not exist. So, three possible outcomes exist, one of which is two boys. (I guess a shorter way of putting it is that different phrasings of the question lead to different sets of possible outcomes from which you draw the odds.)
*Here's hoping a porn search leads to a story problem.
Did the One is a boy born on a Tuesday make more sense to anybody else?
407: I've seen this kind of gimmick, so yes. I think it's dumb, though.
I guess I meant did it have any substantive importance.
I spent my high-school math career with my teammates joking about raping me. (No, they never joked to me about raping each other. This was special for the girl.) Also, my extended family and the school counselors told me I'd regret being good at science and math, because if you beat boys at something they won't want to date you. The rape jokes had removed the charm of dating, anyway, so on I went -- but it was hard being a teammate when I had to arrange never to be alone with the losers without admitting that that's what I was doing.
New disgust: "the film's challenge was finding a way to "unite the beautiful body and mathematics," and the "beauty of a woman's body" served as a metaphor for the task. " Not even the beauty of a woman, I note.
I don't know about the Mandarins/Lifers/Talents thing; I've been worrying that the country was being run by Castiglione's Courtiers, viz. the Challenger crash, Vista, financial groupthink off a cliff. (I hypothesize that hipsters are larval courtiers.)
That is horrible, clew. Congratulations on surviving.
My favorite use of the kind of probability question above is that, if you generalize a bit, you find that there's no way for a culture to affect the sex ratio by merely choosing when to have more children -- if there's an imbalanced sex ratio, either the sperm or the conceptions are being filtered.
OK, I get that, I think.
Just to check, if the statement is: "I have a boy. I also have another child. What is the probability that the other child is also a boy?"
Then the answer has to be .5, right, because the second child has a 50/50 chance (OK, not quite) of being a boy.
It just seems bizarre to me that this question produces a different result than "I have one boy. What is the probability that both of my children are boys?" I get the demonstration that these questions produce different results, but it's conceptually hard to grasp.
Shit, clew. I wish it had been different. That shouldn't happen.
Huh. I thought the probability was zero because the kid about whom the parent says nothing is obviously a girl.
That is horrible, clew.
It sure would be nice if more people believed that rape jokes were out of bounds.
I'd say that if you know one is a boy born on tuesday then you're in the following setup. There are 14 a priori equally likely birth situations for one child, namely (boy, sunday), (girl, sunday), (boy, monday), ... So for two children there are 14^2 = 196 possibilities. When you find out that one of the kids is a boy born on tuesday, that eliminates a bunch of possibilities, we need to figure out how many possibilities are left and then among those how many have two boys.
If the first kid is a boy born tuesday there's 14 possibilities for the second kid. If the second kid is a boy born tuesday there's 14 possibilities for the first kid. But we've overcounted one situation, namely both kids are boys born on tuesday. So there's actually exactly 27 possibilities. Of those 27, we see that 13 of them have both kids being boys, and 14 are one boy and one girl.
Hence, the odds that the they're both boys is 13/27 or just over 48%.
This is intuitively plausible because "boy born on tuesday" usually distinguishes two kids (other than in the rare case where they're both boys born on tuesday) and so should be more similar to the situation where you've completely distinguished the two (by saying the older one) then it is to the situation where you haven't distinguished them at all.
I guess I meant did it have any substantive importance.
It probably actually does, if you're modelling situations where you're provided with oddball facts. I waste my time strictly in inapplicable stuff, though.
396: Yeah, the Bushes probably don't belong in there as much.
I think we've talked the immigrant family pattern to death here before, but I think the question of how over-achievers get made is also salient. A friend, who is both a Talent and an over-achiever, told me once that there's a body of research that suggests that one of the big predictors for over-achievement is in fact coming from a seriously dysfunctional family life. Which, of course, no one would wish on their kid. I think the other predictor was something along the lines of being an only child of very bright parents or something fairly intuitive like that. That same friend is married to a Lifer. And his mother is a Talent and her father is a Lifer, and I bet you anything their kid is going to be a Mandarin. (Partly because that's their stated goal for her, and they're very directed people, but also precisely because they are not Mandarins themselves.)
Are you going to fall sick and then choose to die?
If I fell sick, I might choose to die.
413.2,.3: No. If you said "What is the probability that the younger of my two children is a boy?" the answer would be .5. The fact that the boy you have revealed could be either the older or the younger makes the probability .33.
417: But you only have 14 possible conditions like that if gender and day of birth covaried somehow.
413: Not quite. If you say, "My eldest child is a boy, what is the probability that I have two boys", the answer is 1/2, because it's the same as asking "What is the probability that my youngest child is a boy?", obviously 1/2. On the other hand, if you say "One of my children is a boy, what is the probability that I have two boys?", the answer is 1/3, because there are three possibilities instead of two -- GB, BG, BB -- and only one of them is two boys.
I either don't understand the 'Saying he was born on Tuesday changes the odds' argument, or it's nonsense. Is there anyone who understands it and thinks it's valid who can walk me through it?
And Jesus, clew, that sucks.
And sympathies to clew. As horrible as teenage nerd boys can be, that's over the top.
The Tuesday information is important:
Looking at the set of two child families 1/2 have one of each and 1/4 have two boys. Of the mixed group 1/7 will have a boy born on Tuesday. Of the only boy group 27/49 will have at least one Tuesday boy (1/7+1/7-1/49 (to avoid double counting)), so when you calculate your final ratio you keep almost twice as many double boy families.
Also, to clew: That is disgusting. I'm sorry. When I was on the all-male Quiz Bowl/Knowledge Bowl team in HS, there were some attempts made at that kind of horseshit, and I tried hard to quash them. It wasn't as big an issue in Speech and Debate, since those were majority-female at our HS. But yeah, yuck.
OK, I know this is an exercise in talking to a retard for all of you. But I really don't get 421. Who cares about age or who is the older or the younger child? There are two children. One of them exists and is a boy. We know that. Then, there is another child, who also exists. That child was born either before or after the boy. And when that child was born, he or she had a roughly .5 chance of being a boy and a .5 chance of being a girl. Right?
So why is there a different answer for ""I have a boy. I also have another child. What is the probability that the other child is also a boy?"
IOW double boy families are about twice as likely to pass through the "boy born on a Tuesday" seive as single boy families.
An important thing to keep in mind about silly probability puzzles is that probability is a question about *your state of knowledge* not about the actual world. So it shouldn't surprise you that when you *get more knowledge*, like that it was the older child who was a boy rather than just that one child was a boy, that it changes the probability.
I don't even have a child born on a Tuesday.
Let alone many children, to necesitate a child rack.
Actually, I quite like children born on Tuesdays.
a child rack
Must have been BPA in the bottles or something.
Ah. 417 should have cleared up the Tuesday thing for me, but it actually took 426 to do it.
428: As a fellow semi-retard, try it this way. You've got a stadium full of two kid families, and you're making announcements over the PA. If you say, "Everyone who doesn't have at least one boy, leave," all the families with two girls leave, and everyone else stays. If you say "Everyone whose oldest kid isn't a boy, leave", then more families will leave -- the two girl families, and the girl then boy families.
Your question is "What fraction of the remaining families are two boy families", and it should be clear that the answer is different depending on which class of families you ruled out (told to leave the stadium) with your initial conditions.
And a version of the same argument solves my Tuesday confusion.
Who cares about age or who is the older or the younger child? There are two children. One of them exists and is a boy. We know that. Then, there is another child, who also exists. That child was born either before or after the boy. And when that child was born, he or she had a roughly .5 chance of being a boy and a .5 chance of being a girl. Right?
There's a fifty percent chance that any individual birth event is the event of a boy's birth. We aren't, however, asking the question, "what was the probability that the birth of my other child was the birth of a boy", but the question, "what is the probability that I have two boys, given that I have a boy?". This is a question about the way children can be distributed across two births. The "given" clause it's what's throwing you off, making you think that we're asking about the birth of the other child considered in itself.
Think of it this way: we don't even know which is the "other" child. If we did (if it were known that the elder is a boy and we're talking about the younger, or vice versa), then we really would be talking just about the event of the other birth.
Since we're asking about both births, and placing a constraint on one (but which one is unknown!), we need to look at the ways someone could have two children such that at least one is a boy. There are three such ways: BB, BG, and GB. Since the probability with each birth is independent of the probability of any other birth, and since P(G) = P(B), we can just tot them up.
I mean we tot up the double-boy outcomes and divide by the total possible outcomes.
438 is very nicely put. By using space (lots of families in a giant stadium) in the place of the more usual time (flipping coins over and over again in sequence) you've made the situation much more intuitive.
438.1 and 439: Woohoo! I'm trying a new thing where I add value with my comments.
we tot up the double-boy outcomes
Sure beats furiously totting up rectums.
talking to a retard
fellow semi-retard
frowny face.
Also, to clew: That is disgusting. I'm sorry.
That, very much.
Thinking about it, the math team I was on in HS had, IIRC, 2 girls (including one of the co-captains) and 7 boys. I don't remember any behavior like that which clew describes; but that doesn't mean it didn't happen.
I'm sure it was a modestly sexist environment, but Id like to think that it wasn't more than modestly sexist, but I really don't know.
I was far too lazy for any competition that required serious preparation, and I suspect that my Knowledge Bowl team, and really my whole high school class, was moderately severely affected by sexism. In hindsight, a whole lot of that banter had to have seemed less innocuous from the other side.
445: Oy. You're right. It's funny, I've got that one out of my, um, primary vocabulary? I don't reach for it spontaneously, but it doesn't register for me as something not to say if there's something I'm particularly responding to. (I made a 'wicked retahded' joke here in relation to Jimmy Fallon a while back, and Will dinged me for it. I should learn faster than this.)
Pwnage hurts so much less when you have company.
Togolosh, if it helps ease the pwnage pain, your answer made the most sense to me. Maybe tog AND heebie can teach me math!
I propose a script along the lines of the "I hate football" game that, anytime you type "retard", changes it into The N Word.
Great, I come back from lunch and the math problem has already broken out and been buried!
If Shearer wants to use the Putnam as a measure of talent, it could be countered with the Intel Science Talent Search
Women kicking ass in the Intels doesn't surprise me much at all. By the time you get to the experimental sciences (pretty much anything outside super-esoteric theoretical physics), I don't think even the "variability of math talent" nature arguments suggest there should be more men at the tippy-top.
I can't really put a good finger on why I feel this way. If it's just because I've seen a lot of women excel in the sciences and not many in math, or if it actually has some relation to my understanding of the fields and how they might fundamentally differ. My uncertainty about this suggests that field-specific sexism may be a big part of the extreme differential, though.
Further to 448: Has anyone else had the experience where you've said something unintentionally unpleasant, along the lines of my 438, no one said anything about it at the time, and afterward you realize (a) that it was a bad thing to have said and (b) at least one member of your audience probably thought so, and just didn't have the energy to say anything about it, and (c) now it's too far in the past to apologize without absurdity because there's no reason to think that anyone remembers it specifically, but they now have a vague sense of you as 'someone who says stuff like that'.
I hate being in that position.
451: I don't have stats in front of me, but is women's representation in math drastically lower than in all other STEM fields (and from what I've heard philosophy should probably be counted along with them)?
210: There was a guy who majored in Classics who had transferred from BYU. He didn't seem super excellent smart, I mean more than anyone else, but he took some time off and then graduated summa. (One of his comments the first year about love poetry seemed kind of dumb even.)
Right now, I am reading this thread, because I am too tired to do actual work. Therefore, I am feeling that I will never be able to amount to much, because I'm often tired. I said to a friend the other day, "If I were the sort of person who had more energy than I do, I'd get a part time job at Nordstrom's for the discount." He decided that this should be a new catchphrase. "If I were the sort of person who had more energy, I'd write a book."
It's a fun--but depressing--game.
452: Sure, I have a few egregious ones from 30+ years ago that haunt me from time to time. Maybe that's what Facebook is for ...
457: I sort of tried that with respect to some of the stuff mentioned in 447. It didn't work.
I've always been some what skeptical of field specific sexism as an explanation of the gender disparity in math. Although I certainly think that mathematicians have plenty of gender biases (as do all people), I've just never seen much to suggest that they're more sexist than other fields.
For a very old example, mathematicians were generally great supporters of Emmy Noether (e.g. she gave an ICM plenary), while it was the humanities professors who blocked her appointment as privatdozent.
I have no real evidence of this, but my feeling has been that the main difference with math comes more from the sexism of primary and secondary math teachers.
457: Sometimes, it seems to me my only vivid memories from childhood and youth are moments of embarrassment and/or shame.
No real idea what this is, other than an early google hit for 'women representation stem fields', but if the graph on the first page is accurate, math isn't an outlier among STEM fields in terms of extreme underrepresentation of women. A 'nature' argument that math underrepresentation is innate, but in the other STEM fields there are social explanations, is still possible, but it doesn't jump out of the data.
I can only assume that 452ish phenomena are addressed in Awkwardness., the book.
460.last: That, and non-teacher social pressure. But some is certainly teachers: I told you guys about the fall parent teacher conference where the teacher told me that Sally was at the top of her class in math, but "she seems bored with it, and I'm worried that she's hitting that middle-school age where girls lose interest in math." I restrained myself from setting her on fire, and suggested that she go find Sally something more interesting to do than learning long division over again, so maybe she wouldn't be so bored. Hadn't occurred to her that that might be the problem. (To do her justice, she dug out materials for some algebra independent study thing that kept Sally and her best friend the piano prodigy happily occupied for the rest of the year.)
461: Well yeah, there's the deserved shame at the moment, and then the insidious " retroactively revealed shame" that LB describes here. Not to mention the shame at the moment that is retroactively revealed to not have been worthy of shame. And I so should have tried to get on with [redacted] in 12th grade. In my experience thinking about any and all of them too much (beyond as corrective exemplars) is corrosive to good emotional health.
463: Kotsko wrote a book on Awkwardness? That is the best thing ever. I'm going to need to devote a shelf to books by people I know from Unfogged, soon.
452: Unsurprisingly, yes.
The other side of that is that I assume most bad things I witness from people around me who I don't know are due to similar errors. It makes the world seem much less unpleasant.
Mostly, I was thinking that Cecily's harrumph in 445 is a kind and greatly appreciated sort of thing to do, because it gives one a timely chance to set oneself straight, and avoids later fretting.
468: C'mon, no positive spin allowed. (Although you are of course, correct.)
Just sent the book link to the Curb Your Enthusiasm fan club in my family; I can only watch it fleetingly as some moments literally send me out of the room in agony.
468: There's an art to the friendly harrumph that E. Messily has pitch-perfect in 445.
I can only watch it fleetingly as some moments literally send me out of the room in agony
Dear lord, THIS.
as some moments literally send me out of the room in agony.
Heh, my wife's like that. Ditto to parts of The Office. God I love those shows.
I endorse 417, and feel dumb for initially missing the significance of Tuesday.
471, 473: Fingers in the ears, squinting though my eyelashes to see if the bad bit is over yet, here.
and from what I've heard philosophy should probably be counted along with them
In the past [and in the present] that'd definitely been true at faculty level. Not so much at grad school level, I think, but it varies a lot.
However, my experience of undergraduate study was that more than half the students were women. So there's clearly something there, if the percentages are going from, say 50 - 60% final year undergraduates to more like 25 - 40% postgraduate.* I wouldn't be surprised if the percentage drops again at junior faculty level.
* figures pulled out of my arse, but roughly in line with my anecdotal experience.
472: That's right, E. Messily! Shin-kicker for hire!
454, 462: When I'm talking about the extreme under-representation of women in math, I'm not really talking about university degrees (though there was certainly a much bigger gender skew than that chart shows in my undergrad math cohort). I'm more referring to the high school and college competitions that were the equivalent of the Intel Talent Search in math, where there's a drawn out series of tests and competitions geared toward selecting a group of 200-300 students across the entire country and then trying to sort them out via a very hard test.
The top groups from these competitions were always extremely gender skewed. And the degree of skew at each level of the escalating competition steadily grew. It would probably be closer to, say, counting the gender of published authors in top math journals rather than looking at degree counts as a measure of field skew. And I suspect on that metric, math might look more extreme than a number of the other STEM fields. But heebie and unfoggedtarian would know this much better than me, since I didn't pursue grad study in math.
469: I still haven't watched the end of the episode of the Brady Bunch where Marsha has two dates on the same night.
I should learn faster than this.
Well, it's hard when you're ret--
Crap.
Now I know why I dropped that large rock on my shin a couple of weeks ago: to correct myself for laughing at 480.
478: See 460, 464. Innate differences certainly can't be ruled out by any data we have now. But the sort of competitions you're describing are populated by kids who think of themselves as really good at math, partially because that's what the people around them tell them. It's not hard to imagine a social mechanism creating a gender differential there.
When I was a kid I was unable to watch certain "I love lucy" episodes.
GB--In Boston, people don't say, "Oh you must be really smart." They just sort of say, "Oh.." And accept you as part of their clan if that is where they went to school.
My experience is that on the West Coast people admire you for having gone to an Ivy--especially Harvard. On the East Coast it's less a matter of being admired and more a matter of not having the door shut to certain options which would be available to people who didn't have a BA from an Ivy League school
479: You should go ahead and watch it. I can assure you that everything works out fine in the end.
On the East Coast it's less a matter of being admired and more a matter of not having the door shut to certain options which would be available to people who didn't have a BA from an Ivy League school
Why the fuck did I move here? If I'd stayed in Michigan, I'd be a goddess by now.
479: I still haven't watched the end of the episode of the Brady Bunch where Marsha has two dates on the same night.
As a young teen I thought the part of Arrowsmith where Arrowsmith invites his two fiancées to lunch and announces, I'm not making any excuses for myself. I couldn't help it. I'm engaged to both of you, and want to know-- was the coolest thing. I am sure I said that in front of people who now years later I realize were probably too kind say anything about the problems with my assholish enthusiasm.
482: Oh, absolutely. That's why in 343 I said that there are undoubtedly gender bias barriers that keep female participation artificially low in these competitions and math in general. I only have some reservations about saying that parity at the extreme top ranks might ever be possible in these sort of ultra-stylized math competitions, whereas I see it as very possible if not downright likely in every other field.
I mean, it's not so much that there was a gender skew in these competitions which makes me pessimistic. It was the sheer size of the gender skew and the degree to which it strengthened after each level of (very gender-blind) selectivity.
Just really rough numbers from my high school experience:
- The math teams at most schools were skewed male, but not by much. Probably 1/3 or more female on average.
- When you got to the state competitions between schools and looked at the top five individuals in each grade (these were the people who got awards in Illinois), it was closer to 1/5 female among the award winners. And those competitions generally weren't that hard conceptually, so often the differences among the top finishers depended more on function under time constraints and ability to avoid careless errors than on raw math whateverness (itself both a function of study/practice and aptitude).
- When you got to the national competition series, they generally started with a very broad set of participants demographically similar to math teams at each high school (i.e. 1/3-1/4 women, thereabouts). Then they gave them all a pretty hard multiple-choice test. The top performers on that tended to skew more male than all test-takers, and are invited to take a second, more open-form test. The top performers from that are finally invited to take the USAMO, which is incredibly open-form. You're essentially writing proofs for points.
At each step, it's been a fairly gender-blind selection process of who can advance, since it's simply based off raw scores on tests with no names. Yet the top performers on the USAMO were almost uniformly male. Among the top 50-100, there were probably about 4-8 women in the years that I remember.
And that's the source of my pessimism. I think we can drastically increase the participation rate of women by pulling down early and late gender barriers in education. I think we could easily double, triple, or even quadruple the number of women placing highly in these kinds of competitions. But that still wouldn't bring it to full gender parity, and I'm unsure if that's fully possible.
But yes, we should try.
And more importantly, my experiences were from an exceedingly stylized form of competition that means nearly nothing in the real world. It probably doesn't even have too much relevance to the performance of math professors, who need all kinds of other skills to publish and teach which almost certainly do not have male-biased gender skews (if anything, it's the other way!).
475:
I also do this.
My wife claims to find it cute. My own own feelings are swallowed in the spiral of mortification.
It sure would be nice if more people believed that rape jokes were out of bounds.
At my highschool, when a boys team lost very badly, they'd often say, "we got raped."
Sorry that 491 is so long, this topic just sort of makes me feel like I'm in a minefield. I wanted to be really careful in explaining the anecdata behind my doubts, and exactly how narrow of a result they apply to.
(490 just baiting Ari. Some of my best friends, etc., etc.)
Yeah, I can't stand to see people seriously embarrassed. It's better when it is clearly acting (so, something like The Office is manageable, sometimes), but I cannot watch reality shows. (Trust me, not complaining about that one.)
491: Sure. As I said in the initial post, no one knows what the outcome would be in a perfectly gender-egalitarian world. Given that we're not in one, though, no sense worrying about the final state of affairs until we get closer to it.
495: I don't think that Davis is all that good, but I think it's probably better than Irvine--though there may be some good professors. The undergrads not so much and the professional schools are extra anti-intellectual, but it's not the worst of the UC schools.
498: Two-thirds of the people I know with UCD connections are very good.
494: And to expand on 497, as one of the most crankily hostile people around on this topic, saying "I'm not certain that women would be represented equally at high levels of mathematical achievement even in a world free of gender bias," isn't offensive at all. I said the same thing in the OP. Adding "My personal impression is that they probably wouldn't be equally represented," (which I understand to be fairish a quick summary of 491) might get you some argument about social factors that would explain your experiences in the absence of innate differences, but still isn't offensive at all.
To get to irritating or offensive, you'd have to be claiming that gender bias isn't a significant factor at all, or that it's all a thing of the past, and that the lack of hard proof that women are, as a group, equal to men in innate mathematical capacity is equivalent to proof that women are not equal to men in innate mathematical capacity.
499: More mutual appreciation. Though I did like Dodgeball.
502 gets it exactly right.
To get to irritating or offensive, you'd have to be claiming that gender bias isn't a significant factor at all, or that it's all a thing of the past, and that the lack of hard proof that women are, as a group, equal to men in innate mathematical capacity is equivalent to proof that women are not equal to men in innate mathematical capacity.
And if you go on to congratulate yourself for your courage in making that claim....
...you can write for Slate.
Given that we're not in one, though, no sense worrying about the final state of affairs until we get closer to it.
Yeah. From a policy standpoint, and when dealing with individuals, this is really the right way to go about things. The question of the true state of the world still bugs me though, because I guess the notion of semi-stark gender differences just doesn't sit right with me. And math competitions were an area where the differences really did seem stark.
508 is supposed to directly follow 506.
504: Thanks, I thought I vaguely remembered it coming up here.
a startling number of us have an actual phobia-level aversion to fictional representations of awkwardness and embarassment.
Bunch of weenies, the lot of you. I'm streaming this episode right now. Glorious.
http://www.youtube.com/watch?v=-j7wr-wsmcI
495: I don't think that Davis is all that good, but I think it's probably better than Irvine--though there may be some good professors.
"There may be"? Christ. There are a lot of very good professors at both Davis and Irvine.
The "I can't stand watching embarassment" discussion is at the end of this thread. Stormcrow, LB, Tweety, and OFE all cop to it.
I am here to say ME TOO. I was famous in my family as a child for having to leave the room whenever such things came on TV.
512: Indeed. Who would have thought?
(It's comments like 495 that make me insecure about my credentials and never want to move East.)
Um, not 495. Misread the numbers.
I guess the notion of semi-stark gender differences just doesn't sit right with me. And math competitions were an area where the differences really did seem stark.
If you'd be happier with some social explanations that would make it easier for you to think that maybe the innate differences weren't so stark: (1) stereotype threat. Note that you noticed a dearth of girls doing well at a stage that you identified as not that difficult conceptually -- given that it's unlikely that the difference there was about a difference at the far right tail of math capacity, there seems to be a fair shot that it was more about whatever happens when you give a test to someone who feels as if they're in a group that's expected to do poorly.
(2) Feedback from peers and teachers, leading to boys investing more time and effort on prepping for this sort of test than girls. I never spent any time on this sort of thing, so I don't have detailed knowledge here, but upthread there's a lot of talk about the difference specialized test prepping, and knowledge of the relevant strategies, makes on these tests. If girls are led to believe that they don't have the potential for excelling at this sort of thing, they probably are much less likely to invest the effort in learning the necessary skills for these tests (or to be supported by teachers in learning those skills) than boys are.
(3) See clew's awful story above.
None of this eliminates the possibility that there is an innate difference, of course. But if that possibility bothers you, there are perfectly decent reasons for thinking your observations don't establish it.
To nobody's surprise, I'm Team gswift on this issue.
The "I can't stand watching embarassment" discussion is at the end of this thread. Stormcrow, LB, Tweety, and OFE all cop to it.
I am happy to be a memeber of a category that includes such august company.
Furthermore, the gender gap is much worse in engineering than in math. Engineering isn't harder than math. I can't imagine anything but pure social structure for the gap in Engineering.
Also, I have a giant chip on my shoulder about the lack of encouragement I ever got in math. I was never told I was good at math, and I would parrot right back that I was bad at math, growing up. I was advised by my teacher not to take Calculus as a senior in high school. I was always a super vocal kid in class who knew what was going on, but never encouraged towards any sort of competition or anything. I must have been a giant complainer or something, but I don't really remember being especially so.
In college, consistently told that while I'd done well in the previous class, I'd probably find the next one too hard. And on and on.
Massively underprepared for grad school because everyone else had these mysterious nurturing experiences that I lacked. But caught up in the first year or two because I'm AWESOME.
The "I can't stand watching embarassment" discussion is at the end of this thread. Stormcrow, LB, Tweety, and OFE all cop to it.
Tragedy is when I get a hangnail. Comedy is when you fall in a sewer and die
Also, I have the following theory: compared to other PhDs, I lagged developmentally. I just didn't hit the wall that PGD described upthread somewhere.
To Po-Mo's story in 491, that is precisely the kind of thing I was thinking of when I wrote comment 28.
(which I'll vainly repost:
Here's my belief: male/female brains are probably different, but not necessarily better/worse at math and science. However, dominating the rhetoric and shaping the approaches and perspective for 2000 years will favor the brain that is most similar to the historical brains. In other words, 2000 years of women dominating math would have a different presentation, even if the actual nature of the theorems discovered was identical, and that presentation would lend itself to girls and women making sense of the material more immediately.)
This is an overheated article, but there is something real going on:
http://www.theatlantic.com/magazine/archive/2010/07/the-end-of-men/8135
It is odd to see gender stereotypes brought out to explain why women are doing well. I am certainly happy that the outlook is better for my daughters than for girls of 40 years ago.
Re:491
Taking the USAMO was probably the most humbling experience of my educational life. I think I solved about one quarter of one of the six problems. It was also probably the moment I realized that to be successful at math you needed not just to be smart, but to be an offscale genius. And clearly I wasn't.
Our math teams had about the same distribution as yours (also in Illinois). I wonder if we ever met.
I was advised by my teacher not to take Calculus as a senior in high school.
I had to bluster my way into BC Calc as well (long, unnerving conversation where I kept on having to repeat "Are you telling me that you think I shouldn't take this, but it's up to me? In which case sign me up. Or that I may not take this? In which case when can my parents make an appointment to come see you?" Eventually the gatekeeper agreed that it was up to me, and signed me up. But I can't attribute that to gender bias -- it was more that she took issue with my extraordinarily sketchy homework record.
488: 322 was a joke, BG. All the UCs are good schools.
Here is a photo from that puzzle conference:
http://www.newscientist.com/data/images/ns/cms/dn18950/dn18950-1_300.jpg
Seriously, those guys are freaks. There are are all kinds of aspergery men in engineering, math and physics. People call it the "male brain" but these guys are not very masculine.
527.last and the embarrassment subthread unite in perhaps my single most mortifying high school moment: when the (very nice but not especially bright) jock who sat in front of me in Algebra II decided that since he was screwed anyway, he might as well get a laugh by answering the teacher's question about why he hadn't done his homework by repeating the answer I'd just given, which was that it was a lot like the previous night's homework and I'd gotten that OK so I slacked off on doing it again. Unfortunately, he got not just a laugh but also a half-hour diatribe from the teacher about his inadequacies as a math student, differences between his performance on the last test and mine, and on and on.
I think I've told this story here before, but the mortification lingers.
There's something suggestive about the distribution of this apparently widespread, yet socially invisible phobia.
The high proportion of bloggers on that list suggests that it may not be invisible for that much longer.
Why are you mortified by what your teacher did? I understand how it could have been a difficult situation with the peer group, but I don't see why it would linger as if you'd stolen the footrest from a wheel chair or something.
Moby, did you steal a wheelchair footrest?
I will squirm in my seat whenever watching anything embarrassing, and it often seems that by far my most emotionally salient memories are those that inspire shame.
528: I should note that 514.last was not entirely serious, either. Besides, clearly UC Sunnydale is at the bottom of the heap.
Is that where it ended up in the series finale?
Our math teams had about the same distribution as yours (also in Illinois). I wonder if we ever met.
Hey, F! Quite possibly. I was at IMSA from 1999-2002, and did ICTM, ARML, USAMO, the whole nasty lot through all three years (except USAMO, which I only qualified for in my last two years).
I'd also say to count me in with the people who can't stand to watch embarrassment humor, but now it just feels all bandwagon-y. (People can't understand why I never liked Seinfeld, but it was just a big show about four people who suck at life! It's painful!)
There's something suggestive about the distribution of this apparently widespread, yet socially invisible phobia.
Grad school makes you squeamish?
It was also probably the moment I realized that to be successful at math you needed not just to be smart, but to be an offscale genius.
I believe you believe this, but it's not actually true.
I'm a Mandarin? Sweet! Your ass is mine, Tony Stark.
540: This probably also goes to 375, which talks about hitting a wall somewhere around Diff. Eq. which felt like absolute incapacity. I hit the same wall, around the same spot, and it felt impassible to me too -- I wonder if you, or anyone else who went further in math, remembers that as a hard spot to get past, but not actually insuperable once you figured out what was going on.
Look, some of us are getting stuck on simple probability theory.
Dude, I got stuck on exactly the same point you did -- it's just that I could see it with two options but not with fourteen. Probability is really hard for me -- if I skip a step at all, my intuition goes haring off in the wrong direction. Luckily, most real world problems are pretty simple.
I have the diligence of Talent, the credentials of a Lifer, and the easily peelable rind of a Mandarin.
I gave up on that value added thing.
Ah. Off by about a decade, but I did all those too, and looked at IMSA but decided to do the public school thing. It's interesting to see that in that decade, a) USAMO takers apparently tripled, and b) IMSA really has joined the ranks of Thomas Jefferson, NCSSM, and the other magnet schools in number of participants.
Count me in the cringers, too, though it's strange what will set it off. I think mostly it's the predictability of it. Conventional sitcoms are the worst because you can see it coming from a mile away, and you know they're going to milk the embarrassment/misunderstanding for a good long time. I could never watch I Love Lucy, but The Office is not so bad.
533: In addition to 534.2, the contrast between my standing as a math student who could get away with making a reasoned decision not to do the homework and his as one who couldn't was a major theme of the teacher's rant.
He was actually far and away the best math teacher I ever had, but he was hell on students for whom his approach wasn't effective, including not only the lousy math students but also some of the capable-but-conventional types.
544 -- That's reassuring!
Part of feeling that you're "good" at an academic subject is confidence in trusting your instincts. For me, I never got close to that point in math; I remember even in high school, "solving" problems (I was actually pretty good, grades-wise) but having essentially zero confidence that I was right. What if I'd overlooked some giant error??? How would I be sure????
Whereas in the more verbal subjects, even if I made big mistakes, I always had a pretty firm sense that my intuitions were at least somewhere close to solid ground.
Also, as I think someone pointed out above, it is in many ways more important how relatively good you are at a subject than how absolutely good you are. People tend to favor, and schools and peers tend to pressure people into, the areas that they are best at, even if they're sort of OK in other areas. That's how I ended up with my perception that I am "bad" at Math -- I wasn't that bad, and I'm sure that if I worked hard at it, I could have done OK, and, I dunno, ended up at a bad engineering school or something. But I was so much relatively worse in Math than in other areas.
375, 542
I hit a wall too, it was just farther down the road. Real Analysis was what finally killed me. It was the hardest class I ever took.
498: Not so fast, BG. Davis is pretty famous in the life sciences. UCD's Ecology program is generally one of the top three programs in the country, occasionally reaching first.
Their history professors, however, they select purely on the basis of looks.
550.2: "Looks" s/b "nipples"
Delurking to say that I too have to leave the room during awkward scenes on TV, which is one of the reasons why I've stopped watching sitcoms.
What if I'd overlooked some giant error??? How would I be sure????
You've probably heard this before -- but for most day to day calculations or probability questions it's not that difficult to work up a back of the envelope approximation that will give you a plausible range for the correct answer, and it's worth developing the habit of doing so.
(I had a fun moment a couple of months ago when I referenced an anecdote from an amusing book about HALO parachute training in which he claims to have opened his parachute slightly before he was level with the deck of the ship. We were trying to figure out whether that was plausible, and I started doing some back-of-an-envelope calculations and had a strong "I'd forgotten how satisfying this can be" reaction. I don't have much reason to do things like that, but it's fun to have an excuse to exercise those skills every once in a while.)
Was 498 serious or a joke? If it was serious, it's pretty goddamn stupid, but I thought BG was joking.
543, 544: probably is hard for everybody, to a first approximation, including statisticians. It takes a long time, and a lot of staring at problems, before it begins to seem remotely intuitive.
Real Analysis was what finally killed me. It was the hardest class I ever took.
You're making me embarrassed to call myself a math major. I graduated without taking either Diff Eq or real analysis.
[Thinking about people mentioning saying that it created social awkwardness when they would say that they were a math major my line was, "I'm a double major in mathematics and political philosophy. I really like abstractions." Saying that never seemed to change people's impressions of me . . . ]
543, 544: probably is hard for everybody, to a first approximation, including statisticians. It takes a long time, and a lot of staring at problems, before it begins to seem remotely intuitive.
It's worth repeating, however, that the sample problem is designed to capture a particular conceptual difficulty. Many probability and statistics problems are more intuitive.
451 Women kicking ass in the Intels doesn't surprise me much at all. By the time you get to the experimental sciences (pretty much anything outside super-esoteric theoretical physics), I don't think even the "variability of math talent" nature arguments suggest there should be more men at the tippy-top.
Arg. The Intel STS is not just experimental sciences; also math and theoretical science (and computer science/algorithms/engineering -- a pretty wide variety of stuff). At least one of the women winners I know did a theoretical project, and two of them are in my field, which is, uh, semi-esoteric theoretical physics? They're no slouches in math, at any rate.
I've gathered that BG wasn't much impressed with Davis before (I vaguely remember something about not liking the local apples, either), so I assumed she wasn't joking.
Regarding hitting a wall, it's hard to say:
I wasn't able to grasp any of my quals courses my first time through. I had to methodically go through my notes and do lots of problems over the summer before I could take the quals.
During the course itself, I didn't feel like I was hitting a wall exactly, so much as that the course was going too fast for me to keep up.
I think my low point in math was when I pulled multiple consecutive days of only two or three hours sleep trying to do some homework full of problems like "show that PSL(2,5) is isomorphic to A5". I never really grokked the theory of finite groups. Or pretty much anything discrete.
The question is, what on earth is BG's Davis animus based on?
I didn't realize the guy who taught that class was important enough to merit a Wikipedia page.
563: Maybe she sided with bob in some mcmanus/ari showdown.
557: eh I dunno if that's true.
Sure, I don't know either. It depends on what the universe of problems from which you are drawing is.
I know that, for me, there are a lot of cases in which knowing that the variance for the sum of n samples from the same distribution is equal to the variance for one sample time sqrt(n).
Is that intuitive, no. Is that going to be something that most people have need for on a regular basis, no. But it's a very handy thing to be able to remember and pull out if you're looking at a relevant situation.
But, come to think of it, most of the cases where that's come up for me have been talking about gaming. So take that for what it's worth.
err, replace "variance" with "standard deviation" in the previous comment.
have been talking about gaming
NickS, are you a professional gambler?
If so, when exactly should we hold them/fold them? Under what circumstances is walking away an appropriate tactic? Running?
No, not at all. But I was an RPG (table-top) geek for most of my adolescence, and old habits die hard.
Which is just to say that I don't actually game any more, but it would be fun if there was a good opportunity, and I still talk about the idea with friends.
Never count your XP while you're sitting at the table. There'll be time enough for countin' when the campaign's done.
On the comedic embarrassment subject, isn't seeing others in painfully uncomfortable situations, and having a reaction of similar discomfort... just empathy?
I wouldn't say it's been so bad that I've had to leave a room, but I'll certainly join the chorus of not enjoying that sort of comedic situation so much.
551: Nipples s/b "haunting resemblance to Aquaman"
549 - My brother! My issues were compounded by the scheduling mistake -- which my undergraduate advisor should have corrected but failed to -- of taking Complex Analysis first.
They threw me in the deep end of the math pool and I drowned. Thankfully it cured me of any notions that I should go to grad school.
569: Do you want the girl answers or the boy answers?
The Intel STS is not just experimental sciences
Oops! Did not know that at all, so sorry if it came off wrong. All the people I knew in the competition, and the projects that I remember seeing from high school, were in the experimental sciences.
549, 573: me too, exactly there, about three weeks into Math 207. Embarrassing, but also kind of liberating.
While I'm joining groups, count me in for the squirming at vicarious embarrassment. So awful.
Sometimes, if I'm watching a TV show and sense that something embarrassing is about to happen, I'll pause the DVR or Hulu, find a recap of the episode online, and read it to figure out if the embarrassment actually happens. Somehow this ameliorates the issue.
I used to hate vicarious embarassment, but as I've gotten older and more bitter, I enjoy it more and more. Fuck you, other people.
The last few hours I've been distracted and intermittently reading the thread all out of order and randomly replying out of place. Sorry about that. To continue:
Re: gender ratios in various competitions, my high school Science Olympiad team was like 50/50 and it was the most absurdly fun group of people I've ever had the good fortune to hang out around. I still get nostalgic for that. Scavhunt was wackier but only like 25% as much fun.
Parenthetical, my comments were much harsher than I meant for them to be. Just in a bad mood and ashamed of my own failed credentialing.
Obviously there are excellent people in the History department--Ari and Rauchway being the only ones I'm familiar with. I did know an undergrad who was studying meieval stuff, and it kind of shocked me that there were no actual professors in that area--only a lecturer.
Many fine schools have barely anyone teaching medieval history. Not much call for it, you know.
At Swartmore it's a hodgepodge of various people.
neb, my animus comes mostly from having gone there. Mostly, I just don't like the town and was being cranky about the school. One thing I will say about private schools is that while the administrations can be infuriating some things are more customer service oriented, like they always offer the classes people need to graduate so that they can finish in 4 years.
I find 211 interesting because it lists four of the nine schools I applied to for undergrad. I attended one of them, the only one whose merit package was sufficient enough that my parents didn't threaten that they'd have to sell the house to help me pay tuition there. I'm still deeply, deeply in debt because what my parents meant is that *I* would never own a house if I went to any of them, because they were only helping a tiny bit. Had I known how much debt I'd be in, I might have chosen differently.
It's the Hamlet game in math! I didn't have much intuition at abstract algebra, and in analysis lost it at complex analysis, or thereabouts. I wasn't especially technically ept before then, but I had enough intuition and enough ways to cross-check the intuition that I could comfortably practice the scutwork. Sitzfliesch counts.
Other rules for girls that have come to mind: it's not OK to beat boys. That is, you can beat loser boys, but it's not OK to beat all the boys, especially not at a Boy Thing; that's rude and showing off. And it's not OK to ignore everyone else for a month and neglect your looks; you have to pretend that your good grades are sort of accidental. I was in high school in the early 80s, and half my family is Southern, which let me in for more of both of these than may be current -- I should hope! -- and college was immediately OK. Nor does 'you can't beat the boys' seem to be nearly as powerful for students nowadays of Asian and Indian extraction; on casual inquiry, they don't think of math skills as being so specifically male.
I was hoping the Berkeley math prof porn movie was a joke, but failing that, that we could tie together a couple of threads. Gemmuns.
Swarthmore's not a large research university. Mostly, I think I just didn't like the culture, but really, I don't want to get into an argument about this.
And I stand by my assertion that Washington state apples are better than the ones from the Central valley.
I'm in a foul enough mood that my writing is getting even more atrocious than it normally is. I'm also exhausted.
591: See what I mean. I'm going to retire for the evening.
585: I guess they're fairly typical choices for Midwestern concerned-about-money-but-still-wanting-a-prestigious-school people to apply to. The unusual thing about the one you attended -- if I've inferred correctly from past comments -- is that (at least when I applied, I think a few years after you) they had a very straightforward system of financial aid based on SAT score. Everyone with over a 1500 got full tuition, I think, and it went down from there. I didn't see anywhere else with a policy like that -- it was always just some mysterious process by which they chose people to give scholarships to.
593: Northeastern had, for a while, a system where anybody who was a National Merit Scholarship finalist got a full ride. A friend of mine (a year older than me; the last year of the program) likes to brag that he was the reason they eliminated that particular program.
593: That's why I went there. I got a far more prestigious merit-based scholarship at another school, with slightly more financial support, but nearly everyone I met there came from a lot of money. At the school I attended, there were more middle-class people like me who were also fairly smart. (I was well above the cutoff for that prize, SAT-wise.) I didn't want to be one of two recipients of aid. I don't know if I made the best choice, but it was a good school, and my classmates weren't snobs.
And no, it wasn't full tuition for over 1500. It was like 2/3 tuition, and for a lower score, IIRC.
560: I wish I could remember where it was, but I saw some interesting research suggesting that the amount of time it takes people who are good at math to do math problems (I think this was even just at the calculus level) is significantly longer than the amount of time that most people give up after. I think it was something like 30-60 seconds for good students to solve the problem, and bad students give up after under 5 seconds.
I wouldn't be at all surprised if this phenomenon repeats itself at more advanced levels. That is, what it really takes to have success in math isn't that you don't hit a wall but that you have something in you that makes you unable/unwilling to stay stuck at that wall. When I first learned calculus I certainly remember a feeling of hitting a wall, but I spent two weeks fighting through it and then I got it.
In my case it's an obsessive inability to not think about something I'm stuck on, but for other people it could be something different that gets them through that wall.
597 was me.
It's tricky the way that education funding is trickier for people whose parents have a moderate amount of money than for people with not very much money. My parents made less money than the tuition at the school I went to, but it didn't matter because of need-based financial aid. Whereas friends of mine whose parents made 6 times what I did (but who weren't as good with money) ended up with more debt than me.
I saw some interesting research suggesting that the amount of time it takes people who are good at math to do math problems (I think this was even just at the calculus level) is significantly longer than the amount of time that most people give up after. I think it was something like 30-60 seconds for good students to solve the problem, and bad students give up after under 5 seconds.
That makes sense, but of course one of the prerequisites for being willing to spend more time on a problem is some sense that eventually you will be capable of figuring it out. That may be one of the reasons why the good at math/bad at math mentality becomes so important.
593, 595 -- not to pry too much, so feel free to not answer, but why were schools like Wash U or CWRU more attractive than going to BigStateU? Were the private schools cheaper if you were smart enough to get the relevant scholarships? [Not that WashU or CWRU aren't very good schools, they are, but in my own mind I wouldn't have ranked them as automatically or inherently better than the also very good midwestern public universities]. Just curious about the thought process.
600: They're smaller. I had no interest in going to a big school.
in my own mind I wouldn't have ranked them as automatically or inherently better than the also very good midwestern public universities
It's like Cosma Shalizi means nothing to you.
Or alternately like I can't read.
If it's not clear, I had very mood-based priorities at the time. I wanted to go to a school that (a) did not have any of my high school classmates there, (b) was about twice as big as my high school, (c) did not have a significantly wealthy student population, (d) was not sports- or fraternity-oriented, (e) had a good mix of racial and ethnic groups, (f) was not overwhelmingly female, (g) had good arts and sciences programs, and (h) was at least a few hundred miles from home.
High school me would have been thrilled with the chance to attend this university, but I probably would have had a hard time getting my parents to chip in for the tuition.
It's a shame that there aren't more small public universities.
(f) was not overwhelmingly female,
Aha! Here's one of the main reasons for the (relatively) new affirmative action for white males (referenced way upthread, I think). (Not that your school had this policy, AWB, I doubt that it did). Most 18-year olds, male or female (and perhaps also gay or straight? maybe that too), do not want to attend a same-sex college, and who can blame them? I think it does put the college admissions office in a bit of a bind: if using only grades and SAT scores results in 60-40 female-male ratio, or 65-35 or whatever, and then the school starts to look less attractive to females, etc., etc., what should they do? I don't have a problem with AA for males, so long as it's kept within some reasonable range (I'm not prepared to define "reasonable" here) and balanced against other competing claims to inclusion and so on.
Anyway, in terms of whether or not you made the best choice, I think it's almost impossible to know, and there's probably not much percentage in second-guessing the decisions years after the fact. You made the best decision that you could, based on your priorities (and on the information available to you) at the time.
582: Oh, I really didn't take it badly - I was joking in 514 (or 512, or whatever number I said something in. I'm too lazy to look it up.). Undergrad is different than graduate, for one thing, just as the professional schools are different.
Also, Davis does (really, did, things have changed now) have medieval historians, assuming you were there in the not so distant past.
Sorry you're having a bad day!
I wouldn't be at all surprised if this phenomenon repeats itself at more advanced levels. That is, what it really takes to have success in math isn't that you don't hit a wall but that you have something in you that makes you unable/unwilling to stay stuck at that wall.
I was musing something similar to this. That when you all describe hitting a wall in Diff Eq or Real Analysis or Abstract Algebra, it was actually very context dependent: being unable to do the given assignment in the given time frame, while juggling three other classes and whatever else.
I suspect that, in absolute terms, any of you guys could have gone line by line through the textbook and mastered the material. Which is what mathematicians are expected to do with each other's papers or new areas if they actually want to understand. It just takes more time investment than most people have to give, especially if up until that point you could do the homework by paying attention during lecture.
And no, it wasn't full tuition for over 1500. It was like 2/3 tuition, and for a lower score, IIRC.
I'm about 90% sure that when I applied (2000) it was full tuition, because I remember being glad to know early in the application process that there was at least one non-state-school option where I wouldn't have to pay tuition. I'm less sure of what the cutoff was for getting full tuition. I can't find any of the nice tables of SAT score to money on their website now, so maybe they discontinued the program.
f using only grades and SAT scores results in 60-40 female-male ratio, or 65-35 or whatever, and then the school starts to look less attractive to females, etc., etc., what should they do?
Not worry about it, since if having too many women makes the school unattractive to women, you'll find a sustainable fixed point without having to interfere?
604: That strikes me a pretty well thought-out set of priorities for a high school senior. I just toured a bunch of schools in New England and applied early to the one I thought I liked best when I visited. This strategy did not get me what I would call an ideal outcome, though I think things worked out okay.
I went to the school that my older brothers went to because then maybe we'll all hang out together and be BFF.
593, 595 -- not to pry too much, so feel free to not answer, but why were schools like Wash U or CWRU more attractive than going to BigStateU? Were the private schools cheaper if you were smart enough to get the relevant scholarships?
I think they were unambiguously better than my local BigStateU (UofLouisville) or the next-closest one (U.Kentucky). UofL had actually, around this time, tried to scrap their physics department entirely, arguing that it was unnecessary since they had so many engineering departments.
UIUC is a good university, but IIRC their out-of-state tuition was pretty high, and there weren't scholarship options, so it was clearly more expensive.
But really I just wanted to go to Chicago and I did and god knows where I would have ended up if I had chosen any of the other places I was considering, none of which would have properly set me up to go to the right grad schools and meet the right people.
Oh, and also I wanted to get away from home, naturally.
612: My sister went to the same school as my brother, but not the one I went to.
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Huh. I've never seen this before:
Thank you! Your message has been received. PLEASE NOTE that correspondence received by and from the Office of the Governor may be considered "public record" information under the Right-to-Know Law and such correspondence may be made available for public access.
This must be coming from PA's new Open Records law. I wonder if you could do a request based on a constituent's name, or if it has to be issue- or agency-based.
This will be interesting to see litigated at some point, especially if I'm not the guinea pig.
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606: I was 17 and had few girlfriends, and did not know that middle-class compsci dorks are as likely to date-rape chicks as footballing frat boys. I'm sure you know I teach at a women's college now, and, at another college, teach courses in women's studies.
609: Are you younger than me, essear? I didn't know that. I entered in 1997.
Since this is now mostly a college thread, I just saw that Nebraska is joining the Big 10. I'm not sure what to think yet.
618, 609: That would certainly explain the difference in the funding situation. Princeton set off a financial aid bidding war in (I think) 1998. So it's to be expected that packages were different before and after then.
Not worry about it, since if having too many women makes the school unattractive to women, you'll find a sustainable fixed point without having to interfere?
But perhaps the achievement of that fixed point will involve the loss of some higher-scoring females who can go elsewhere? My understanding (but I may be wrong about this) is that, whereas with the very elite schools it's the students who are competing against one another to gain admission, below that level it's the schools competing against each other to attract the most desirable students possible. But I don't claim to understand the US college admissions process, which is anything but transparent.
613: I desperately wanted to go to Chicago, and cried from joy when I got in, until we got the financial aid package and my parents said no. UofC gave me something, but it was a little over half tuition. One of the problems was that my dad was making not quite twice tuition, but had been without a job for several years before and after that, so they didn't have anything to help me with, and were stuck in a fairly expensive house that they're only now finally about to sell.
609: Are you younger than me, essear? I didn't know that. I entered in 1997.
Yes. If I remember correctly, in one of the threads around here we worked out that neb, (), and I are within a few months of being the same age.
621: The other issue is not just that high-achieving women don't always want to go to a school where they can't get laid, but that men often choose not to go to schools that might mark them as feminine. In fact, I'd say it's more the latter than the former.
On the topic of UC Davis: it has the top viticulture and enology department in the US. Which is not to say that university education is in any way essential to good winemaking—and I hasten to add that I'm as anti-credentialism as the next Emerson—but it deserves to be mentioned.
625: I'd say a UC Davis education is at least as likely to be an obstacle to good winemaking.
neb, (), and I are within a few months of being the same age
If that's the case, then I get to play, too. I'm less than one month's neb's senior.
626: I think @be sch0ener went there when he was on Sabbatical from his teaching job at my undergrad institution. But his techniques aren't exactly standard curriculum.
624: And here I'd been thinking you were my age or older, for some reason. We need another UnfoggeDCon.
I'm actually a year older than you guys. Otto and I are the same age, though.
Now I've looked up birthdays on Facebook to check. Otto is a full year older than I am. Paren, you're about 4 months older than I am (previous calendar year, yes).
The only people I see playing chess regularly are playing on tables on the sidewalk on Market Street, and the tables, if not the same players, are almost always there. I guess when I went by on a rainy day a couple of weeks ago, the tables weren't out, so it's not quite a non-stop chess game, but it seems like it.
All you young children appear to me as though I'm looking through the wrong end of a telescope.
Or maybe just the wrong end of a pair of opera glasses?
Heebie sees a tiny eye, Moby a giant eye.
isn't seeing others in painfully uncomfortable situations, and having a reaction of similar discomfort... just empathy?
Real people, yes. Fictional characters, I'm not so sure.
I just can't seem to get the hang of these bifocals.
638: Look through the little part when you want to read and the big part otherwise.
Most 18-year olds, male or female (and perhaps also gay or straight? maybe that too), do not want to attend a same-sex college, and who can blame them?
And then there are the few, the proud...
164: I also generally think of things like 'good fit' as, while nice if you can get it, really impossible to achieve in any educated fashion, barring the occasional really unusual school.
It just occurred to me that, having gone to Antioch, my parents might have had an unrealistic belief in the ability to select a school based on fit.
Heck, I'm the only one in my family that went to a "conventional" school. My brother went to Evergreen.
Mrs. -sky went to Evergreen. I knew some kids there in 1999 who got course credit for organizing the WTO protests. Better earned than anything I ever did for an A-/B+.
NickS, were you there for the supersexy "May I touch your knee now" innovation?
640: We've discussed that before. I still remember the brochure I got from them. They didn't have a website at the time, probably because it was during the Reagan administration.
I arrived in the early 90's. The year before I got there, a student knew how to connect the modem to the solitary phone line in order to send e-mail to his early adopter friends at real colleges. Then he left, and no one had internet for the next three years.
644: I didn't recall that you went there. That makes you an outlier pretty much anywhere.
NickS, were you there for the supersexy "May I touch your knee now" innovation?
I knew the antecedent in that comment was unclear when I wrote that comment. My parents both went to Antioch (and met there) which, I was suggesting, may have affected the type of advice that they gave about choosing colleges.
I completely missed that you went to Deep Springs.
Ok, I've finally caught up on the thread. (I did a lot of math when I was a kid.) What do people mean by "Differential Equations"? I remember a linear algebra/"elementary" differential equations course and a multivariable course being pre-requisites for higher math courses, and I got the impression that the wall courses came after those two. Certainly, the grading on those two courses seemed "normal"* while the distributions for the later courses were apparently in the "no one got higher than 28/100, and 23 was an A" range. Is the "elementary" doing a lot of work there? I guess you'd have to see a syllabus to really say.
*Not in the strict statistical sense, but in the 90( or so)/100 = A sense.
There is, by the way, a brief description on Antioch from around the time that my parents were there in Bill Moyers' book Listening To America but, unfortunately, google books is not particularly helpful.
Everybody at the Berkeley meetup was a stripling (except me). Witty and lithe withal (except me), but still.
647: On the internet, I'm not wearing the overalls.
I vaguely remembered that someone here went there, but not who. The fact that the founder's (or whoever it was) name kept showing up in various places in the brochure they sent made me wonder if there was something cultish going on. That was probably unfair.
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It is with great pride in my city of birth that I award my Cup to Chicago.
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652: George Washington's name is on a bunch of stuff. Of course, he didn't put it there himself.
516
If you'd be happier with some social explanations that would make it easier for you to think that maybe the innate differences weren't so stark: (1) stereotype threat. Note that you noticed a dearth of girls doing well at a stage that you identified as not that difficult conceptually -- given that it's unlikely that the difference there was about a difference at the far right tail of math capacity, there seems to be a fair shot that it was more about whatever happens when you give a test to someone who feels as if they're in a group that's expected to do poorly.
If the distributions are normal with the male mean or variance higher then you would see this pattern of an increasing fraction of males as you move to the right. The far right is not disconnected from the rest of the distributions.
418: [boy-girl problem] This is intuitively plausible because "boy born on tuesday" usually distinguishes two kids (other than in the rare case where they're both boys born on tuesday) and so should be more similar to the situation where you've completely distinguished the two (by saying the older one) then it is to the situation where you haven't distinguished them at all.
Worked through this with the family when I got home, and for the discrete case got it to %boy=(2n-1)/(4n-1) where n is the number of equal probability intervals (7 for the day of the week formulation), and %boy=(2-p)/(4-p) for the general case where p=the probability of satisfying the "constraining" condition. Neatly shows the special cases of 1/3 for p=1 (no conditions, just "a boy") and 1/2 for p=0 (boy "uniquely" identified).
653: Well done, Lord Stanley.
516
None of this eliminates the possibility that there is an innate difference, of course. But if that possibility bothers you, there are perfectly decent reasons for thinking your observations don't establish it.
Sure and you can also find reasons not to believe in evolution if you find that offensive. But at some point you are abandoning science for faith.
387
... Or just that, as Shearer opined, it's an especially big pity that they have to worry their pretty heads about all this silly status business?
Um, actually I didn't.
But at some point you are abandoning science for faith.
James, I missed your response to my 338. What evidence do you have for the lack of discrimination in chess, beyond your faith that it is so?
338
So? Why should that sort of bias be discounted.
Not saying it should be discounted just that it is different problem from concert musicians where according to 41 moving to objective evaluations quickly increased the number of successful women.
Sure and you can also find reasons not to believe in evolution if you find that offensive. But at some point you are abandoning science for faith.
You might be able to take this tone if there were actually any convincing evidence whatsoever of the proposition you think is true.
660
James, I missed your response to my 338. What evidence do you have for the lack of discrimination in chess, beyond your faith that it is so?
I didn't claim that there is no discrimination in chess just that talent can be objectively evaluated. The lack of women at the top is real not a reflection of biased judging.
I used to not believe in evolution until I noticed that my beak was just perfect for slurping yogurt from discarded containers.
ENTITLEMENTS IS BAD!
And now I've been reading this old thread at Marginal Revolution and it's making me grumpy.
'SCUSE ME, ENTAILMENTS IS BAD.
665: So was Just Shoot Me.
662
You might be able to take this tone if there were actually any convincing evidence whatsoever of the proposition you think is true.
"Convincing" is doing a lot of work here. What probability do you want? 50%, 80%, 95%, 99%, 99.9%?
I'M MAD AS HELL, AND I'M NOT GOING TO TAKE THIS ANYMORE!
Mr. Finch, excuse me. Just one more thing.
GO THE HELL AWAY COLUMBO AND LEAVE ME TO MY SHEEP
dammit, that was supposed to be OPINIONATED FALKLANDS. then I hit refresh to see if the gag had progressed.
now 672 reads like a Deep Springs callback.
We've been around 2,000 years and people still call us asking for his agent.
supposed to be OPINIONATED FALKLANDS
DECÍS VOS.
"Convincing" is doing a lot of work here. What probability do you want? 50%, 80%, 95%, 99%, 99.9%?
To be clear, I was responding to your response to LB in which you appear to claim that believing there may not be innate differences in mathematical ability between men and women is abandoning science for faith. So you are, apparently, claiming that it's possible to establish at a certain confidence level that there are such innate differences? I think LB's comment 516 gives a few reasons why this is very difficult. How would control for things like stereotype threat?
But actually I think arguing over whether studies have or haven't shown a difference in variance of male and female abilities is missing the real point, which is that the number of people scoring in the top x percentile on an exam is a pretty shitty measure of how many qualified people there are for a certain kind of job. And there are enough demonstrable inequities around that it's kind of monstrous absurd to point to questionable differences in poorly-understood measurements and call them a justification for not addressing the evident problems. I'll have enough respect for your intelligence to not dredge up the obvious historical parallels.
679
To be clear, I was responding to your response to LB in which you appear to claim that believing there may not be innate differences in mathematical ability between men and women is abandoning science for faith. ...
Nothing is certain so it is ok to believe that it is possible that there are no innate differences. Similarly there is some chance that the theory of evolution is in fact wrong. But when you start looking for excuses to ignore evidence for such differences or to label such evidence unconvincing or generally to weight the scales in one direction then you are no longer pursuing the truth wherever it leads.
370
Shearer could be one of those people with a very narrow view of research ability, I suppose, which might skew how Putnam skill correlates with research skill. ...
I have tried to be careful to say the problem solving ability that the Putnam exam measures is only a component of mathematical ability. But it is an important component. If you have a lot of it you have a greatly enhanced chance of a successful career in mathematics.
But only if you're born on a Tuesday.
James, how do you account for the increase in elite women over time?
491
And more importantly, my experiences were from an exceedingly stylized form of competition that means nearly nothing in the real world. It probably doesn't even have too much relevance to the performance of math professors, who need all kinds of other skills to publish and teach which almost certainly do not have male-biased gender skews (if anything, it's the other way!).
It is my understanding that doing well on the Putnam is in fact rather predictive of real world success.
One possible caveat is that I don't think cramming for the Putnam used to be typical. If in fact there is now a lot of test prep going on this may reduce the degree to which the Putnam measures raw ability.
Here is the blind auditions article:
http://econ.duke.edu/~hf14/teaching/povertydisc/readings/goldin-rouse99.pdf
Skimmed thread, didn't see it mentioned, will comment since I considered this rather extensively on my facebook page:
For the Tuesday information to change the probability that both children are boys, you have to assume that you asked the guy "Do you have a child born on a Tuesday?" If you asked him "What day was your child born?" or you asked him nothing at all and he just volunteered the information, the probability doesn't change with the information about the day of birth. The real answer to the question is: "underspecified: what did you do to get that information?"
But when you start looking for excuses to ignore evidence for such differences or to label such evidence unconvincing or generally to weight the scales in one direction then you are no longer pursuing the truth wherever it leads.
Because evidence is never unconvincing on its own; clearly I must be weighting the scales! The criterion for "convincing", perhaps, is "accords with James B. Shearer's preconceptions, which are equivalent to 'the truth'".
Maybe I do need to pull out one of these historical parallels. Suppose it's, I don't know, 1920 and you're talking to a highly respected psychologist, like, say, Lewis Terman. He's a bigshot at Stanford, so he must be a careful, scientific type, right? And he explains to you that he has detailed statistical evidence that black people and Mexicans are not suited to careers that involve dealing with abstract thought. So the fact that his colleagues in the Stanford math department are all white is totally to be expected! Would you praise him for his careful use of statistics and pursuit of the truth wherever it leads? Or would you wonder if, you know, maybe there are other effects at work here? But no, surely the latter would be like doubting the theory of evolution.
684
James, how do you account for the increase in elite women over time?
More opportunity. And in some cases affirmative action. I am not claiming there weren't barriers in the past. I doubt however they are the entire explanantion for gender disparities.
Not saying it should be discounted
Yes, I know you're not saying it should be discounted - any more than creationists are saying that science should be discounted. You're just discounting it. I want to know why. Can you explain?
688 is even more correct than 687.
689 reminds me that I went looking for Donald Mackenzie's book on the history of statistics and did not realize until I opened it that it has a lot of stuff about eugenics. I of course have not read it, as I never read books that I mention in comment threads.
...and to refine, I really mean "Do you have a boy born on a Tuesday?" Even "Do you have a child born on a Tuesday?" doesn't do the work you need, actually.
I just couldn't let a discussion of this problem go by with that point unmade! (If indeed it was unmade; long thread.) I gave it too much thought and attention for that, and in the end I didn't think 13/27 was a very good or complete answer.
Let's see how Shearer deals with a woman showing up after 300 comments and explaining to everyone that they were wrong about math. Maybe his head will explode.
Tia! Your point was indeed unmade earlier in the thread.
What's the probability that a baby born on a Friday will be a girl and named on Tuesday Thursday?
692
... Can you explain?
I tried in 661 and 663. One more try. When major league baseball started employing black ball players they quickly became numerous and successful. This does not explain why blacks are underrepresented in other fields which had and have no such employment bar. Of course there may be other explanations (other than innate lack of ability) but in baseball at least these other factors were not critical compared to the employment bar. So the baseball experience is not very relevant to fields without a collective employment bar.
According to 41 the problem for women musicians was not that they were untalented (for whatever reason) but that they were being judged subjectively in a biased manner. When the bias was corrected it became apparent that there were many talented women musicians. But this is not the case in chess or mathematics where the standards are less subjective. So the experience of concert musicians is not particularly relevant. Which is not to say that the lack of current talent is innate and not due to sexist sorting at earlier points. But there aren't currently a large number of unrecognized world class women chess players.
695, 697: Although if Tia's reasoning is what I suspect it is (don't know what is on her Facebook, my apologies if I assume poorly)--potential bias introduced by the selection of which information you know (such as being "volunteered" by the parent) --then lemmy caution may have meant to imply something similar with his, Parents will tell you anything about their kids in the comment (392) where he introduced the problem to the thread (but then again, he did not subsequently press it). And the same concern applies to any of the information needed for the initial setup of this type of problem (this is also implied in Tia's 695.1 refinement as I read it), not just the addition of the day of birth info.
If Kobe were invoked only once in a 701 comments what are the chances he will be invoked a second time in the thread?
Argh. This is what I mean about probability being hard. I'd gotten halfway to Tia's argument in an incoherent kind of way (that is, I recall thinking "What if the kid is there? You'd be able to see all sorts of lower probability things about him than what day of the week he was born, and that can't change the odds.") but I didn't successfully get it thought out enough to articulate. Although I'm still confused now -- the 13/27 argument works for me if the setup is "consider a family where the only fact you know is that there are two children, one of which is a boy born on Tuesday." But I'm really confused about what the line is in a more naturally phrased situation between when the Tuesday information affects the probability, and when it doesn't-- I don't think whether the information is requested or volunteered is right.
It's something about the sequence of when the information comes in, but I can't quite get there.
And now I think Tia's wrong again. If I do the stadium thing (filled with randomly selected families at the beginning, everyone who doesn't match the facts I know about my target family leaves, the probability of two boys is equal to the fraction of two-boy families left) the timing and source of the information doesn't matter. Argh. This is what kills me on probabilty -- my certainty swings around wildly.
The timing and source of the information doesn't matter. I thought there was a comment above that explained it as I'm about to, but I can't find it: what's most meaningful to me is to think about it the other way around: of all the possible combinations of children that the guy could have, how likely is it in each case that one of the children will be a boy born on a tuesday? Then, since you know that information, you can work backwards to figure out how relatively likely it is that the "two boys" situation is the one that obtains. Having more information about the boy would indeed change the probability, but not necessarily usefully; the reason the "born on the day of the week" criteria works so neatly is that it's a presumptively uniform distribution over a small probability space.
702, 703: I should wait for the more expert, but I am pretty sure that any bias affecting any part of how you got *any* of the information throws it off. So even your "consider a family where the only fact you know is that there are two children, one of which is a boy born on Tuesday." can be fraught if unbeknownst to you, the family was picked from a pool which biases the answer (in an extreme case--list of families with two boys). In the stadium example this can mean who gets into the stadium to begin with, or a bias in which group is asked to leave that is dependent on the real answer.
Yeah, a lot of the counterintuitiveness of probability problems comes from precise, but misleading, wording. If we use your stadium scenario, after you have eliminated all families without two children and at least one boy, in one interpretation you eliminate all families without a bboat; in the other you randomly select a family and ask what day one of their sons is born. Unsurprisingly, regardless of their answer they were still selected from a crowd with 2/3 single boy families.
700, and this will probably work for 702:
I don't know what you mean by bias, but I think I haven't made my reasoning clear. Further, 13/27 is wrong, or incomplete, as an answer to: "consider a family where the only fact you know is that there are two children, one of which is a boy born on Tuesday," because this statement doesn't include the question you asked, and it needs to.
The issue is that the information that one is a boy born on a Tuesday has to come as a result of passing a test you posed for it to make it more probable that one is a boy. "Boy born on a Tuesday" must have been defined as a success relative to some other outcome, so that two boys gives you more opportunity to achieve that success. If the "born a Tuesday" part wasn't predefined as a success relative to some other outcome, you've gotten no information relevant to whether the other child is a boy from the information that one is born on a Tuesday.
I will think for a little bit about how to be clearer and try this again.
Which is not to say that the lack of current talent is innate and not due to sexist sorting at earlier points.
Well okay then.
But there aren't currently a large number of unrecognized world class women chess players.
I think the relevance of the music example was that it shows how insidious these sorts of bias are - and that there can be large, systematic effects that aren't visible until somebody tries to measure them.
705: Yeah, that's my current thinking. Someone says something else convincing, though, and watch me spin like a weathervane.
706: But as someone said above, probability questions are about your state of knowlege. If you don't know about those biases, you can't account for them and they're not part of the problem.
709. The thing about the music example is that although women are now accepted as musicians, even in the Vienna Philharmonic, they're largely ghettoised in certain roles in music instead. Name three women trombonists.
Asking people to leave the stadium is in fact equivalent to posing a question. You predefined what a success was--that's the essential element.
It might be helpful to think about the fact that if instead you said to yourself ahead of time "I'm going to ask everyone in my stadium full of people with two children who doesn't have a boy born on a weekday to leave," and then went up to everyone and asked "is one of your children a boy, and if so what day were they born?", the proportion of people with two boys left in the stadium wouldn't reflect the 1/7 probability of being born on a Tuesday versus any other day of the week -- even though you now know exactly what day they were born -- it would reflect the 5/7 probability of being born on a weekday. And for any individual person who said, "one of them is a boy born on a Tuesday" you would have the *same* information, but the question you posed, and what counts as a success relative to that question, would determine how you calculated the probability that there other child was a boy (somewhat closer, in that case, to 1/3 than 1/2, because they passed a less severe test). If you don't ask a question that defines a success, no change.
Here's the best example I can think of, and I'm pretty sure it's a classic one in explaining the difference forward and backward reasoning in conditional probability. I draw a card, and I get the three of clubs. What are the chances! It's a low probability, 1 in 52 event! Does it give me any information relative to any other question, like, is the deck stacked? Only if a priori I asked a question that would make a 3 of clubs a success relative to another card.
Name three women trombonists.
I can't name a trombonist.
I don't understand the relevance of 712. The question is contained in the problem being asked.
I played trombone in high school.
(Steve Turre, Bill Watrous, Nils Landgren, Bruce Fowler)
I mean, yes, if you said "I have two children. One of them is a boy born on a tuesday. What is the chance my other child was born on a tuesday?" none of the information provided (besides that the asker had two children) would be relevant. But that's not the situation.
710.2: I actually agree with that as long as you are in the realm of the "toy problem". Apparently I assumed wrong on what Tia's reasoning was and need to work though her 712.
I can't name a female trombonist, but then I can only name about three female jazz musicians period (that aren't vocalists).
One of my trombonists is a female born on a Tuesday. What's the probability that you can name my other trombonists?
718: jazz is a different world, though; I don't think they do gender-blind auditions for jazz ensembles.
I'm not sure I can name any classical musicians that aren't Yo-Yo Ma.
I'm not sure I'd equate "prevented from playing trombone" to being confined to a musical ghetto.
713. Well, five minutes ago I could only have named the utterly awesome Annie Whitehead, as a woman trombonist, but google tells me there's a facebook group full of such, which seems promising.
I'm not sure I'd equate "prevented from playing trombone" to being confined to a musical ghetto.
You would if you wanted to play the trombone.
700
I had meant to indicate you can ignore the "born on a Tuesday" info and that by the puzzle's logic adding additional voluntered information, like that he liked star wars or his exact time of birth would move the probability closer to 1/2. This makes no sense. Tia's comment is a better explanation why than what I had thought through.
There may be some voluntered information that may work to change the probability:
"I have two kids. They are different grade levels in school. One of them is a boy in your son james's class."
I think the last sentence does move the probability that they are both boys to, or close to, 1/2.
714: Okay, here
is where I first encountered this problem.
Here is the quote where the problem is posed: "Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. It consisted of the following three sentences: 'I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?'"
In order for the answer to be other than 1/3, you, the probability calculator, had to have defined Tuesday to be a success a priori relative to some other outcome. Otherwise the answer is just 1/3. If Tuesday is a success relative to any other day, the answer is 13/27. If Tuesday is a success because it is a weekday, it's something else. If Tuesday is a success because it starts with a T, it's something else again.
I assumed you all were responding to the same version of the problem.
716 just isn't responsive to what I'm saying. And for clarity, I'm using "Tuesday is a success" as shorthand for "boy born on a Tuesday" is a success.
I don't begin to know what you mean by "Tuesday is a success".
I assumed you all were responding to the same version of the problem.
We are. For those of us who lack subscriptions to New Scientist, here's a Google explanation.
Which I don't understand.
Regarding the puzzle in 392 as stated (with the additional information being volunteered) it is ill-posed as you need to know when this information (as opposed to some other information) will be volunteered.
If however the information is the answer to a yes or no question then things become a simple matter of counting cases.
The usual example is if you know there are two children and ask if the oldest child is a boy and the answer is yes then there are two cases remaining in one of which the other child is a boy. But if you ask if one (meaning at least one) of the children is a boy and the answer is yes then there are three cases remaining with the other child being a boy in just one of them.
In this example there are 196 cases to begin with. Answering yes to the question is one (meaning at least one) a boy born on Tuesday leaves 27 cases. In 24 cases the children are born on different days of the week in which case the other child is a boy 1/2 the time. In 3 cases the children were born on the same day in which the other child is a boy 1/3 of the time. So combining the child is a boy (12+1)/(24+3) = 13/27 of the time. The point is being born on Tuesday usually but not always uniquely identifies one of the children so the answer is between 1/3 and 1/2 but closer to 1/2.
I think this is equivalent to what Tia is saying.
Lemmy, I disagree. Only a *test* of "boy conjoint with another event" that can be counted as a success relative to another event changes the probability that the other one is a boy. The test part is essential.
If Tuesday is a success relative to any other day, the answer is 13/27.
But in such a problem, wouldn't this ("relative to any other day") be the assumption? Absent other (more oddly specific) information, I'd assume, what Tweety said in 705.last.
Ah, I see. You're focusing on the underspecifying of "boy born on a tuesday as opposed to another day of the week". That doesn't particularly bother me; it strikes me as the most relevant plain english reading of what he's saying.
726: OK, now I understand what you mean by a "success", in this case it is the listener's (not necessarily correct) assumption that the puzzle presenter by mentioning "Tuesday", is partitioning the space day-by-day.
728:
The probability of an event is number of successes/possible outcomes. By "boy born on a Tuesday" is a success, I mean: you've defined what counts as a success within your sample space, and it is boy born on a Tuesday, and nothing else (or it is boy born on a weekday, or boy born on a day that starts with T).
If you haven't done that, and in the original formulation of the problem, you haven't, then there's no reason to say the probability of being born on a Tuesday is 1/7 (and thus the probability of being a boy born a Tuesday is less still). Maybe the probability is 5/7 (born on a weekday). Without specifying that "boy born on a Tuesday" passes a test, and without specifying what test it passes, it does not make it more likely that the other child is a boy.
734. Actually, "Tuesday" simply has to be an exclusive partition, you don't even have to assume days. If your categorisation was along the lines of "Boys born on a Tuesday", "Boys who look like flies from a great distance", "Boys who belong to the Emperor", etc. it would still work provided you stipulated that a child can only be a member of one category.
So, this contrast between ways of dividing the week was meant to be illustrative, and I think I succeeded in communicating most of what I meant, so that's good, but I don't think the "plain English" reading solves the problem with the way the problem is posed. The way the problem is posed, the "boy born on a Tuesday information" passes no test at all. You really need to assume that the speaker said it in response to the question "is one a boy born on a Tuesday?" to get to the answer 13/27. That is not a natural reading to me.
Maybe the probability is 5/7 (born on a weekday).
Maybe it's 3/7 (days whose fourth letter is d). Maybe it's 7/7 (days ending in 'day'). Maybe what is actually meant by the parameter is boys born on top of someone whose name is Tuesday.
736: Yeah just realized that. It really is just your assumption that is is "Tuesday" versus "not Tuesday".
736: Right. And the key is the stipulation.
I mean, if we're getting into things that were underspecified in the problem, wouldn't the implicit binary gender space be a bigger problem?
741: My thought as well, being told that it is a boy does not pass any pre-defined test I had.
738: I'm not sure if this is meant to be sarcastic--to suggest that I'm raising some quibbling objection that relies on some arcane and silly reading. If it is, I promise you that you don't properly understand me yet/I haven't made myself clear. I'm really raising a quite central objection -- there is no additional information relevant to whether the second child is a boy if you haven't partitioned the space, as OFE put it, and in the original formulation of the question you haven't. Gary just volunteers: one is a boy born on a Tuesday.
741: No. Obviously we assume as a convention of these sorts of problems that there are two sexes, each of equal probability, as we are assuming 7 days, each of equal probability. But the point is that the followup question asks about the sex of the children, making the prior information that one of them is a boy relevant. Obviously "both are boys" is more likely if one is a boy. "Both are boys" is only more likely given that one is a boy born on a Tuesday if boy born on a Tuesday has passed a test--is defined as a success relative to some other state of the universe. The relevances of sex and day of the week are not symmetrical in the problem. The final question is about the sex of the children; the prior information about sex is relevant. For "born on a Tuesday" to be relevant it needs to pass a test, conjoint with "boy."
741, 742: For instance:
I have two children. One is born on a Tuesday and is a boy [JPS - the order of clauses does not matter, just making it explicit]. What is the probability both children were born on Tuesday?
OK 744.last addresses 745 at one level, but The final question is about the sex of the children; the prior information about sex is relevant. its not clear to me why this is necessarily so any more than day of the week or other partitioning.
And I think see the issue in 746, I will go do some work now. Should have quit with (2-p)/(4-p). Good provocative question.
742: I was just going to come in with that.
To Tia's use of the word 'success': The way I'm thinking of this, P(two boys) is equivalent to "If I pull one family from all the possible families in the world that satisfy what I know about this family, what's the probability that my random draw will get a two-boy family?" which is equivalent to "What fraction of all the possible families in the world that satisfy what I know about this family have two boys?"
I think the way Tia is using 'success' here is that unless you decided ahead of time that you care about Tuesday-birth, then the pool of 'all possible families in the world that satisfy what I know about this family' still contains families with no Tuesday-born boys. But that (with caveats about watching me spin like a weathervane) doesn't hold: whether or not you cared about it beforehand, there is a fact of the world that states how many two-child families there are with a Tuesday boy, and another fact of how many of those are two-boy families, and given that you know that the family you're interested in is in the pool "two-child families with a Tuesday boy", P(two boys if you know that one child in the family is a Tuesday boy) has to be (number of two-boy families with a Tuesday boy)/(number of two-child families with a Tuesday boy).
Any information you get about the family, regardless of when you get it or whether you care about it, affects the makeup of the population you're taking a random draw from, so it affects the probability.
745: And in that case, everything I've said about Tuesday now reverses to apply to boy. The Tuesday part is now defined by the final question as success. But you needed to have asked a question/posed a test about sex, conjoint with day, like "is one a boy born on a Tuesday?" in order to have relevant information about the probability that both are born on a Tuesday.
744.1: I do understand your objection, it just doesn't speak to what I found interesting about the problem.
750: Does my 749 give you pause? You persuaded me at the beginning, but I've flipped back, and you're now making arguments that I don't follow -- that is, I'm not clear exactly on what a lot of the terms you're using mean. Doesn't mean you're wrong, but I can't hang on to your argument enough to be convinced by it.
The final question is about the sex of the other child. You have to define the circumstance where both children are boys as a success. (Boy, that terminology strikes me as weird. Maybe because it's experimental statistics language and I'm used to pure probability language?)
753 cont'd, explicated: which is to say, the gender of the first child is no more relevant to the gender of the second child sans implicit partitioning than the day of the week is.
What is the probability that your children have sex on Tuesday?
Tuesday is the sexiest day of the week.
I find Tuesday's nipples very distracting.
Re: all the "I can't stand watching embarrassment" stuff, I used to be the same way and I'm actually surprised I didn't comment on it in the thread linked in 504. I'm not sure if I grew out of it (because really, empathy is overrated, right?) or if it's just a matter of finding good humor that happens to be based on awkwardness in some parts.
Maybe the relevant distinction is deservedness. On most sitcoms like "Frasier" or "Friends" or whatever, the protagonists are generally nice guys and good people and all that, with a few minor whimsical flaws but nothing so bad they ever actually are contemptible people, who get in miscommunications and caught in lies just due to the cruel writersin The Wedding Crashers, on the other hand, the protagonists are such vapid, immature people that getting caught by their love interests' family is no less than they deserve. Or in "The Office", Michael isn't precisely a bad person but he's (a) the Everyman's boss, and (b) so socially inept that he usually doesn't realize how stupid he looks. So why not laugh at it?
616
This must be coming from PA's new Open Records law. I wonder if you could do a request based on a constituent's name, or if it has to be issue- or agency-based.
This will be interesting to see litigated at some point, especially if I'm not the guinea pig.
I don't know PA's thing, nor exactly what kind of message elicited that response, but public comments on federal government rulemakings are all available online. You can find them by searching for the issue or agency or, yes, the commenter's name, but it's not 100 percent reliable - some might get sorted by their company's name rather than by individual, some might be filed under the name of only one co-signer, etc.
629: Name the date. Or I'll throw something out there, just to get it started: July 30. Or if that's too short-notice, September 3. Both are Fridays.
699
Which is not to say that the lack of current talent is innate and not due to sexist sorting at earlier points.
Well, great. So what are you disagreeing with, again? It's like you're having a totally normal conversation in a code that unfortunately just resembles what everyone else is talking about purely by coincidence but has nothing to do with it.
on terminology, for a moment:
I'm really surprised by people's pause at the word "success" because it's coming from probability -- one speaks of a "success" in a binomial trial, for instance. I know I didn't make this up! Anyway, here is an example of the way I use "success," if it will help at all. Here is another. Hope that's clarifying! The "test" language is probably coming more from experimental statistics. I can choose some other if it's not helpful, but I thought that it would be useful as an umbrella term to encompass both asking questions and telling people to leave the stadium.
LB, you're not giving me pause, but I'll think about formulating a response. In the meantime, here's another person making the same point I'm trying to. Perhaps he does it more clearly. I agree with him in every particular, except that I feel he's a little too kind to the answer of 13/27, since the original problem doesn't state a data generating mechanism at all.
Monday's nipple stays in place,
Tuesday's nipple looks best in lace,
Wednesday's nipple is ready to go...
I find the linked comment clear and comprehensible, but unconvincing. Of course we can change the probability if we make assumptions about what led the speaker to say that he had a boy born on Tuesday. But if we don't make additional assumptions, the 13/27 argument holds.
To clarify what's puzzling me about your use of the word 'success' -- it's not that it's totally unclear. I understand roughly what you mean. It's the sharp distinction between "I have two children, of which one is a boy", where 'one is a boy' is a 'success', but "I have two children, of which one is a boy born on Tuesday" is not a 'success'. Those two sentences seem to contain information of an equivalent level of relevance, however you learned either of them.
761: But Thursday's nipple? Total ho.
Between you and KR, I'm going to lose the reference points that I use to tell what is appropriate.
762: One further clarification I'd make, since I think my "success" language may have led to some confusion in this regard, is that you don't have to have gotten a "yes" to whatever your question was, but you have to have posed one that partitioned the sample space. "No" to the question "is one a boy born on a Tuesday" also budges the probability away from 1/3, but much less.
I don't understand what Tia's saying at all. Of course your prior on what the probability is that a child is born on Tuesday is relevant in order to make the problem well-defined. But barring very weird circumstances surely we can all agree that the probability of a child being born on Tuesday is 1/7, right?
I don't see why it's relevant that the probability is different *if you choose to forget some of the information that you have*, after all probability is a measure of your knowledge not of the world.
I'll also note that Andrew Gelman makes the same point (maybe more clearly?) in his p.p.s. here. As he says, you need a model for what Foshee might be saying. Maybe interesting to think about while I work on being more clear?
699: Shearer, you can assert that mathematics is more objective than musicianship, but that won't make it any more true.
For example, there's good research in the field of economics (larger sample size, but sharing the relevant property with math) which shows that *having a last name earlier in the alphabet* correlates with "objective" measures of success (like Nobel prizes and whatnot). Given that there's solid proof that there's discrimination against *people whose names are late in the alphabet* it stands to reason that gender discrimination is also able to mess up "objective" measures of success in the field.
For another example, the top prize in math (the fields medal) has rules that make it harder for women who have children to win it (a 40-year age cutoff). One can easily argue that Uhlenbeck (and perhaps Ratner, though she was enough older than 40 that it's more of a stretch) would have won it otherwise.
767: Gelman also says it is a stupid trick because the assumptions are never made clear.
As he says, you need a model for what Foshee might be saying.
But you haven't got any information beyond what he said -- to make a model that would give you a different answer than the answer you get if your information is "X is true" rather than "Foshee said X", wouldn't you need more information? And in the absence of that information, don't the two cases reduce to the same thing?
I don't think Karen Uhlenbeck has any kids.
767: So is the point that you might know from prior interactions that Foshee has a very weird tic where he only says something is true about one of his children *if it is also true about the other one as well.* Then given that you know this, you would get a different answer.
That's true enough, but also hardly relevant as neither you nor I know anything about Foshee and so should come to the same answer.
One way to think about probability that makes some of these "why do seemingly random additional facts change things so much" more plausible, is to think of probability in terms of betting odds. The probability of thing X given information Y is exactly the odds that you as a bank would need to give in order for you not to lose all your money by people betting on the proposition. From this point of view having extra knowledge about Foshee is like insider trading, of course you can make money with insider trading.
My apologies, but this this seems relevant to this sort of story problem.
771: perhaps you're right. Let me find the blog post where I thought I'd gleaned this info from.
BTW, Tia, nice to see you. Hope everything's good.
769: and I more or less agree with him! The answer should be "underspecified."
770: Well, yeah, sort of. In the absence of any information about a test you may have posed the two cases reduce to 1/3, not 13/27. Still working on being clearer.
No: in the absence of such a model, the problem is undefined. If you don't specify a selection process (eg random draws from the population at large) you can arrange any answer you want.
At the dinner I attended last night (MIT fraternity/sorority/ILG alums), the organizer had to stall for a moment and told the following joke:
"A classical statistician, a Baysean statistician, and an SPSS programmer walk into a bar.
What are the odds of that?"
767: So is the point that you might know from prior interactions that Foshee has a very weird tic where he only says something is true about one of his children *if it is also true about the other one as well.* Then given that you know this, you would get a different answer.
No, that's not the point. Sorry, I know I'm not being very helpful at saying what the point is at this point, I'm just trying to jump in and correct things I know to be misunderstandings.
If I was born on a Tuesday, what are the odds I'll be pwned on a Friday?
776: What's losing me about your argument is the distinction between 'one is a boy' and 'one is a boy born on Tuesday'. If we know 'one is a boy', I think you agree that the odds that both are boys is 1/3, and that holds whether I asked him the question or he volunteered it -- you don't seem to think of the question as underspecified without more information about 'a test you may have posed' (this loses me again. While obviously all the words are clear, I don't know how to tell the difference in a story problem between information I know as the result of a test I've posed, and other information.)
If the 'one is a boy' problem isn't underspecified, what is it that makes the 'one is a boy born on Tuesday' underspecified?
Seems to me the factions in this thread are those who are treating the problem as a serious(ish) exercise in probability and those who are treating it as a (genuinely) amusing party trick. Never the twain.
This is a case of casual wording obscuring an interestingly counterintuitive problem.
Me, I'm just waiting for Unfoggetarian: "Pause endlessly, then go in" (9) to show up because I've got "logic" that gets me to either place [and on work-delayed preview, here he is], but am leaning toward 13/27 within the bounds of plain reading. However, in Sifu's 754 you can't talk about the "first" and "second" child--as soon as you narrow it to a specific child, you are back at 1/2, the boring way--the original 1/3 problem only "works" because when the speaker says "and one of them is a boy" there are some possible cases where it is not clear even after all is revealed which was the "first" and which the "second" child (and the speaker can make the statement without even needing to choose). In this model, the further partitioning from the extra information retains some of that indeterminacy, so it is still not 1/2, but it changes the probability because the relative proportion of the "indeterminate cases" changes.
[Also on preview, I think LB's 782 gets to the nub.]
771: Ah, ok, I was going off of the comment timestamped 10:57:41 at this blog post. I was unable to find Clark's essay anywhere on the internet so couldn't determine which mathematician he was discussing with any certainty. However, Uhlenbeck seemed by far the most plausible candidate for who he was referring to. But he may have meant someone else, and he also may have been wrong.
"A classical statistician, a Baysean statistician, and an SPSS programmer walk into a bar."
I haven't used SPSS much in the past ten years. Is it still a going deal in some places?
If you don't specify a selection process (eg random draws from the population at large) you can arrange any answer you want.
Okay, this I can hold onto. My starting assumption has been that if I don't know anything more specific, and I want an answer based on my current state of knowledge, then I have to assume 'random draws from the population at large'. That's how I got to say that the probability of any kid being a boy is 1/2, because I don't have a more specific selection process that might tell me I'm pulling from a single-sex school or something.
I suspect what Tia's saying is something which makes sense if you buy into the "classical statistics" paradigm, which has never made any sense to me. The idea there is something like you always have some "null hypothesis" and if you failed to make a "null hypothesis" you never learn anything. I've never understood it.
786: Maybe there's a kid I'm forgetting about. Somehow I got the impression that she didn't have any, though. I can't seem to verify it online, either.
788. In fact if you want the odds of the kid being a boy to be 1/2 you probably also need to know the age of both the kids and the social background of the parents. At birth, I believe its something like 21/20.
782:
The final question is about whether both children are boys, not about days of the week or anything. The reason the "boy born on a Tuesday" condition can raise the probability that both are boys is because it's more probable that at least one boy satisfies that condition in two boy families than it is in one boy families.
(I was working on expressing this in sample space terms, but I'm not ready for that.)
But for that to be true, there has to have been a condition to be satisfied in the first place. This could take the form of asking "is one a boy born on a Tuesday?" It could take the form of a database search where you query: of families with at least one boy, how many have one boy born on a Tuesday, and then from that set, ask for families with two boys. It could take the form of asking a stadium full of single parents of two children to leave if at least one child is not a boy born on a Tuesday, and then counting up how many have two boy families. In all of these cases, you have asked for a condition to be satisfied. You have posed a test.
If Foshee just says to you, one is a boy born on a Tuesday, but you didn't do anything to get that information, it is no longer true that it is more probable that a two boy family will fulfill that condition than a one boy family. There is no condition!
I will try to think about how to talk about this in sample space terms, and when it is analytically appropriate to restrict your population, but maybe Eggplant can do it better.
Cosma posted in this thread several hundred comments too soon, apparently.
If you ask him if one of his sons was born on a tuesday, the more sons he has the more likely he is to say yes. This changes the probability. If he volunteers that one of the sons was born on a specific day, say Tuesday, this doesn't change the probabilities because he could always say some other day if that were true for the son. Would he be more likely to say he had a son born on Any specific day, say Tuesday, if he had two sons? I don't think so. What is the big deal about Tuesday. There are 6 other equally good days of the week. If Tuesday were a lucky day for boys to be born on maybe this would be different.
793: If Foshee just says to you, one is a boy born on a Tuesday, but you didn't do anything to get that information, it is no longer true that it is more probable that a two boy family will fulfill that condition than a one boy family. There is no condition!
But couldn't you say the same thing about his just saying to you, "one is a boy"? What's the difference that makes "one is a boy" a condition, while "one is a boy born on Tuesday" isn't a condition?
The final question is about whether both children are boys, not about days of the week or anything. The reason the "boy born on a Tuesday" condition can raise the probability that both are boys is because it's more probable that at least one boy satisfies that condition in two boy families than it is in one boy families.
Hi tia!
Let me try this. Imagine it as a party game. Let's imagine three different versions of a probability game played at a party at which everybody has two children.
First Version:When asked, "give me information about your children?" people will tell the sex of a child, younger or older based on a hidden random process (say that each person draws a white or black ball (equal probability) and conceals it. If they drew a white ball they give the sex of their younger child, if they drew a black ball they give the sex of their older child.
In that version if somebody says that they have a boy, then the odds of them having two boys are 1/3.
Second Version: Same setup, except the parent gives the sex and day of week up which the selected child was born. In that case, the odds are still 1/3, the added information doesn't change anything.
Third Version: Same setup, except rather than randomizing the child for which information is shared the parent will give information about a child born on tuesday if such a child exists (randomized if both children are born on Tuesday), and a random child otherwise. That's when we get to the 13/27 odds.
I understand Tia to be asking whether we have any reason to assume that we're playing the third game rather than the second.
(and I have to go, so if I've made a mistake and somebody corrects me I won't find out about it for an hour).
789: I'm not sure about this one way or the other, but I don't think it's right. I actually think I may be making a point more relevant to Bayesian statistics. I think I am objecting to having an inverse problem and calling it a forward problem.
797 last to 796: There's nothing special about being a boy -- instead of saying 'one is a boy', he might just as well have said, 'one is a girl'. But he did say 'one is a boy', so you have that information.
That's right, Nick.
And by the way, I'm sure someone will tell me I didn't use forward and inverse problem right there. I was just sort of guessing at what larger issues this might map on to.
There's nothing special about being a boy
Not even more innate mathematical ability?
Every now and again, I like to flit back to the original topic.
Anyway, I'm off to be decancerized. I'll probably be checking in by iPhone later on.
797: No.
What's different about "one is a boy" is that the final question is whether both are boys. "One is a boy" raises the probability that both are boys from 1/4 to 1/3.
"One is a boy born on a Tuesday" only raises the probability beyond the way that "one is a boy" does if it is more likely that a two boy family than a one boy family will satisfy that condition. So there has to be a condition in the first place. This is not true of "one is a boy". "One is a boy" all on its own increases the probability that both are boys from 1/4 to 1/3.
Good luck, LB! May the scalpel (or whatever) be sure and swift.
I pretty much agree with shearer in 699. There does seem to be cetain types of imbalances that are easier to fix than others. Open up MLB to blacks and blacks can played MLB in decent numbers pretty quicky. Chess is different in that it it the imbalance really reflects current actual talent levels. There could easily be sexism in recruitment and training though.
The blind audition paper explicitly stated that journals should do blind judging as well. This could make a difference. In the blind audition situation both sexes were more likely to go to the next round. Maybe paper referrees will read the papers closer if they don't know who sent them.
There does seem to be cetain types of imbalances that are easier to fix than others. Open up MLB to blacks and blacks can played MLB in decent numbers pretty quicky.
Surely this has nothing to do with ideas about race and physical prowess.
I keep considering wading into the probability discussion and then changing my mind.
But here's a question that I think might distinguish different ways people are thinking about the issue: suppose you run into a man and a young boy. He tells you "this is my son, and I have one other child". What's the probability that he has two boys?
808: Still not following. I see what you're saying (that 'one is a boy' always changes the odds, but 'born on Tuesday' only changes the odds if it's a prior condition) but not why it's true. Eh. The fact that I can't follow a probabilty argument doesn't say much about the quality of the argument--more about how confused I get.
811: There could easily be sexism in recruitment and training though.
That's what is actually going on, which is why a focus on genetics is potentially troublesome. The end state in a bias-free world might well be skewed according to genetics (I'd be astonished if it was not), but in the presence of known bias speculation about genetics tends to serve as either a distraction from bias or a justification for it.
I've been thinking myself in circles on this one. If you just meet someone who tells you "I have two children; at least one is a boy" then the answer is obviously 1/3. But once you see the boy -- this one is a boy -- then it would seem the probability of the other being a boy is 1/2. On the other hand, given the initial question that has the answer 1/3, you know there is a boy, so in some sense you haven't gained new information by seeing a particular boy.
I'm confused.
This is also why the only way I can handle conversations about Boltzmann brains or the mediocrity principle or whatever is by turning them into jokes.
Say you meet a pregant woman who introduces you to her son. What are the odds her baby is a boy?
As far as I can tell the "in some sense you haven't gained new information" is Tia's argument for 1/3 rather than 13/27. Everyone is born on a day of the week, so just being told which one doesn't seem to buy you anything. And yet it does -- I think Tia's argument is just wrong. But it does feel as if it should be right.
It's almost as if although the answer to the "I have two children; at least one is a boy" is 1/3, it's a 1/3 that really wants to be 1/2. All it takes is a tiny nudge in any direction and the answer to the question changes to 1/2 or something close to 1/2.
No, but if you put your ear to it you hear a muffled trombone.
That one's 1/2 because the kid you see is the older boy. Essear has now confused me about what if you can see the kid.
It's like you don't memorize the threads, Moby.
Here's a variation problem that helps me, at least:
Suppose he said "I've got five boys born on Tuesdays, and six children total. What is the probability that I've got six boys?"
Now it seems more clear (to me, at least) that the Tuesday information is meaningful, because if the extra child is a boy, there are a lot more ways to distribute the Tuesday birthdays, but if the extra child is a girl, the Tuesday birthdays are forced.
But 'older' isn't the only way to distinguish people. The point is that as an abstract question about number of children, it's about probability given identical, independently distributed objects. But people are distinguishable -- as soon as you start getting any information about them, you shouldn't any longer be able to treat them as identical.
824: The "seeing the boy" situation really does need a bit more specification.
Using the stadium starting with 2-child families.
Case 1: Every family that *could* show a boy stays. Answer: 1/3
Case 2: Families stayed if some random selection process (such as birth order) yielded a boy. Answer: 1/2
808 gets it right. Assume that right after Foshee steps down from the microphone, a second person with at least one boy gets up and says "I have two children. One is a boy born on a Monday. What is the probability I have two boys?" Then a third gets up and says "I have two children. One is a boy born on a Friday. What is the probability I have two boys?" This continues until everyone in the room with at least one boy, 30 people in all, has stepped up. Then we see how many of them actually have two boys. Are you expecting the answer to be 10, or 15? And if the former, how can the probability for Foshee or any other individual one have been roughly 1/2? Is there anything in his question to indicate you're not just seeing one instance of this potential parade of parents?
You need something that does that to change the probability. The only way it would be different is if a call went out in advance for someone with a boy born specifically on a Tuesday (or a weekday, or a day starting with "T"), in which case a two-boy family would be more likely to have one and therefore to be picked to get up in front of the room.
I've been thinking myself in circles on this one. If you just meet someone who tells you "I have two children; at least one is a boy" then the answer is obviously 1/3. But once you see the boy -- this one is a boy -- then it would seem the probability of the other being a boy is 1/2. On the other hand, given the initial question that has the answer 1/3, you know there is a boy, so in some sense you haven't gained new information by seeing a particular boy.
Arrgggh, I have some half formed thoughts about this, but today is a busy day at work and I don't really have time to work through them.
So let me try this quickly, but first I would encourage people to read 798 again.
The question about any probability problem is, "what constraints does this information place on the probability space?" This is related to Tia's "what question did you ask to get this information" / "is this question being used as a filter."
In LB's stadium example, "everybody who isn't part of a family with two children, at least one of which is a boy born on Tuesday" uses both bits (boy and Thursday) as filters.
The second party game in 798 is a way to get that information without using it as a filter.
One other way to look at the value of the information is, "am I getting more information about an entity which was selected by some other process?" (in the 798 example, the drawing of balls is the process that selects which child you get information about, further information about the child doesn't narrow the possible options) vs "am I getting information about a complete system?" (LB's stadium example is asking for information about the family, not about the child).
That last distinction is difficult for me to explain, but I'll try to think of an illustrative example.
Assume that right after Foshee steps down from the microphone, a second person with at least one boy gets up and says "I have two children. One is a boy born on a Monday. What is the probability I have two boys?" Then a third gets up and says "I have two children. One is a boy born on a Friday. What is the probability I have two boys?" This continues until everyone in the room with at least one boy, 30 people in all, has stepped up. Then we see how many of them actually have two boys.
This is a different problem.
I hate trying to articulate this stuff, but you've kind of pulled the birthday problem here - "What's the probability that any two people in this room share a birthday?" When you don't specify a day, your probability goes way up.
824: But both situations involve distinguishable children. We know that of the families with two children and at least one boy 2/3 will have a girl. If you were to meet a bunch of such parents toting only one child chosen at random 2/3 of the time you would meet a boy and correctly conclude the other has a 1/2 chance of being a boy. 1/3 of the time you would meet a girl and know the other was a boy.
831: But each of those people specified a day. The important question, Tia's question, is whether that day was specified in order to select the person. If it was, then yes, we're in the ~1/2 situation. If it wasn't, we're in the standard 1/3 situation. And the person's naming a day doesn't indicate which situation we're in.
There's nothing special about being a boy -- instead of saying 'one is a boy', he might just as well have said, 'one is a girl'. But he did say 'one is a boy', so you have that information.
If the question was "how many of your kids were born on tuesday? " volunteering that you have a boy"born on tuesday" would make a difference in the probabilities. But that isn't the question.
Consider this:
"I have two children. One of them is a boy with the social security number "983-96-1497" What is the probability I have two boys? "
Is the answer really 1/2 just because he told me the random-ass social security number of his boy? Pretty much every boy has a random-ass social security number.
I differ from tia in that I think the answer to the question:
"I have two children. One of them is a boy with the social security number "867-53-0900" What is the probability I have two boys? "
really is close to 1/2. He has a boy whose first 7 digits of his social security number are the same as a popular Tommy Tutone hit and another kid who has a 50% chance of being a boy.
13/27 is the answer to this question: of two-children families that have at least one boy born on a Tuesday, what proportion have two boys? This is a fine question to ask. It assumes that the population of interest is families with boys born on Tuesday.
Now we're looking forward. We're trying to predict something about a specific family, the Foshee family. We have a piece of information about the Foshee family--two children, one is a boy born on a Tuesday. Our question as posed in the original problem is "what is the probability both Foshee children are boys?"
So now we need a strategy to answer this question. The information about number of children and sex has immediate bearing on the last question regardless of how we got it. Together, they determine the number of ways to have two boys, and the number of ways to have not two boys in the Foshee family. This is the central question that determines the initial sample space we're working from. The denominator in this fraction: Number of ways to have two boys/(Number of ways to have two boys + number of ways to have not two boys) is the sample space.
The information about Tuesday is different. It does not determine the number of ways to have two boys and not two boys in the Foshee family. We need to know: is restricting the sample space to boys born on a Tuesday a legitimate means to answer this question, to make a forward looking prediction about whether the unknown Foshee child is a boy? This is the part that depends on how we got the information. If we asked the question "is one a boy born on a Tuesday?" and got the answer yes, we can legitimately restrict the sample space to make a forward looking prediction about whether both children are boys, excluding every family that does not include one boy born on a Tuesday. We can do this because our question imposed a condition on the data that further reduced the sample space. (Alternatively: we imposed a condition that two boy families were more likely to fulfill). Now our denominator is smaller, and our P(two boys) is bigger. The other kid is still more likely a girl, but only with a very slight edge, 14/27.
But say we didn't ask that question, and we just asked what day the boy was born. This is equivalent to having a database of two-child, at-least-one boy families in which you have day of the week information for one boy child for all the families. You just asked about the day of the week, you didn't ask about Tuesday. You look at the entry for Foshee, and you see that Foshee's known male child was born on a Tuesday. You know the same thing, but tt is not a legitimate analysis strategy in this case to restrict the sample space. We didn't impose any condition on the data that justifies throwing out families that satisfy "two children, one is a boy". Now we predict with 2/3 confidence that the sex of the unknown child is female.
If you look at the information that the known Foshee boy is born on a Tuesday without having some idea beforehand that you were interested in boys born on Tuesday, or boys born on some day of the week in particular, and tried to work backward from seeing that the boy was born on Tuesday that and claim it was an unlikely event, you will do a bad job of predicting the sex of the other Foshee child. Someone who took 14:13 odds on "other child is a boy" when they'd asked *a priori "is one a boy born on a Tuesday?", and gotten a yes, would have $0 expected value for their bet (I think -- I don't really know how gambling odds work, but presumably you see my point). Someone who only asked "what day of the week is the boy born" and gotten the answer "Tuesday" would have negative expected value if they took those odds on "other child is a boy." This is equivalent to taking, in the long run, 14:13 odds on the other child being a boy no matter what the Foshee entry in the database said. And there are still twice as many ways to have only one boy as there are to have two boys. We shouldn't take anything less than 2:1 odds. We didn't get any other information that should change our appraisal of that likelihood.
So, the answer to "of two-children families that have at least one boy born on a Tuesday, what proportion have two boys? " is 13/27. This is not necessarily the way you should try to make a forward looking prediction. That depends on how you generated the data.
People will differ in the interpretation they naturally leap to in the way the question was posed. But on full consideration, I don't think that it's implied in the statement "I have two children. One of them is a boy born on a Tuesday" that you asked "is one born on a Tuesday?" to get that information. I, like Andrew Gelman, ultimately found the formulation of the problem unsatisfying, because it masked very important assumptions.
(For anyone going with their gut -- I do think it's worth noting that AG is also claiming you have to model the question Foshee was asked. I know this is an appeal to authority; I'm just saying that if you're going to use shortcuts you might as well take that into consideration.)
The important question, Tia's question, is whether that day was specified in order to select the person.
This isn't an important question, as far as I can tell. This is a conditional probability question, and having a condition affects the size of the pool you have to count up.
837 posted without seeing 836, for what that's worth.
I should say that you now have me back to absolute agnosticism -- I was sure you were wrong and now I'm not sure of anything. But the reliance on 'the question Foshee was asked' loses me: as the problem was stated, no one asked him anything. He just stood up and volunteered info.
Let's see if I can make my 832 clearer.
We know of the two child families with at least one boy 1/3 will have two boys. So when we select a family from that pool and meet one randomly chosen child who happens to be a boy, one might think that we have to conclude there is only a 1/3 chance the other is as well, but this would be an error. We now are describing an experiment with three outcomes: boy-girl family presenting boy, boy-girl family presenting girl, and boy-boy family presenting boy. The probabilities of these three cases are 1/3 (2/3*1/2), 1/3 (2/3*1/2), and 1/3 (1/3*1). Given we met a boy we must be in the first or third case, and so the probability ghat the other child is a boy is 1/2 ((1/3)/(1/3+1/3)) as it should be.
836 is 900 words and 4000 characters long. At that point, you may as well just collect some actual data and try to get an abstract submitted.
837: It's only a conditional probability question if that was a condition. If Foshee was chosen on the basis that he had at least one child and for no other reason, and then told to mention the day of the week his child was born, it's not a condition.
840 is good.
Tia and Mr. Blandings are wrong. Information is information, whether you asked for it or not.
Information is information, whether you asked for it or not.
I send away to Pueblo, CO when I want information.
It's worth noting that this really is like many other issues in statistics, where you have to know the data generating mechanism. For instance, the probability of at least one p = .05 increases with the number of tests you did; i.e. the probability of any given result depends on your data generating mechanism. Similarly, the probability of hearing "one is a boy born on a Tuesday" changes depending on the question you ask, and is undefined if the question you asked was "what day was the child born?" If this probability is undefined, it has no bearing on "other one is a boy."
Also similarly, in order to make predictions, you have to generate a model and then test it out of sample. A good model fit to a set of data is obviously guaranteed if you used that data to generate the model. Seeing you have a boy born on a Tuesday, and retroactively deciding that this is informative is like claiming you have good model fit using only in sample testing--it's claiming you have a low probability event when you only do if you *predefined the event you were testing for*, that is, if you tested your model out of sample.
These are just other examples of how the question you ask determines the probability of an event; it's not like it's some weird spooky thing no one's ever heard of.
Tia and Mr. Blandings are wrong. Information is information, whether you asked for it or not.
Eh, look at my 798, are you trying to tell me that there's a difference between scenario 1 and scenario 2?
844: But in the circumstances suggested in 843, the information is that the child was born on a day of the week. The probability that a child was born on a day of the week is 1.
839 last to 843: while I'm still lost and floundering, 'why he was chosen' doesn't seem to be a meaningful question about him in the problem as stated -- he volunteered.
"Wir werden auf natürlichem Wege durchschnittlich dümmer", zitiert die Nachrichtenagentur dpa Sarrazin am Donnerstag. Der 65-Jährige brachte dies dem Bericht zufolge mit Hilfe umfangreicher Zahlen in Zusammenhang mit Zuwanderern "aus der Türkei, dem Nahen und Mittleren Osten und Afrika". Sie wiesen weniger Bildung auf als Einwanderer aus anderen Ländern.Einwanderer bekämen zudem mehr Kinder als Deutsche, sagte Sarrazin. Es gebe "eine unterschiedliche Vermehrung von Bevölkerungsgruppen mit unterschiedlicher Intelligenz"
Summary: Germany is becoming 'stupider' because of immigrants from Africa and the Middle East which are 'population groups with a lower intelligence' and they're having more kids than us smarter native Germans. He is a member of the Bundesbank board and a former SPD finance minister for Berlin.
844: But in the circumstances suggested in 843, the information is that the child was born on a day of the week.
No, the information is that the child was born on Tuesday. This is a subtle but important difference.
847: Yes, I am.
Everyone agrees with 840, right? I don't see how one can think seeing the child (randomly) changes the answer from 1/3 to 1/2 (which is obviously correct) and not think that knowing the child is born on a Tuesday changes the answer from 1/3 to 13/27.
846 me, and Information is information, whether you asked for it or not. is very strange to me for reasons stated in 846. It matters all the time how you got information in assessing the probability of an event.
One could work through the Tuesday problem in a similar manner to my 840 in the case where the family chosen should tell the birth day of their son (or a son chosen at random if they have two). Counting the possible outcomes b-g family saying Monday, ...) you would find that you can just get rid of the day information.
839: I know! Which makes two answers, "1/3" or "underspecified", better answers to the problem than 13/27. You could include 13/27 in a more complete specification of multiple ways to construe the problem and the answers under different conditions.
847: Yes, I am.
Okay, I really think that you're crazy on that one.
I think that once you've randomly decided which child you are getting information about, getting more information about that same child doesn't help you determine anything about the other child.
(just to be clear, I think scenarios 2 and 3 create different probability distributions, but scenarios 1 and 2 give you exactly the same amount of information and the number of boys in the family).
Imagine there's a ( in front of b-g in 834.
848 seems right to me. If the answer to the original question was 13/27, it would be 13/27 if Fosbee had specified Wednesday, or Saturday, or any day of the week. And so it would be true even if he hadn't specified any day at all. Specifying Tuesday adds no information.
Further to 848:
Go back to 829. Assume each of us who is discussing this here walks into the room at a different time, in each case just long enough to hear one speaker, and without knowing there are other speakers. Each of us will hear the question exactly as posed in the original problem. Apparently, each of us will also have been given "information" that is supposed to lead us to the conclusion that the probability that the speaker we heard has another boy is 13/27. Yet only approximately 1/3 of all the speakers will in fact have an additional boy. Why should this information be impacting our conclusions about probability?
I was going to write something like "My cat's breath smells like cat food," or "HULK SMASH COMPUTER" but 826 and 840 actually make sense to me and seem understandable. Thanks, smart and clear people!
Or, I should say, I'm hoping that 826 and 840 are correct, because they are clear statements that are easily graspible by morons like me.
OT: I now officially have less cancer. (assuming that no cancer at all isn't a valid option.)
859: I have enough trouble imagining the square root of -1.
Actually, now that I've tried to follow the logic of 840 I seem to have concluded the answer is 1/2. But it's time for lunch. I'm sure you'll all reach a consensus in the meantime.
840 is just another version of "my older child is a boy".
866: Yes, the logic of 840 does yield 1/2. The key assumption though is: So when we select a family from that pool and meet one randomly chosen child who happens to be a boy 9and it is an assumption). That is Case 2 in my 828. The alternative is that any family with one boy shows them to you (not assuming that you are seeing a randomly chosen child)--in that case 1/3.
OK, lunch can wait a few minutes:
These are just other examples of how the question you ask determines the probability of an event; it's not like it's some weird spooky thing no one's ever heard of.
I'm familiar with a lot of cases like that, but I thought here we were starting from a well-defined question: a parent volunteers the gender and birth date of one of his two children (chosen randomly), the answer is that it is a boy born on a Tuesday, and we are asked to determine the probability that both children are boys. No? This is well-defined. Maybe you had a different definition in mind.
... And so I Monte Carloed it just to be sure. 50%.
The alternative is that any family with one boy shows them to you (not assuming that you are seeing a randomly chosen child)--in that case 1/3.
But that's a wacky assumption; I don't see where it would have come up in the context of the question as posed.
... And so I Monte Carloed it just to be sure. 50%.
In my opinion, the whole question can now be considered a wet-ware virus.
871: Why is it wacky? There is someone showing you a boy--one of their two children. Who was asked to leave LB's stadium? You have no idea. Maybe it was , "If you have a boy, stay". Doe snot seem wacky to me. I actually am for the 13/27 on the Tuesday, but for your scenario (which for me cleverly shows the dilemma ) I think plain reading can yield either interpretation.
And so I Monte Carloed it just to be sure. 50%.
Yes, of course. Monte Carlo the other interpretation, 33%.
But you would get the same result if you ran it again with Sunday, Monday, etc. And therefore the answer in the aggregate for all days (i.e., without the day) would be 50%, and it's not. Run a single scenario where the parent volunteers the day and it's whatever day it turns out to be in each case (i.e., one of seven options each with an equal probability), and the answer will be 33%.
I'm familiar with a lot of cases like that, but I thought here we were starting from a well-defined question: a parent volunteers the gender and birth date of one of his two children (chosen randomly), the answer is that it is a boy born on a Tuesday, and we are asked to determine the probability that both children are boys. No? This is well-defined. Maybe you had a different definition in mind.
... And so I Monte Carloed it just to be sure. 50%.
If the parenthetical is in response to 798, then I'm really confused about what it was that you used in the Monte Carlo situation.
Or, to put it another way, I believe that if you simulate that scenario and look at only outcomes in which the parent tells you, "I have a boy born on Tuesday" that you will end up with results close to 1/2, but that doesn't tell my why you're interested in results that include Tuesday.
13/27 is the answer to this question: of two-children families that have at least one boy born on a Tuesday, what proportion have two boys? This is a fine question to ask.
Comity!
870: essear, what did you actually do in your simulation?
It shouldn't be 50% in any case. Did you make a specific child a boy born on a Tuesday, as opposed to either child? That's what would make it 50%
Anyway, I think it would be really easy for a simulation to obscure what I'm trying to say if you didn't model in asking the question. If, for instance, in your simulation you included gender and days of the week, and then selected the two child, at least one boy born on a Tuesday families, and counted up how many had two boys you would get 13/27.
However, if you generate a random day of birth, and then (knowing the specific day of birth for every point in your simulation, not just the Tuesdays!) then counted up the number of two child families with two boys and divided it by the number of two child families with at least one boy you'd get 1/3. This is NickS's party game 2. You asked the simulation the question: what day was the child born? You did not ask it a question that allows you to throw out trials that did not include boys born on a Tuesday. Asking a specific question buys you the right to throw out non-comforming trials, changing the population/sample space/denominator/please insert word that y'all find clear.
1) Tia! Has enough time has passed since you were last here that a fruit basket is in order?
2) Less cancer on LB: Hooray!
3) I'm on gswift's and apo's team in terms of not feeling any aversion to fictional portrayals of awkardness and embarassment. In fact I often quite like them. And I don't think it has any relation to one's capacity for empathy for real people (just as I don't think people who enjoy horror movies would enjoy having the bejeezus scared out of them by an axe-wielding maniac in real life).
In fact, as proof of my empathy, I'm feeling very sad right now that so many of you otherwise fine-seeming people are incapable of appreciating a major variety of comedic pleasure. Poor things.
877 is, of course, correct.
878 asks the questions that I was trying to ask in 876 more succinctly.
879: people are incapable of appreciating a major variety of comedic pleasure. Poor things.
I'm still drawn to it, but like a moth to a light, sometimes I get singed. It is also a subtle thing, the US version of The Office does not really bother me since I find most of the characters so broadly drawn--Larry David somehow hits closer to home.
No one is exactly embarrassing themselves, but:
One of my favorite scenes in real life is to watch a terribly nice person trying to smooth over someone's antisocial behavior in order to make them feel loved and welcomed. Especially if they don't know each other very well. It is such a funny arms race.
882: Oh come on, heebie. Sir Kraab isn't terribly nice, and my behavior isn't that antisocial.
883: But it's true that you don't know each other very well?
So let me try this quickly, but first I would encourage people to read 798 again.
I second NickS's self-recommendation. I've been trying to follow this, and that was the first comment that made me feel I had a glimmer of understanding.
Tia's 836 and 878 are excellent. Go team Tia.
Wait!
I was thinking about some other examples, and I finally figured out what was wrong with 798.
I am correct that scenarios 1 & 2 are the same, but essar is correct that, in both of those scenarios if the person tells you that they have a boy the odds that the person has 2 boys are 50% not 33% as I had said.
The reason for that is the logic worked out in 840. There are three scenarios in which the parent might say that they have a boy, but those scenarios are not equally weighted.
In they have Younger (boy) and older (girl) there is a 50% chance that they will answer the question by saying that they have a boy.
In they have Younger (girl) and older (boy) there is a 50% chance that they will answer the question by saying that they have a boy.
But, if they have 2 boys, there is a 100% chance that they will say that they have a boy.
So, while the 2 boys scenario is half as likely, it is weighted twice as heavily in terms of the outcome that we're looking for (the parent saying that they have a boy).
I was trying to think of examples in which you would know that somebody has at least one boy, out of two children, that would end up with the 1/3 odds.
The only example that I could come up with was that you see that they have a bumper sticker on their car for [all boys school]. In almost any scenario that involves you getting information about a specific one of their children the weighting issue above will mean that once you find out about 1 boy the odds that the sibling is a boy are 50%.
Which, I guess, means that Tweety was correct, upthread, that these issues are not intuitive.
Oh, and thanks very much for 886.
I do think it's a relatively clear example of the distinction that tia was making, even if the actual odds are not what I said they were (and it doesn't map directly to the problem at hand).
888: I'm glad you saw the light.
No, no, I still think you're crazy to believe that scenario 2 gives you any more information than scenario 1.
I just concede that you were right about the probabilities for both scenario 1 and 2 (but not that they're different from each other).
(I am, by the way, only being this belligerent in this argument because I'm pretty confident that I'm not going to offend you. No insult is intended.)
NickS, you were right the first time.
total possible states of reality (8). They are all of equal probability:
younger girl older girl white ball
younger girl older girl black ball
younger boy older boy white ball
younger boy older boy black ball
younger boy older girl white ball
younger boy older girl black ball
younger girl older boy white ball
younger girl older boy black ball
total number of states that satisfy the condition one child is a boy (6). They are all of equal probability:
younger boy older boy white ball
younger boy older boy black ball
younger boy older girl white ball
younger boy older girl black ball
younger girl older boy white ball
younger girl older boy black ball
Of those states, total number that satisfy the condition both are boys (2). They are all of equal probability:
younger boy older boy white ball
younger boy older boy black ball
Probability, given that one is a boy, of them both being boys: 1/3
All of this is orthogonal to my main point, which is this:
I am correct that scenarios 1 & 2 are the same
total number of states that satisfy the condition one child is a boy (6). They are all of equal probability:
Right, but the real question is how many states satisfy the condition that the parent will give information about a child who is a boy and that is only 4.
younger boy older boy white ball
younger boy older boy black ball
younger boy older girl white ball
younger girl older boy black ball
In these two cases
younger boy older girl black ball
younger girl older boy white ball
The parent will say, "I have a girl" or "I have a girl who was born on (day of week)" depending on whether you're talking about scenario 1 or 2.
But I agree, that doesn't alter the fact that the key distinction is that scenarios 1 & 2 are the same.
894: but the point of a conditional probability problem is that you presumed you got that information. Maybe you were setting up something different that I don't quite understand yet, and you and essear are having a conversation about something else. Are you trying to illustrate something different than "I have two children. At least one of them is a boy. What is the probability that the other one is?" The answer to that is definitely 1/3, but possibly you are trying to demonstrate something different I don't quite understand yet.
No, no, I still think you're crazy to believe that scenario 2 gives you any more information than scenario 1.
Agreed! Well, not that I'm crazy, but that this was wrong. I was conflating your scenario 1 with the other scenario where you're simply told someone has two children and one of them is a boy.
(I am, by the way, only being this belligerent in this argument because I'm pretty confident that I'm not going to offend you. No insult is intended.)
Understood, and heebie's 882 makes me worry I've been too belligerent to people also. Calling people wrong and being overly blunt is how we argue in (the male-dominated culture of [sad face were emoticons not depricated]) theoretical physics. I don't actually think any of you are stupid or crazy.
Are you trying to illustrate something different than "I have two children. At least one of them is a boy. What is the probability that the other one is?"
I was trying to illustrate that problem but failed.
If you played the party game described in 798 and, after being told "I have a boy" said, "I'll give people 2 to 1 odds that this person has a boy and a girl" you would lose money quickly.
The scenario in which somebody, following the rules in 798, tells you "I have a boy" does not map to the conditional probability problem "I have two children. At least one of them is a boy. What is the probability that the other one is?"
...oh wait, don't go to any explaining effort--I think I may be seeing it.
This doesn't have to do with my earlier point, but I do see why this game is different than the standard setup.
In summary, here are some answers on which I think we all can agree: 1/3, 13/27, 1/2.
I think we're approaching comity, so let me write down some statements that I believe are true:
1. If you know someone has two children and that at least one of those is a boy, the probability that both are boys is 1/3, because the two children must be treated as indistinguishable.
2. If you know someone has two children and a specific, randomly chosen one is a boy, the probability is now 1/2, because you have distinguished the children.
Now here's where this gets potentially more controversial?
3. If you know someone has two children and that at least one of them is a boy born on a Tuesday, the probability that both are boys is 13/27. (As Tia said in 836, "13/27 is the answer to this question: of two-children families that have at least one boy born on a Tuesday, what proportion have two boys?" We may disagree on whether the statement I made is isomorphic to that statement.)
What I don't understand is what the argument is supposed to be that there is an interpretation of the scenario where you're given the Tuesday information and the answer is still 1/3. I think JP was the first to point out a different reasoning that the answer can be 1/3 -- if you run into someone with a child and it's a boy, but this choice is not random (say it's a sexist world where only boys are allowed out in public) then my #2 above reverts back to being #1 and the probability is 1/3. But this doesn't seem to address the Tuesday issue.
Sorry if I'm missing something obvious, but I've read all the arguments and still don't understand how to phrase a sharp question that, in the presence of the Tuesday information, has the answer 1/3 rather than 13/27 or 1/2.
Well, not that I'm crazy, but that this was wrong.
So, wait, is this comity for me, too? Because this is what I've been trying to argue: asking "what day of the week was the boy child born" does not get more information relevant to the sex of the other child than just "one is a boy." In order for the Tuesday information to be informative in the way the 13/27 answer assumes, you have to have gotten it in Nick's third game.
I do see why this game is different than the standard setup.
But, as I said in 888, most real world scenarios will more closely resemble the game than the "standard setup."
If you want to try to come up with a real world scenario that maps to the "standard setup" you have to be very careful or you will make the same mistake that I did.
901.3: This is just restating what Tia and others have said, but it seems to me there's a real difference between these two cases:
(1) Parent says: "I have two kids"; I ask: "Do you have a boy born on a Tuesday?"; Parent replies: "Yes"
and
(2) Parent volunteers: "I have two kids, at least one of whom is a boy, and he was born on [Day of the Week X]"
The odds of (1) are considerably higher if the parent has two boys than if the parent only has one boy. The odds of (2) are not any higher if the parent has two boys, because all boys are born on some day of the week, and there's no constraint, in case (2), on what day the parent reveals--the parent chooses a particular Day X to make the statement true. So having a specific value for X does not add any information relevant to the odds of whether the other kid is a boy or girl. Or, to put it still differently, having a second boy wouldn't make it any more likely that one boy was born on Day X, when the parent gets to pick X.
The problem as originally posed reads unambiguously to me as if it's case (2).
This:
If you know someone has two children and that at least one of them is a boy born on a Tuesday, the probability that both are boys is 13/27.
is not the same as this!:
"13/27 is the answer to this question: of two-children families that have at least one boy born on a Tuesday, what proportion have two boys?"
Probability = number of successes/(number of successes + failures) and calling those two formulations equivalent begs the question that any family with a non-Tuesday born son can be thrown out of the denominator--that it doesn't have to be considered a failure at all.
How "on a Tuesday" changes the denominator, and thus the probability, varies with how you got that information.
I've read all the arguments and still don't understand how to phrase a sharp question that, in the presence of the Tuesday information, has the answer 1/3 rather than 13/27 or 1/2.
"On what day of the week was at least one boy born?" is the question. This generates a probability of 1/3.
If you filter out of the sample space families with boys not born on a Tuesday, you've in essence posed the question "Is one a boy born on a Tuesday" and only kept families in the sample space if the answer is yes. This could be a legitimate thing to do under some circumstances. But if you're doing that because you've already seen that the boy is born on a Tuesday, so you decide retrospectively to throw all the families with non-Tuesday born children out, you're going to make an error in predicting the novel data.
If all you asked to get your data in your spreadsheet (after you heard at least one child was a boy) is "Tell me, what day of the week was at least one boy born?" you aren't getting information that will budge your prediction for novel data away from 1/3 chance of two boys.
In sum:
If you're only trying to state the proportion of two-child-at least-one-Tuesday-born-boy-having families with two boys, 13/27 and Bob's your uncle. You could even argue this is the situation the original problem sets up, and I'd disagree, but I'm not really that interested in that if we could get to comity on the underlying issue.
If you're trying to make a forward looking prediction and define an *expected* probability of a second boy you need to know the data-generating mechanism. To me, this is the situation the problem sets up, but again, I don't really care about that.
I don't understand what you mean about making predictions regarding novel data. I'm saying that if you have a random sample of many people with two children, then given the further information about an element of that sample that they have at least one child who is a boy and was born on a Tuesday, the probability that they have two boys is 13/27.
In other words, we're asking a conditional probability question: given some information, what is the probability of some other statement being true? And the information we're given, by assumption, is that at least one of the two children is a boy born on a Tuesday.
Your "novel data" argument seems to be that given that one family has a boy born on a Tuesday we can't infer anything about other families whose children may not have been born on Tuesday, which seems like a non sequitur. But I must be misunderstanding.
If you're trying to make a forward looking prediction and define an *expected* probability of a second boy you need to know the data-generating mechanism.
I'm just working with the default assumption that the data-generating mechanism samples all birthdays and sexes with uniform probability. Suppose your data comes from interviewing many people, all with two children, and recording the sex and birthday of all of the children. Then the question we're posing isn't "we interviewed Bob, who has one child who is a boy born on a Tuesday; next we'll interview Fred;if Fred has at least boy, what is the probability that he has two?" It's "we interviewed Bob, who has one child born on a Tuesday; what is the probability that Bob has two boys?" In which case you must only compare Bob to that part of your sample that meets the specified criteria.
908:Your "novel data" argument seems to be that given that one family has a boy born on a Tuesday we can't infer anything about other families whose children may not have been born on Tuesday, which seems like a non sequitur. But I must be misunderstanding.
The "novel data" I'm talking about predicting is not about any other families. It's about the Foshee family, predicting the sex of the other child. If you ask Gary Foshee:
"Do you have at least one boy?"
and he says yes
and then you ask
"Please tell me the day of the week at least one boy child you have was born?"
and he says Tuesday
you can't move from 1/3. I know you say you've read all the arguments, but can I ask what you think about my database of two child at least one boy families where in one column, for every family, you see the day of birth of the one male child? So you're scrolling down it, and you come to the Foshee line, and it says Tuesday. It's important that you don't query the database to only select families with Tuesday born boys -- you just see that the boy Foshee was talking about was born on a Tuesday, but it could have been any day.
Is it that you disagree that this is equivalent to asking the question "Please tell me the day of the week at least one boy child you have was born?"
Or do you think that seeing that the Foshee line says Tuesday is going to change your prediction for the gender of the other child, so that now that you've seen the answer it is in fact more likely that the second child is a boy?
I'm pretty sure you have to think at least one of those things to get to your way of seeing the problem.
910: Ah! Got it. I'm a moron, sorry. Yes, I see this point of view now.
I tend to think that the originally posed question -- in which someone simply volunteers, out of the blue, that they have a child who is a boy and was born on a Tuesday -- is most reasonably interpreted to have probability 1/2. But I see that 1/3 makes sense in the context of the database you envision.
Also, I think the setup envisioned in 910 is basically the same as the one Stormcrow proposed in 869 -- by asking specifically for the birthday of a male child, the database has a built-in male/female asymmetry.
I tend to think that the originally posed question -- in which someone simply volunteers, out of the blue, that they have a child who is a boy and was born on a Tuesday -- is most reasonably interpreted to have probability 1/2. But I see that 1/3 makes sense in the context of the database you envision.
Worth noting: I agree with you there, and note that neither of those two probabilities are 13/27 which means that you're still not duplicating the original problem.
The 13/27 number essentially only works if you imagine that somebody tells you, "I have two children, including one boy born on a tuesday, now solve this as a probability problem, calculating the odds that both of my children are male." It's hard to come up with a real world scenario in which you would acquire the information in precisely that fashion.
(But I still basically agree with everything you've said)
WWWWAAAAAHOOOOO
not a moron at all, essear, and I'm very excited to have successfully communicated. Thank you for being so patient with my clumsy attempts to put this into words.
I actually don't disagree with you about the 1/2 in the natural language sense. In a natural language sense, "I have a boy" would logically be interpreted as referring to a specific child. To really state the 1/3 situation clearly, you need to say "I have two children. At least one is a boy," which I've been trying to do in my statements of this problem.
Meanwhile, IMO, the explicit statement of the problem that gets you to 13/27 is very, very far removed from a natural language interpretation of "I have two children. One is a boy born on a Tuesday," since you really need to have set up a query not even mentioned in the question. For that to be the "right" answer you have to assume a bunch of conventions of conditional probability problems not even close (IMO) to being implied by the actual words.
913: Well, I would change it to:
"I have two children, including one boy born on a tuesday, now solve this as a conditional probability problem in which you assume that you asked 'was at least one boy born on a Tuesday,' calculating the odds that both of my children are male."
Oh god, did I need this page earlier. I was trying to grasp at this with phrases like "forward and backward probability" but I couldn't find it. But here's exactly what I'm talking about.
In general it does not make much sense to ask after observation of a remarkable series of events "What is the probability of this?"; this is a conditional probability based upon observation.
So I'm going to change that to just one mildly remarkable event, the 1/7 born on a Tuesday event. The probability of Tuesday is conditioned on the observation you made to get the Tuesday information. It does not make sense to ask after observing this low probability event: what is the probability of this event? You need to know what observations you made to get that information.
So certainly any casually phrased probability question is completely undefined. For example, suppose you go from door to door finding all families with two children and then torture the parents until they say "I have a boy born on tuesday." Then the probability that said family has two boys is only 1/4. On the other hand, suppose a genetic virus has taken over the population and now all children are boys, now the probability is 1.
So I totally understand how there are reasonable interpretations that give 1/2 or 13/27. Namely:
1/2: You go door to door, people randomly pick a child of theirs and tell you that child's gender and birthday. Alternately you ask a stadium "pick a kid and tell me if it's a boy born on tuesday" and make everyone else leave. Alternately, you're in conversation and you say "tell me the gender and birthday of one of your kids" and they reply "well one of them was a boy born on tuesday."
13/27: You go door to door, and people tell you if they have a kid who is a boy born on Tuesday. Alternately you ask a stadium of people "leave if you don't have a boy born on Tuesday." Alternately, you're in conversation and you make a slur against boys born on tuesday and the person gently coughs and points out that they have a boy born on tuesday.
What I don't understand is how you get 1/3 in interpretations that are as natural as the above. You need to do things like insult boys, have them point out that they have a son, then say "oh what day of the week was he born on." Certainly that's a possible situation, but it seems much less plausible to me than either the 1/2 or 13/27 situations. Less plausible because it requires an asymmetry in how the two pieces of information appear. Though it's certainly a possible situation, it seems a less natural way to interpret the meaning of the sentence than interpreting both parts symmetrically. But I might just be missing something in sentence interpretation.
The natural situation is the one actually in the problem. Someone spontaneously offers the information for no reason that you can discern.
You have a prior of 1/3 based on the information that at least one is a boy (this is accepting the conditional probability convention that one is a boy means "at least one is a boy"). Now you have to figure out what additional information the "on a Tuesday" grants, and whether to update your prior. The additional information is conditioned on the observation you made that would restrict the domain of responses--and there was none! He could have said anything. It's totally random (except, sort of, that you know you're in a conditional probability problem and know that to make people like Foshee happy you should make all kinds of weird assumptions). He could have said I have at least one boy who likes to pick his nose. He could have said I have at least one boy who has leukemia. Without an observation process that restricts the domain of responses it isn't cause to update your prior.
(And once again, "two children" and "at least one is a boy" are not like "on a Tuesday" here because they define the number of ways to have two boys or not have two boys.)
If you'd asked, "is at least one a boy born on a Tuesday" (given that at least one is a boy) then you'd have made an observation that would make the outcome have a probability of 1/7 conditioned on that observation. (or 6/7 if the answer was no).
This is why I think decent answers to this question could include 1/2 (essear's natural language approach, as I understand it, assuming "one child" means "a specified child"), "underspecified" (please tell me what kind of experiment we are in and why he said that), 1/3 (assume we understand that one child means "at least one child' but don't assume we asked "is one a boy born on a Tuesday") or, least satisfying, to my mind, from a logical interpretation of the situation approach, 13/27, which is the probability given that I just asked Foshee whether he had a boy born on a Tuesday.
If I were trying to predict whether Foshee's other child was a boy (what I meant by "novel data" above), the only way I would use that 13/27 probability is if I knew that one boy child had satisfied a condition with 1/7 probability. I would not think that if someone just came up to me and said "I have a son born on a Tuesday." I wouldn't think that if someone said "one is a boy who picks his nose," and I wouldn't think that if he said "one is a boy who has leukemia." None of this will help me update my prior probability of 1/3 (assuming the usual conditional probability approach to the one is a boy question).
If you were somehow in a life situation where someone said to you "at least one of my two children is a boy. Further, one of my children is a boy of which this random fact is true. [Fact picked truly at random follows]" you would want at least 2:1 odds on both kids being a boy. In the setup of the problem, Tuesday is nothing more than a random fact, uttered without prompting for no discernible reason. If you know what prompted it, then you're getting somewhere.
I'm tired. Y'all should take it up with Gelman. :-p
Erm, that is to say, it's not natural. It's totally bizarre. It's not like what would happen in life but it is, in fact, the problem as stated.
I just want to make sure that we've covered all the bases in this conversation: has anyone suggested that Tia's arguments about the relevance or otherwise of the boy's being born on Tuesday must be flawed because she's a girl?
oh, and just in case I wasn't clear
13/27: You go door to door, and people tell you if they have a kid who is a boy born on Tuesday.
I totally grant (and have been all along) that this question gets you 13/27. It's just that--like I keep saying--you have to assume that this question (or some variant) got asked. I think there's fundamental comity at this point. I mean, if people find it natural to think that question got asked when someone gets up at a podium and says "one of my kids is a boy born on a Tuesday" I'm no one to argue with what they find "natural."
So comity?
782
If the 'one is a boy' problem isn't underspecified, what is it that makes the 'one is a boy born on Tuesday' underspecified?
As I attempted to explain in 730 the "one is a boy problem" is also underspecified if the information is just volunteered as you don't know that the probability that this information will be volunteered is the same for the three cases where at least one child is a boy. For example in the cases where one child is a boy and one child is a girl the person could alternatively volunteer that "one is a girl". If they do this half the time then the probability that the other child is a boy is 1/2 as the mixed cases get half the weight of the both boys case.
921: That is a good point, actually. I think a related confusion came up with NickS's 798, where the probability of the information being volunteered changed with the underlying situation.
For me, it feels much more normal to assume that the probability of volunteering information is constant across cases than it is to assume someone was responding to an unstated question. But both are assumptions.
where the probability of the information being volunteered changed with the underlying situation.
I'm not sure that accurately captures the distinction.
The difference is between asking somebody (or somebody volunteering) "do you have a (one or more) male child?" vs. "Tell me the sex of one of your children."
The situation is the same, but the question is different.
(and, I note, that in the first case it's a question about the parent -- "do you have . . ." and in the second case it's a question about the child. I don't want to make too much of that except that the former style of question makes it easier to ask questions about the family taken as a whole unit ("do you have either any left handed children born on a weekend, or children with red hair?") that would be silly to ask of an individual.)
Sorry Nick, I actually never paid too close attention to what happened there after I vaguely understood that your scenario wasn't like "At least one is a boy." I'm probably inaccurately mapping it onto James's point. Which is still a good one!
I really like the aspect of these problems that exposes how your process of investigation changes the probability of the answer. I actually find it the most interesting and relevant part of them. I think they're illustrative both about how to identify a truly improbable result, as opposed to something you just reasoned backwards about after you saw it, and, as James is making me further see, examining the ancillary hypotheses you're using to get that result. Anyway, it's because I liked thinking about this and had already devoted so much energy to it that I devoted so much energy to it here.
We should all write a paper on how to use deceptively simple-looking probability puzzles as a pedagogical tool to clarify subtle issues in probability.
920: We're very close to comity except for one minor point:
It doesn't matter whether you *ask them a question* all you need is *some way of knowing* that what they're doing is telling you "I have at least one child who is a boy born on tuesday" if that in fact is true. For example, you live be in a very strange culture where revealing precisely this information is the only polite way to behave upon meeting someone new.
For another example, suppose we're playing a game with the following rules: You pick up two cards (from a very large deck), if you have at least one red ace you *must* discard a red ace (but you don't have to discard both if you two of them). After that people place bets at odds of their choosing on whether your remaining card is red. Which odds should you be willing to take and which odds not? Here there's no question being asked, *but* because you're playing a game with specified rules you still know exactly what information is being revealed.
That said it is still an important point that you're making that if you're gathering information by asking questions, it matters exactly what questions you're asking rather than just the content of the answers.
It doesn't matter whether you *ask them a question* all you need is *some way of knowing* that what they're doing is telling you "I have at least one child who is a boy born on tuesday" if that in fact is true. For example, you live be in a very strange culture where revealing precisely this information is the only polite way to behave upon meeting someone new.
comitycomitycomity!!
I never meant to imply otherwise, and I'm sorry I was sloppy in my language. Upthread I tried "pose a test" as an umbrella term for all the ways you could know that what they're doing is telling you "I have at least one child who is a boy born on tuesday" if that in fact is true. But I don't think it was very clear to people.
It's funny you should mention red aces--I wrote this whole thing about red cards and black cards to abstract the problem away from boys and Tuesdays, but then I was like, meh, I think I have comity with the people left in the thread.
(another term I tried was "data generating mechanism" which I think I borrowed from the Gelman thread.)
Comity!
Though now we'll never hit 1000.
We have two comment threads. One of them hit 1000 on a Tuesday. What are the odds that the other one will hit 1000?
Oh, sorry, bad question. Probability is only good for predicting things that have already happened, like the existence of someone's kids.
We have two comment threads. One of them hit 1000 on a Tuesday. What are the odds that the other one will hit 1000?
Is this well-posed?
We could revert to the original topic and discuss cognitive differences in the sexes. Today I accumulated some empirical evidence that women pay much more attention than men do to what shoes others are wearing (or at least are more likely to render such attention into words).
The original original topic was how big an asshole is John Tierney? I'm sure there are 67 comments in that.
927
It doesn't matter whether you *ask them a question* all you need is *some way of knowing* that what they're doing is telling you "I have at least one child who is a boy born on tuesday" if that in fact is true. ...
I think this is wrong or at least unclear. The question can be implicit but you have to know what it was and that it is always asked and answered.
For another example, suppose we're playing a game with the following rules: You pick up two cards (from a very large deck), if you have at least one red ace you *must* discard a red ace (but you don't have to discard both if you two of them). After that people place bets at odds of their choosing on whether your remaining card is red. Which odds should you be willing to take and which odds not? Here there's no question being asked, *but* because you're playing a game with specified rules you still know exactly what information is being revealed.
As stated you appear to be allowed to discard both red aces in which case you don't know exactly what information is being revealed.
I'm at comity (not that anyone cares) with the the info-gathering requirements as described by U:"Pe,tgi"(9) in 927 and semi-comity overall. My minor point (which gets me emphatically to 916.last).
I realized going to bed that what bothered me about Tuesday being described as added "extraneous" information is that it assumes you know in advance the question to be asked. When you read the utterance as a whole it is easy to make that (what I view as a) mistake. "Two children" and "boy" only seem to be more essential data after the fact. And this then knocks out the 1/3 interpretation (from 927.2: You have a prior of 1/3 based on the information that at least one is a boy) unless you imagine the 2 children and boy data being gathered in a different manner than the born on Tuesday information (a stretch since the boy and Tuesday were revealed in the same sentence).
This is basically just an application of what James' reiterates in 921 and as he points out it applies to the standard 2 children/1 boy problem and makes the 1/3 answer require further assumptions. So you may toss the 13/27 answer, but iif you are consistent it does not take you to 1/3 but to 1/2. (Or you can just treat the whole thing as a detached "toy problem" and accept the 13/27th thing based on assuming the right questions were asked.)
I think all of this is implicit in the comity states, but I do think that the "addition of extraneous information" construct is quite misleading.
927.2: That said it is still an important point that you're making that if you're gathering information by asking questions, it matters exactly what questions you're asking rather than just the content of the answers.
And I certainly agree with this.
935.3: it does not take you to 1/3 but to 1/2, or undefined/need more information.
935: Yes. I think I now understand what Tia was saying, and that it makes sense, but this, especially the last sentence, sums up what I was sticking at.
Okay, I think we agree on the underlying facts of the matter. I think "after the fact" is a red herring, and I'm not very invested in trying to adjudicate terms like "consistent", or "natural", but here's how I see the situation:
"two children" really is different in kind from the other information. It just defines the problem. Foshee could have an infinite number of children, and then we'd be lost. The significance of it doesn't depend on Foshee's motivational state, except in that we believe him to be truthful. You also need to know as a starting point that boy and girl are two mutually exhaustive equal probability outcomes. Tuesday and not-Tuesday are by definition mutually exhaustive outcomes, but you need to know that the probability of Tuesday in that scheme is 1/7.
"one boy", as James pointed out, entails the assumption that the speaker would be equally likely to point that out in all cases when it was true.
IMO, and I'm aware that it's O, this is a fairly natural assumption to make. To believe otherwise is to postulate a "pathological" Foshee, in Todd Graves's terms on the Gelman thread. You also need
to understand that by "one boy" Foshee means "at least one boy."
These are conventions of these sorts of problems that I accept, though I thank James for making explicit the assumption about the probability of the "one boy" utterance. Making these assumptions, and no more, get you to 1/3.
I have internalized these assumptions to the degree that I'd just answer 1/3 by rote if posed the question without "on a Tuesday" since that's what the intro texts on probability I've looked at have taught--I did object on first encountering them that the meaning of "one boy" was ambiguous the way these problems are often stated.
Getting to 13/27 requires an assumption that, given the setup, I find totally bizarre--that Foshee would have said something about the day of his child's birth if and only if the child were born on Tuesday. I don't think this is particularly implied by the conventions of these problems. I don't know of anything conventional that would have required someone to whisper in the back room "tell them if your child is born on a Tuesday" with any more probability than "tell them what day your child is born."
What's coming is a hypothesis testing perspective, but to me, assumptions of no difference between conditions are much more natural than assumptions of large and unmotivated differences between conditions. For the 13/27 answer, you have to believe not just that Foshee would have reported on a Tuesday in all cases when it was true, but for some reason, he wouldn't report anything about day of the week if it wasn't Tuesday. The parallel isn't true of boy. The information you get from "at least one boy" is not dependent on what Foshee would have said in the two girls case. He could have said "I have two girls" and it wouldn't affect the informativeness of "at least one boy." (If someone can demonstrate to me that that's false, have at it, but I don't think it is.)
So I think you can consistently make the assumptions required for a 1/3 answer, and not for a 13/27 answer. In fact, I think the assumptions required to get to a 13/27 answer are different in kind from the assumptions necessary for a 1/3 answer.
But this doesn't matter that much to me, because I think it hinges on opinions about what's natural that might be matters of taste at their core. I don't think (and never did) that "the" answer to the problem was 1/3. Days ago on my facebook I said I thought the answer was "underspecified". If the thread's acknowledging that the informativeness of "on a Tuesday" depends on the prompt I am a happy camper. I am happy to acknowledge that the informativeness of "one boy" depends on a non-pathological reporter who would say that consistently in all cases in which it was true.
He could have said "I have two girls" and it wouldn't affect the informativeness of "at least one boy." (If someone can demonstrate to me that that's false, have at it, but I don't think it is.)
I've thought about this further and it seems to me that something to notice is that there's basically only one condition that is not "at least one boy". Also that boy and girl are, in the conventions of probability questions, mutually exhaustive. Perhaps that is part of what allows you to remain agnostic about what else he might have said. The problem with Tuesday is that it doesn't (to my mind) have a natural opposite in not-Tuesday. The days of the week space is much more intuitively divided up by days, not by Tuesday and not-Tuesday. So if Foshee might have said Wednesday, you're screwed out of your 13/27 answer. But perhaps the converse can't happen for girl, because girl is the same as not-boy.
940: I think this is right -- that there's a difference in a natural language understanding of a binary choice (where, as you say boy=not-girl) versus a choice with more options (where Tuesday doesn't unambiguously mean anything in terms of the other options) that I hadn't worked through on my own.
I still don't get this stuff in any comfortable way at all, though -- like, I'm persuaded, but I don't own the argument for myself. Probability is hard. Let's go shopping.
I'm confused about how we can be close to 1,000 comments on a post about sexism and yet we have not yet started discussing food.
I forgot to have dinner last night. I could really use some samosas or some other triangular, filled-pastry type fried food.
I shall be having some in about an hour - supermarket spanakopita bought against the day we were both too tired to cook. Which day has dawned.
I still don't understand why the entrepreneur with the pushcart doesn't come by my work every afternoon at 2:30 to sell me a little savory snack. You can't get a savory baked good in this town to save your life, so why doesn't the hypothetical pushcart person alternate between samosas and empanadas in the winter, and spring rolls in the summer? Small, savory, with some protein, right there at 2:30. Cannot fail.
It will probably be a few $1 sambusas from the tiny basement coffeeshop near work for me. Mmmmm, $1 sambusas!
Speaking of cannot fail, which I was, my other recent genius idea? My friend was thinking of a CSA-type subscription model, only he'd have homemade breads in the box. And I was all, dude. If you're getting away from veggies in the box, you should make it a box of basics. Put milk (some local fancy milk) and eggs (from pampered chickens) in that box and have it show up on people's doorsteps once a week. So long as you'll need an insulated box, might as well put in plain yogurt from the fancy milk and some unbaked pizza dough. I gave him that idea for free, so he'll be rich in no time.
946 sounds good provided the box shows up on people's doorsteps while they're in. Otherwise things will happen to the milk and the pizza dough which should not be discussed on a family blog.
Insulated box, perhaps early morning delivery. But how sweet would it be to have milk and eggs and bread show up on your door? 'Specially if they are fancy-dancy, with pictures of the hens?
947: You need those little insulated metal boxes with a lock that medical places use for things like picking up and dropping off samples after hours. One key for the delivery person, one for the home owner. The box stays on the porch, advertising one's hipness and health consciousness.
Oh certainly. Over here we still have this thing called a milkman, who leaves milk on your doorstep around 5:00 a.m. Some of them do eggs and OJ too, but not with the birth certificates. Don't you have these people in California? Perhaps you could re-institute them.
They exist, even in the wilds of Pasadena. Not universally used, so a little expensive.
Right, just like a milkman, but with eggs and bread (or bread doughs). But, like, the marketing for a CSA which all the hip young families already know.
952 is excellent.
But, like, the marketing for a CSA which all the hip young families already know.
You mean the hip young families don't know about milkmen? Screw them then.
950: The company that does most of the milkman-style delivery here does pretty much a full line of groceries. So every order is different, and there's a much higher degree of customer-service interaction, as the delivery people are carrying the food all the way into the house when the resident is present. A former cow orker had been a deliveryman for this company, and he said it was pretty awful, as the set of people who patronize such a service are prone to have exacting, even to the point of being unrealistic, expectations about product quality and customer service.
I think what Megan is talking about is much more a hybrid of the traditional leave-it-on-the-stoop milkman delivery and CSAs.
Also locally, one of the arts organizations I'm connected with just did a "CSA" -- community supported artists -- project. It was massively successful. It was something like $300 for a piece of art from a very talented pool of local artists. I think they appropriated the idea from something in Chi or Beantown.
I think the people who enjoy the CSA experience and find it satidfying rather than expensive and disappointing, actually enjoy being somewhat surprized by what shows up. I think you could easily expand Megan's concept to include a rotaion of locally sourced bobo-friendly consumables: local honey one week, hand-milled soap another, apple butter the next.
Many of the CSA's I've seen, in several parts of the country, include an option for at least eggs, and often for other things like milk, cheese, meat, jam, bread etc. produced on the farm or by someone the farmer knows.
Most remarkably in the eyes of many Westerners, the success of the dabbawala trade has involved no advanced technology.
Many westerners must be pretty stupid.
958: But it's another excellent reason to marry an Indian. They're so resourceful!
Further to 958, I guess it's kind of the opposite of wowing the natives with a lighter or coke bottle. This time it's the primitives wowing us with their ability to do something without advanced technology.
A milkman sounds so very old-fashioned to me. My grandmother has stories about how they used to get blocks of ice delivered. Thrown off a passing train, or something like that.
My grandmother has stories about how they used to get blocks of ice delivered. Thrown off a passing train, or something like that.
Seems harsh to me. Essear is Danny Devito?
Fresh Milk is another example of Ag policy run wild. Price supports geared for a 10 cow dairy in Wisconsin or Vermont are also received by the 1000 cow dairy in Kern County, CA. Think his per unit cost is the same?
Of the various food home delivery services we had as a kid, the most interesting was Charles Chips. Potato chips so special you couldn't get them in the store! I think they came once a week, so lots of hard feelings if someone ate them all right off the bat. (They actually *were* pretty good, but Wikipedia says since 1996 they have been a different recipe.)
I'm pretty sure I've told this story before, but when my dad was a little kid his mom decided that he should have fresh milk, but they lived much too far from town for a milkman to come, so they bought a cow.
WHY BUY THE COW WHEN THE MILK IS FREE?
966, 967: Back then the style was to tie an oinion to their belts.
To bring the thread full circle, I see you one bob mcmanus comment at 5:
We need more women editors and publishers.
and I raise you one blistering media critique:
The Insight Center for Community Economic Development released a stunning report about the wealth gap for women of color: Single black women have a median wealth of $100 and Hispanic women of $120--dramatically lower than white men ($43,800), white women ($41,500) or black men ($7,900).
[...]Yet almost more jarring is the near-complete lack of interest on the part of corporate media. According to a search of the Nexis database, the weeks following the report's release witnessed one national television news mention, one NPR story, two opinion pieces... and a single newspaper report.
Tim Grant of the Post-Gazette told Extra! that he was "shocked and amazed" that his was the only paper to cover the story, even if in some ways it wasn't entirely surprising....
Grant said that, as an African-American male who covers personal finance, he took great interest in the Insight report, which he said "gave me a whole new perspective on what women of color are dealing with." Two of the paper's top three editors are women, he added, and their strong interest in the story helped land it on the front page. It's a powerful reminder that newsroom diversity can affect editorial priorities.
[O]nly 13 percent of newspaper newsroom employees are minorities, and only 37 percent are women. Women of color are few and far between. And supervisors are almost 90 percent white and two-thirds male. As the old saw goes, news is what happens to or near an editor.
wowing the natives with a lighter or coke bottle
I wowed a lady in the Costco parking lot the other day with my case of Coke in glass bottles. And then I wowed her with the assertion that yes, I am too old enough to remember when pop in glass bottles was the norm.
970: And then I wowed her with the assertion that yes, I am too old enough to remember when pop in glass bottles was the norm.
And then you gave her five dollars.
And you always had to share the bottle with your brother.
969: Also, go Post-Gazette. I feel vaguely guilty that I never buy you anymore but always read you.
And then you gave her five dollars.
And reminisced about how much more Coke five dollars used to buy.
(Anyway, I remember soda in glass bottles, so it's not like it was all that long ago. Or maybe I'm getting old.)
In other news, I'm mildly weirded out by the Unfogged time clock almost agreeing with my local time at the moment. (I'm easily weirded out, I guess.
If the milkman, like the postman, rang twice, you wouldn't have to worry about your milk and eggs going bad. You'd just have to worry about the parentage of your children.
Hmm. That was the wrong stereotype to deploy. Although, I guess you could argue that "postman" could refer to men or women, if you felt like arguing.
Only 24 comments to go.
You know, I didn't really remember how that video went.
And then I wowed her with the assertion that yes, I am too old enough to remember when pop in glass bottles was the norm.
How about sugar and no twist offs?
I don't remember glass bottles for soda, pop, or soft drinks being the norm.
Weren't pretty much all of the small size servings either glass or cans until around the mid nineties or so? In Switzerland I remember even the liter size ones being glass with a deposit and so they'd develop a band of scratches around the bottom where they banged against each other. This lasted at least through the early nineties. No ecus but plenty of sous were found in the process.
Certainly in Scotland, Barrs, the local rival to Coca-Cola and Pepsi, used glass bottles for the larger sizes. With a deposit. As kids we used to go prospecting for empty bottles to return for cash or more soft drinks.
Looking at their website, they still supply glass bottles for almost all sizes.
http://www.irn-bru.co.uk/our-drinks.html
I don't remember soda bottles ever being glass.
When I was a kid the 750ml bottles were glass [this is Barr's, I mean], and the smaller size was cans, or, after some point in the late 70s, plastic bottles. The smaller size now comes in glass, too, but formerly it was only Coke that came in small glass bottles.
And, of course, lots of soft drink manufacturers who supply their drinks in cans or plastic bottles for the retail market supply them in small glass bottles for the pub and catering trades.
well its all just epistemology today, between Shearer's goalpostmoving and the parents. But the boys question is one of language, not of statistics.
You can't tell if its 1/3 or 1/2 because the meaning of the parent's statement depend on why he is saying he has a boy (born on tuesday). Tia sort of got started on it, you need to know what counts as a success, but its the speaker's intentions (or at least assumptions) you need to know about.
but the answer is should be 1/3, because you shouldn't enter a battle of wits with a sicilian when math scolarship is on the line.
When I was a kid the norm was glass bottles (all sizes) with crown corks on the standard size and sometimes twist off on the big ones. I think Fentiman's is the only easily obtainable brand that still uses crown corks.
Also, I didn't realise that dandelion and burdock dates back to the 13th century. That's awesome - it's older than beer, by some definitions.
||
As if anything was on topic at this stage...
Why do I experience cognitive dissonance in learning that a member of the Velvet Underground has been given an OBE?
|>
John Cale is a serious musician, you know, OFE.
Bert Williams gets an MBE today. Nice timing there.
969: When I was a section editor at a large, semi-pro college newspaper, I hired more women of color than the entire rest of the paper combined. It wasn't that hard to find talented women of color who wanted to work on the paper either. If I had been smart, I would have gone for the editor in chief job and made hiring from a diverse pool of applicants a priority across the paper. Oh well.
I remember glass bottles being much more prevalent than they are now, but I don't remember a time when plastic bottles were not dominant. I was just having a conversation about aluminum can design with an engineer of my acquaintance though, where I was reminiscing about the early/mid-1980s shif from straight-sided aluminum cans to the current beveled-on-top design. Saw those for the first time on an airplane and was very impressed, and then within 6 months or so it seemed like the straight-siders were completely off the market.
992+993=
John Cale chips are seriously tasty.
Not to 1000 yet? Well, I guess Unfogged is always slow on Fourth Not-Tuesday.
I'm eating fenugreek sprouts I got at the farmers' market this morning. New food experience!
...early/mid-1980s shif from straight-sided aluminum cans to the current beveled-on-top design.
I can remember pull tab cans.
Kobe's dad can remember the steel can you had to poke two holes into a flat top.
Aluminum cans have gone from ~20 to over 30 cans per pound over the past 40 years. Both thinner gauge walls and the smaller diameter tops (the tops are a thicker gauge) have contributed.
Kobe's dad can remember the steel can you had to poke two holes into a flat top.
Speaking of which, these are the craziest mountain bike pedals that I've ever seen (so crazy, in fact, that you can only by them as a set with a pair of cranks that have been modified to fit the pedals). I think they look neat, but very odd.
According to the lid of a Snapple bottle I saw once, the can opener was invented 50 years after the can.
Sure, before that there were enough real men around that you didn't need a specialized tool.
Can I read 1005 as saying "real man" equates to "tool"?
1004: during the civil war soldiers shot the tops off of canned rations with rifles.
1004: Before then, they used hired help.
1006: I considered italicizing "specialized", but I had too much respect for the hermeneutic abilities of the commentariat.
998: Is fenugreek the stuff that makes your vaginal secretions taste like maple syrup?
Apo's vaginal secretions always taste like maple syrup.
If these sprouts give me a vagina, I'm not sure how I'll feel about that. It is, however, a galactagogue (such a great word) that is used to make cheap "maple" syrup.
So no vagina for you, but you're down with lactating? Cool.
Don't you need to close this thread? Shouldn't we talk about the "football"?
Oh my god, if vaginal secretions could taste like maple syrup, that would be so awesome. I fucking love maple syrup.
Her vaginal secretions taste all synthetic and nasty.
I'm inordinately amused to learn via Facebook that one of the cheerleader/queen-bee types from my high school is now married to someone who is actually named Chet.
1013: I tried that in 269, 4 days ago.
Wait, you probably mean soccer football, not NCAA.
We should totally talk about soccer.
I only have one more year before I am required, for swipple parentin reasons, to give a rat's ass about soccer. I'm going to take advantage of it.
s/b "swipple parentin'" because I don't see why I can't be a bit folksy about it.
Anyway, a tie is good for us, no?
When I break wind, it smells like Kentucky Fried Chicken. I'm going to have to eat healthier next week.
Do these people realize how ridiculous they sound?
Maybe you're about to crap a Double Down.
I've been eating original recipe washed down with Yuengling .
Extrapolating the progression from sun to light rain to thunder to hail outside my window for the last few hours, I can only conclude that a "weather singularity" is impending, when lead boulders will fall from the sky and crush everything in their path.
1026: I couldn't make it past the first page, but it's basically Skynet but with happy-happy fun time, no? I'm going back to the bucket.
1026: One executive sullenly declines to participate in another robot design exercise because no one in his group will consider making a sexbot.
I don't know what's silly about that.
The singularity stuff is stupid because it presumes that mind is all computational. But it's the kind of stupidity characteristic of smart people. See this great Bloggingheads dialogue where the philosophy professor Massimo Pigliucci demolishes a singularity proponent (who is exactly what you'd expect a singularity proponent to be like).
Mr. Orlowksi, the journalist, sees the Singularity as a grand, tech-nerd dream in which engineers, inventors and innovators of every stripe create the greatest of all reset buttons. He says the techies "seem to want a deus ex machina to make everything right again."
Well, yeah, but doesn't everyone?
The "Brinbot" thing isn't all that new. Andy Clark has been writing about similar things for a while.
Why don't they just call "the Singularity" "the Culture"? It depends on free energy, right?
The singularity stuff is stupid because it presumes that mind is all computational.
It may be stupid, but this hardly seems sufficient to establish that.
Do these people realize how ridiculous they sound?
In the minimal common ground shared the nerd-spectrum from LARPing to composing erotic Dr. Doolittle fanoperettas, no, they do not.
See this great Bloggingheads dialogue where the philosophy professor Massimo Pigliucci demolishes a singularity proponent (who is exactly what you'd expect a singularity proponent to be like).
The stuff Yudkowsky says in the first two minutes is already so absurdly stupid that I don't want to keep watching. But maybe I'll try to find the parts where Pigliucci talks.
1038: well, that's why I linked to a long dialogue about it. To be clear, the issue is not with the vague buzzwordy "singularity" notion that we're going to be able to do some wild technological shit in the future, but with the more specific claim that the growth in computational power will allow replication of the human brain's capacities. There are a lot of unsupported assumptions there about the human brain being analogous to a computer, as opposed to a biochemical organism. To take an example from the dialogue, you can perfectly simulate the chemistry of photosynthesis using a computer program, but that program will not convert carbon dioxide into sugars if you put it in the sun, because photosynthesis is fundamentally biochemical.
1039: the entire dialogue is Pigliucci patiently trying to unpack for Yudkowsky the gaps in his reasoning, and Yudkowsky refusing to understand that there could be a problem. The funniest thing is that as Yudkowsky becomes more and more emotional and unable to engage with the logic of the argument, he also becomes more insistent that the human mind can be described through computational algorithms. No hunk of metal will ever replicate the hormonal drivers of nerd histrionics.
Though apparently Yudkowsky somehow manages to get people to pay him for spouting bullshit about the Singularity, so maybe he is pretty smart.
Yeah, I'm only 20 minutes in, but my scoring of the debate is rather different from yours. I'm thoroughly unconvinced by the photosynthesis example.
It's a bit like saying I can write a program to perfectly simulate the operation of an abacus, but at the end it doesn't produce beads in the proper configuration, and thus the computer can't emulate an abacus.
And I'd like an exemption from the analogy ban on the grounds that PGD started it.
1044: well, yes, except that an abacus is just a device for producing answers, so if we produce the answers correctly we might not care about the physical configuration of the beads. (Although I bet there are some abacus collectors who do). But the mind is not just a device for producing answers. And in the photosynthesis example, the point of sugar is to be able to eat it, not to correctly describe its chemical configuration.
...but with the more specific claim that the growth in computational power will allow replication of the human brain's capacities.
They can barely make a computer that can recognize a face, let alone one that can recognize a face while using 95% of calculating capacity to see if a nipple can be detected beneath a sweater.
So the mind is not just for producing answers. What else is it for? And how do those functions make it more like sugar than an abacus?
Pigliucci's speech pattern is amusingly similar to Arianna Huffington's.
The conversation reminds me of the person (in college? later? odd that I've forgotten) who asked me whether humans would know if we were not self-conscious.
And in the photosynthesis example, the point of sugar is to be able to eat it
I beg your pardon. It is not.
That aside, the photosynthesis example seems clear and decisive.
1047 could be read as an oblique reference to the irreproducibility of human desires, motivations, and goals.
The wife, who used to work in an herb store, confirms 1010. Have at it, nosflow.
1052: If you put it on pancakes, what does breakfast taste like?
Occasionally I have these moments where I'm sort of bowled over by how fucking weird it is to be conscious and experiencing things when I'm really just a bag of more-or-less-deterministically moving molecules. But then I realize how lame it is to have one's epiphany be a Neutral Milk Hotel lyric.
The photosynthesis example as PGD reproduces it seems terrible. No one is proposing making computers that model chemical processes in the mind. But if people are proposing computers to which question can be put following which answers are given and that are self-movers, who cares whether they can also produce sugars? I mean, I really don't get why anyone would be given pause by that example.
Yudkowsky is amusingly crazy (as I know from his blogging, haven't watched the BH yet), but whether he's crazy or not doesn't change the fact that the mind is all computational. I'm not even sure what it'd mean to say it wasn't all computational.
1054: You coulda been a philosopher! Except that being weirded out by things all the time can get in the way.
Introducing the Singularity into a thread already past 1000 comments is exactly the kind of thing a bag of more-or-less-deterministically moving molecules would do.
Occasionally I have these moments where I'm sort of bowled over by how fucking weird it is to be conscious and experiencing things when I'm really just a bag of more-or-less-deterministically moving molecules.
That's why I can't buy the 'more-or-less deterministrically moving molecules' part.
Whereas I'm not sure what it means to say that the mind is computational.
If you start thinking in terms of more-or-less deterministically moving molecules you probably start having real problems with dead skin, ingestion, etc.
I am pretty sure there are no people, or even organs, in physics.
"We're no computers, Sebastian -- we're physical."
Shorter 1060: Does not compute.
So the mind is not just for producing answers. What else is it for? And how do those functions make it more like sugar than an abacus?
Well, separate from the question of what the mind is "for" beyond survival (does evolution have purposes?), what is does is interact with the body and the environment to create the particular kind of human consciousness we have. Consciousness is a basically experiential thing, we only know of it existing in bodies, so we have no idea whether it can be separated from its physical substrate any more than a food like sugar can be separated from the actual stuff you eat.
Also, 1051.
the mind is all computational. I'm not even sure what it'd mean to say it wasn't all computational.
are emotions computational? Emotions are part of the mind, perhaps the most important part. What would it mean to simulate the endocrine system?
No one is proposing making computers that model chemical processes in the mind. But if people are proposing computers to which question can be put following which answers are given and that are self-movers, who cares whether they can also produce sugars?
Such computers exist today. They are not human. The question is whether computers can be made to replicate humans just by amping up the speed or complexity of the kinds of things computers do today.
Having thought about my favorite probability problem still more, I'm pretty sure I left this thread with some wrongness in typed on my iphone after a bus + plane redeye that I'd like to correct. The distinction in 940 between boy/girl being mutually exhaustive categories, and any set of days of the week less than seven not being mutually exhaustive, is useful to consider in thinking about why someone like me doesn't think it makes sense to default to thinking that Foshee only would have said the boy's day of birth if it were Tuesday. But it's not the reason "Tuesday" requires more assumptions than "boy."
"Tuesday" requires more assumptions than boy for the reason I gave earlier -- the question is about "boy", and "Tuesday" can only affect the likelihood of "boy" if "Tuesday" means at least one boy passed a test of some definable probability less than one. To test this out for myself I used abstract A, B, C, and 1, 2, 3 categories in which each event has equal probability, and imagined the reporter said:
I have two children. At least one of them is an A who is also a 1. What is the probability that they are both A's?
The base probability that both are A is 1/9. Using James's assumption that the reporter would tell you at least one is A in all cases where that were true--you have 9/45 = 1/5. There are many cases when it's not true, and the informativeness of that statement does not depend on what the reporter says when it's not true--or at least, not for any reason I can see.
If you assume *both* that the reporter would have told you about 1 in all cases when it was true (the same assumption as for A), AND that the reporter would *not* have told you about 2 or 3 in the cases when it was true, then you can exclude a bunch more cases, and get to 9/17.
The number is only informative insofar as it means that at least one A has passed a test, making it more likely there are two of them.
(To the extent this still seems weird, I think if you let go of the 13/27-type answers as a conceptual anchor and think of how weird it was in the beginning that seemingly irrelevant information like "Tuesday" could affect the probability of "boy", it will seem more logical that it can only do it under certain circumastances.)
(Yes, I know I have geeked out about this rather intensely. I didn't want to leave the thread with wrongness!)
The singularity debate may in part be a projection of the nerd desire to be freed of the annoying body. Bodies are a jock thing which have held nerds back since the grade school playground.
OT: Why does the Facebook friend-abacus think I ought to be friends with John Podhoretz? The suggestion is, not to put too fine a point on it, offensive and insane.
The question is whether computers can be made to replicate humans just by amping up the speed or complexity of the kinds of things computers do today.
If that's the question, then the answer is pretty simple. No. For one thing, nobody in their right mind would program a computer anything like a human mind. They'd try to improve it, fix bugs, etc. Before you know it, they've created CHUDs or something.
The singularity debate may in part be a projection of the nerd desire to be freed of the annoying body.
May be!
1069: why would you invent a penis wider than it is long?
Now my Internet connection has quit completely. And the weather sucks. My undisclosed idyllic mountain location is kind of sucking. Do you know how freaking long it takes to load a 1000+ comment thread on an iPhone?
I give-up, why would you invent a penis wider than it is long?
1069: I am putting myself to the fullest possible use, which is all I think that any conscious entity can ever hope to do. What about you, wetware boy?
"give-up"? Who are you, David Lebovitz?
Who are you, David Lebovitz?
I googled to see who that was. Now I'm probably going to buy a cookbook.
Actually, this sort of gets to my point because if you were to build a computer Moby Hick, you'd probably fix the 'extraneous hyphenation' bug and the main other failings I have that are not related to commenting or copy editing. Then, your computer model me wouldn't be me.
Oh Christ, this thread got all stupid, didn't it? (a) shut up about the singularity, (b) obviously yes of course you can model emotions as a part of cognition.
We made it to 1000, guys. You don't have to keep arguing.
God, 1033 is stupid in such a frustrating way. I should leave.
Is AI at the point where there are similar entities that have different "personalities"?
Don't leave, Sifu! Argue! I need entertainment.
Actually, I rather like singularity.
There being stupidly smart people here, there are also Singularitists here, or have been in the past. Pdf23ds, for example.
obviously yes of course you can model emotions as a part of cognition.
you can (maybe) predict their behavioral outcomes. But can you replicate the experience of them? And is the experience of them essential to what they are? Remember, an artificial consciousness needs to have self-generated motivations.
God, 1033 is stupid in such a frustrating way.
1033 is in fact very smart. Even brilliant.
And I'm not even sure you can predict the behavioral outcomes of emotions. Certainly it's one of the most complex things about behavior. Especially once you consider how socially and culturally dependent human emotions are, and how this makes one person's emotions depend on everyone elses.
Emotions are the key. Science only works because it sets up a cultural system that emotionally motivates people to make correct predictions about nature. As a very smart philosopher once said, reason is the slave of the passions.
My spotty internet has still kept me from hearing more than a few minutes of the debate. But here are a few things that bug me about what Yudkowsky says: he seems to assume that positive feedback means endless growth, unlike more or less any example I know of; he seems to imagine the brain is like a simple neural network, signals traveling on axons, eliding the complicated role of ions and neurotransmitters and hormones operating on different timescales; he seems to assume that some measure of understanding or intelligence correlates directly with computational power, when in fact I think they're largely orthogonal; in general, he ignores all the ineffable complexity that's going on in the background when our brains do the amazing things our brains do. I wouldn't say that such brainlike activity couldn't be implemented on a computer, or even emerge spontaneously, but I don't think we understand it well enough to know.
I wouldn't say that such brainlike activity couldn't be implemented on a computer, or even emerge spontaneously, but I don't think we understand it well enough to know.
I'm pretty sure it emerged at least once.
PGD is coming out of the dualist closet, I see.
I'm pretty sure it emerged at least once.
Yes, well. Emerging on a computer that we program to do a specific task would be a little more unexpected, I think. Plus, it took a while for us to get here.
Emotions are the key. Science only works because it sets up a cultural system that emotionally motivates people to make correct predictions about nature. As a very smart philosopher once said, reason is the slave of the passions.
Well, you could imagine an artificial intelligence which is capable of doing great things but doesn't feel like it. Anyone familiar enough with this place shouldn't find that hard to imagine at all.
1091: how's that? The notion that consciousness cannot be separated from its material substrate is materialist, not dualist. The idea that consciousness is some abstract thing that can be replicated in a computer strikes me as closer to being dualist.
1094.1-2: I was attempting to joke about your 1088. The statements suggesting emotion was necessary for reason and emotion couldn't be simulated struck me as a bit dualist.
1094.3: Dualish, maybe.
My favorite commentary on the singularity is this pie chart from Scott Aaronson. I think he somewhat overestimates the "more or less like now" and somewhat underestimates the "brains in computers" scenario, but I generally agree with him that the odds are about half that civilization will collapse in the next 100 or so years.
I'd more or less agree that chart. I'd put some of that "more or less like now" in apocalyptic scenarios, but yeah. I'm more a Singularian out of hope/geekery than expectation.
Eh, he overestimates a lot of other things too, but presumably in the name of humor. ("NP-complete problems efficiently solvable"? I wouldn't give that a visible slice.)
There's sort of a universal failure mode of pie charts -- people give visible slices to absurdly improbable things, and feel compelled to split the probable things in roughly even proportion. (I've seen similar attempts at "what will the LHC discover?" where people have visible slices for black holes. Fail.)
So are we going for 2000 now, or what?
I don't know. I'm pessimistic; I put the odds at about half that civilization will collapse in the next 900 comments.
I'm doing my part to reach Unfoggularity.
How does remotely controlling some robot = becoming part man, part robot? How about becoming all pathetic reporter searching for a hook for a story?
I want to know what group of people builds a Brinbot before a sexbot.
Or do I?
I haven't read the article, and I don't intend to. Does it address the dentistry issue?
You've got to build one bot before you can build six. It's all computational, you know.
This thread reminds me that I saw this book at a library book sale recently.
It seems somehow inappropriate to bring up, but in a convergence of two Unfogged interests, Party Down season 2 ep 7 features Lizzy Caplan wearing clothing that makes the existence of her nipples rather obvious.
The end of this thread, at least. Or what currently seems the end, but may turn out to be the middle, after about 900 more comments.
1108: You don't intend to? Don't you want to find out how many Brinbots you need to make a sexbot?
I'm pretty sure it emerged at least once.
Really, from a computer?
How does remotely controlling some robot = becoming part man, part robot?
Well, you do get weird proprioceptive-ish effects after habituation, and start to have a sense of yourself as being where the robot is, rather than where your body is (if it's hooked up properly), provided the robot is properly made (Andy Clark talks about what might make for being properly made in "A Sense of Presence"). Cf. that guy who controls a third arm hooked up to his belly or something like that. (Or, for a receptive contrast, tactile-visual substitution systems.)
A neat description, from Cole, Sacks, and Waterman, "On the immunity principle: A view from a robot", quoted in Gallagher, How the Body Shapes the Mind (Waterman doesn't have any proprioception of his own body below the neck):
The robot's arms have joints which move like human arms and three fingers on each hand. The arms are viewed by the human subject through a virtual reality set placed over the eyes, with robot cameras set in the robot's head, so that one views the robot arms from a similar viewpoint as one views one's own arms. No direct vision of one's own body is possible, as one sits across the room from the robot. A series of sensors are placed on one's own arms which in turn control the robot arms' movement. Then when one moves, the robot's arms move similarly, after a short delay.
Then one sees and controls the robot's moving arms, without receiving any peripheral feedback from them, (but [for Cole and Sacks] having one's own peripheral feedback from one's unseen arms). We transferred tools from one hand to another, picked up an egg and tied knots. After a few minutes we all became at home with the feeling of being in the robot. Making a movement and seeing it successful led to a strong sense of embodiment within the robot arms and body. This was manifest when one of us thought he had better be careful for if he dropped a wrench it would land on his leg. Only the robot arms had been seen and moved, but the perception was that one's body was in the robot. This feeling was present in able-bodied people who have tried the robot and in a subject [Waterman] with a large fibre sensory neuropathy without the sensations of movement/position sense or light touch below the neck.
Which, of course, is really nothing more but an especially dramatic dramatization of Head's hypothesis in 1920 that a feather in a woman's hat might be incorporated into her body schema, or Merleau-Ponty's similar claim in 1945 (this is much earlier than, for some reason, I thought) regarding a blind man's cane, and might not seem to be much in the way of becoming part man, part robot.
Don't you want to find out how many Brinbots you need to make a sexbot?
Only one, but you have to buy it dinner first.
Or driving a car, for that matter.
Also mentioned by M-P! What a clever fellow he was.
Phenomenologists like him and phenomenologically-inclined cognitive science types would seem to be a natural for the singularity d00ds, since they have a flexible, nonbiological concept of the body, but they attach way too much importance to some concept of the body, and physical interaction with the world, to get on board with the sublime res cogitantes it seems the singularitroids are after.
Don't you want to find out how many Brinbots you need to make a sexbot?
Not even a little.
That's a pretty shitty punchline, teo.
Wait, Merleau-Ponty was a person? I thought it was a car!
What a strange future. I definitely couldn't have seen that comment coming.
This Merleau-Ponty dude does sound pretty clever.
Next thing you guys are going to tell me is that Levi-Strauss was not a composer of songs about jeans ("The Blue Denim", etc.).
That's a pretty shitty punchline, teo.
Noted.
Good Fifth Not-Tuesday morning to everyone.
