Hah, I thought you were talking about this φ.
Man, φ gets all the credit, and ψ lives in the shadows. If you google "2 phi" not only does the google calculator give you 3.23..., it renders it as "2 * the golden ratio". If you google "2 psi" it gives you "2 pounds per square inch". BULL SHIT.
I remember reading a screed against this myth in my early Internet days, maybe as much as 15 years ago.
It all sounds a lot less mystical if you just call it "one plus the square root of five, divided by two".
Minor: the painters he puts in the 19th century were all from the 20th -- the age of golden-ratio fetishism.
I believe Bartok did actually put some golden/Fibonacci time ratios in the first movement of the Music for String Instruments, Percussion and Celesta, but that's chilly stuff, deliberately engineered to sound deliberately engineered.
This sentence cracks me up:
My first suspicions that all was not right with some of the claims made about the aesthetic appeal of the golden ratio were aroused when I admitted to myself that I personally did not find the golden rectangle the most pleasing among all rectangles.
She wasn't the most arousing rectangle, but she had a case.
7. I suppose rectangle porn has a certain purity not found in bike porn.
Who amongst us will be the first to locate the geometry fan-fic?
6.1: Yeah, the phrase "Paul Serusier, Juan Gris, and Giro Severini, all in the early 19th century" pretty much reads as "I know nothing about art! Please disregard this paragraph".
"Futurism is a famous example: it was founded by (mostly British) sculptors who broke from Neoclassicism in Berlin in the 1820s, forming little democratic circles of twenty to forty people with their paint cans in each other's garages."
I had one of those moments reading The Idea Factory (the Bell Labs book) yesterday when near the end I found a sentence quoting Pa/ul Gin/sparg and describing him as a "young physicist" in 2002. He was only slightly shy of 50 years old then. I was suddenly inclined to take the rest of the book less seriously.
Still, I bet people sneer at all those other ratios in the street.
12.2: hah. Does he look youthful?
What'd you think of the book otherwise? (The parts relevant to my prior interests didn't turn up any obvious-to-me howlers, incidentally.)
9: Angle Side Side Inequality 4: Curved Space
For the fifty thousandth time, Angle Side Side does not determine a unique triangle, mister.
It was a pretty interesting book. I guess I was hoping for a bit more of the history of condensed matter theory and basic physics at the Labs, because as far as I know no one has ever written a good popular book about condensed matter physics, but still all the stuff about technological developments was pretty interesting.
Exploration of Distance Metrics On A Two Dimensional Roy Orbison Cling Manifold
16: She said, sternly, finding her hand drawn inexorably toward his throbbing hypotenuse.
17: yeah he definitely seemed to be interested in it from a business/techy perspective rather than a pure science perspective.
For the fifty thousandth time, Angle Side Side does not determine a unique triangle, mister.
You're thinking of Angle Side Side Inequality 3: Alternate Solutions.
Add a "from" to 20, see if that helps.
11: "diagonal" is close enough to "dragon" that Sifu can feel justified in linking herpy again, right?
"We used to be a rhombus but now it feels so right"
"He got so much action on the side he was practically circular."
"I want to be your derivative so I can be tangent to your curves."
"Rectangle? Damn near killed it!"
Unfortunately Geometric Porn App was rejected and suspended by Apple and Google.
10: Or maybe he just doesn't know how centuries are counted. I mean, you gotta admit that it's counterintuitive.
By the way, I'm not reading the linked article, and in lieu of plugging my ears and shouting lalalala, I'm geometrically constructing the golden spiral and chanting 1.618033989...
Or maybe he just doesn't know how centuries are counted.
No, in the same sentence he also mentions Dali and correctly assigns him to the 20th.
Oh and, for the record, I have used the golden ratio in my work. In fact, it's at least possible that some of the windows in H-G's addition were sized that way.
Maybe I should write Devlin.
He was bad at closing tags as well.
Today, all that is about to change, as speaker Chris Pearson show you how the Golden Ratio will help you determine the proper placement of EVERY pixel on your site. When we're done, you'll have typography fit for an adonis, and you'll also have a new found sense of spatial awareness that would make Euclid proud.
Every pixel's sacred.
Nope, not Heebie's house. Rats.
No wonder this house is so refreshingly arousing.
Or at least a lot of rat-holes.
excuse me, sorry to interfere, but my god, a baby growing in her WOMB and mom calling her vagina a rat-hole on a blog is an inacceptable situation
Maybe I'm a rat, and it's all as planned.
For the fifty thousandth time, Angle Side Side does not determine a unique triangle, mister.
Can someone explain (possibly on Standpipe's blog) why not? If you've got the lengths of two sides, and you know the angle between them, then how many triangles could you possibly form from that?
Wouldn't that be Side Angle Side?
If you've got the lengths of two sides, and you know the angle between them
That's side-angle-side, not angle-side-side.
Who amongst us will be the first to locate the geometry fan-fic?
Does this count?
46: imagine you know that one side of a triangle lies along the X axis, and that one side runs from (2, 0) to (0, 1), and that the remaining side has length sqrt(2). Where is the third vertex?
42 made me laugh way too much, but I am at my parents' and slightly Becks-style. And now talking to my dad about the golden ratio.
Kid A just told me Flatland fan fic exists. I have a very old copy of Flatland, because the author was a headmaster of my dad's (and my brother's, and mine for a couple of years) school.
Oh no, it's crossover Flatland and stargate Atlantis!
Numbers totes have mystical significance, if anything does. Tononi has just fallen for a more sophisticated version of the same trap that caught the Platonists and the believers in Golden Ratio.
My dad is now quizzing kid A on her times tables because kid D doesn't know hers.
I just looked at the picture pool.
The parents-to-be have a really high bar. There are some darn cute kids in there.
50: 0, 1, or 2, depending.
Or even 3.
The last time I checked it was no longer previewable on google books, so no link, but in The Manuscript Found in Saragossa there's a few passages that might qualify as geometry/math fanfic.
47 and 48 have clarified things. Thanks.
Ok, here's a puzzle:
There are three people, 1, 2, and 3, each wearing a t-shirt with their number on. One (not number one) always lies, one always tells the truth, one does whatever. You have 3 yes-no questions to determine which each of them are.
Well, we know for starters that #1 is not the liar.
So suppose that #2 is the "do-whatever" person.
Suppose now that I ask either the liar or the truth-teller, "if I ask #2 if you're the liar, will s/he say 'yes'?".
How can either of them answer that question?
"If you don't each tell me which one of you is which, one of you will get a punch in the face, one of you will get punched in the gut, and one of you will find five dollars after being pushed to the ground. Do you understand?"
64 - according to my dad, all three of them know the switcher's secret method for deciding whether to lie or tell the truth, so there will be no confounding questions.
They all know each other.
I got as far as asking them all something like does 1 + 1 = 2, which means you know which is the switcher. But then you've used your questions.
Q1) Ask #2 if #1 is the liar.
A1N) If #2 says "no", then #2 is not the liar. So #3 is the liar.
A1NQ2) Ask #3 if #1 is the truther.
A1NQ2Y) If "yes" then #1 = whatever & #2 = truther.
A1NQ2N) If "no"then #1 =truther & #2 =whatever
A1Y) If #2 says "yes", then #2 not truther.
A1YQ2) Ask #3 if #2 is truther.
A1YQ2Y) If "yes" then #3 not truther, so #1 is.
A1YQ2YQ3) Ask #1 status of either 2 or 3.
A1YQ2N) If "no" then #3 not liar, so #2 is.
A1YQ2NQ3) Ask #2 status of either 1 or 3.
69: we don't really know that #1 is not the liar. Minivet was making a joke.
"One rapper likes big butts and cannot lie. One rapper likes small butts and always lies"...
71: Holy shit, that's the way I read it myself. But I did sort of wonder why it would be set up so the one branch only needed two question...
Now I guess I have to really solve it to save face (partially).
There are three solution before you. One of them always saves face, one of them never saves face, and one of them is unpredictable in its effect on your dignity. You have three chances to salvage any hope of people not making fun of you.
(I totally read it the same way .)
Can the questions be addressed to multiple people at once?
78: I think that counts as a question so you have two left.
Is it important that these are t-shirts, and not, say, sweatshirts?
It's like there's a whole family of nearly but not quite identical brain-teasers.
||
Bah. Invited to a party of moderate debauchery. Thanks to having a child in the house, we can't reasonably go. I suggest having some debauchery of our own once the kid is asleep. Good plan! Except now that the kid is asleep, the name of the game seems to have changed to "falling asleep on the couch".
|>
Since you're presidential, what exactly constitutes "moderate debauchery"?
I just watched Compliance, so I'm game for some wholesome, palate-cleansing voyeurism.
Heavy drinking, enjoying and/or mocking smut in mixed company, heavy flirting.
No wonder there's so little liveblogging.
Hmm, no answer to the puzzler yet this AM. Given the constraints, you can encode the answer in 3 bits so it is theoretically possible. But assuming that the wording is not the "trick" (if it actually *is* letting you know that #1 is not the liar going in), I think it reduces to at a minimum eliminating one person as the "whatever" person in the 1st two questions (plus establishing one more constraint).
Answer reading itthe right way I believe.
Use 1st question to #1 figure out which of #2 or #3 is not whatever (W) and proceed from there.
For instance ask 1 if 2 is more trustworthy than 3.
If 1 is W, cannot predict the answer but in that case neither 2 or 3 are W.
So ignoring the 1=W case:
If answer is Y, 1=T implies 2=W, 3=L. 1=L implies 2=W, 3=T. So 3≠W
If answer is N, 1=T implies 2=L, 3=W. 1=L implies 2=T, 3=W. So 2≠W
Q2: Ask the non-W person if they are W to establish T or L.
Q3 left as an exercise for the reader.
You could try to peg the whatever person first. 67 implies the whatever person is in a guaranteed state each round (true for any question or false for any question), and not giving completely random answers, so you could ask:
"If I were to ask you right now whether you were the whatever person, would you say yes?"
The truther will say no. The liar will lie about his lying and say no. But a truthful whatever person would say yes, and a lying whatever person would lie about his lying and say yes.
So if that question flies, asking it of 1 and 2 would peg the whatever person. For the third question you can ask one of the non-whatevers whether 1+1=2.
Use 1st question to #1 figure out which of #2 or #3 is not whatever (W) and proceed from there.
That is worded badly, of course neither may be W, but with one question you can definitively eliminate one of them as a possibility.
Good problem, I was close to convincing myself that it was not possible because the "whatevers" are so useless.
For instance ask 1 if 2 is more trustworthy than 3.
The lair is trustworthy, too.
91: I don't think 67 implies the whatever person stays constant through the exercise. And the solution in 90 does not rely on that.
93: That's why animals tend to stay in them.
Assume a somewhat better worded question. "Lies more often."
For the third question you can ask one of the non-whatevers whether 1+1=2.
Or you could just ask them whether the whatever person was a liar—more in keeping with this kind of puzzle.
Trying to see if there is a solution starting with my original thought for the 1st question (ask 1 "are you whatever?") which also eliminates 2 of the 6 possible combinations (and basically gets you to my misread of the problem but with one question already used up). But 2 & 3 have one W and 3 non-W possibilities left after that, so not sure it works. Will think about that at the gym.
97.1: supervillains, too! Throws people off the scent.
If 1 is W, cannot predict the answer but in that case neither 2 or 3 are W.
But you can't ignore that case, because you don't know that 1 is W based on the answer here.
No, but we are only at this point attempting to establish either 2 or 3 as definitely not W*, so we have someone who is predictable in their responses (and after the "Are you W" question we know for sure). We only establish whether 1 is actually W in the 3rd question.
*So there are 2 combinations with 1≠W still left in addition to the two with 1=W.
TLW
TWL
WTL
WLT
LWT
LTW
::
either of
WTL WTL
WLT WLT
LWT LTW
TWL TLW
::
Each of those have one "column" with no Ws.
98: Or whether homeopathy works, or whether 9/11 was an inside job.
| | TLM | TML | LTM | LMT | MTL | MLT | |-------------------------------------------------------------------+-----+-----+-----+-----+-----+-----| | 1. #1: does #2 have a greater propensity to lie than #3? | y | n | y | n | ? | ? | | 2a. If no: #3: does #1 have a greater propensity to lie than #2? | | y | | y | n | n | | 3a. If no: #1: Is #2 "whatever"? | | y | | n | | | | 3b. if yes: #2: is #1 "whatever"? | | | | | n | y | | 2b. If yes: #2: does #3 have a greater propensity to lie than #1? | n | | n | | y | y | | 3a. if yes: #2: is #1 "whatever"? | | | | | y | n | | 3b. if no: #1: is #3 "whatever"? | y | | n | | | |
no-yes-yes = tml
no-yes-no = lmt
no-no-no = mtl
no-no-yes = mlt
yes-no-yes = tlm
yes-no-no = ltm
yes-yes-yes = mtl
yes-yes-no = mlt
Or whether, 'Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation.
No, but we are only at this point attempting to establish either 2 or 3 as definitely not W
But you can't do that yet. Q2 is "ask the non-W person", but after Q1, you still don't know which is the non-W person.
108: Sorry. Q2 should have been "ask the non-W person between 2 & 3".
But 90 works. 106 is nice in that you never ask someone about themselves. But the first differentiating question is the key. A lot of paths beyond that point.
108: I assumed a number of things would be obvious to the likely interested person. But yes, precision in language has its place when automata are about.
Right, I eventually realized that if you're assuming that 1=W, then it doesn't matter at that stage.
89
Hmm, no answer to the puzzler yet this AM. Given the constraints, you can encode the answer in 3 bits so it is theoretically possible ...
Of course you don't actually have 3 bits of information because you get no information from any question asked of the whatever guy. So you need to avoid asking questions of the whatever guy as much as possible. This isn't possible for the first question but is for the next two (as in the posted solution) so you are down to 2+2/3 bits of information which is just enough for 6 possibilities.
What if love were stronger than gravity?
That makes no sense, of course, but it's probably more worthwhile that way than the trailer that intended to link to.
I had a hunch when I started reading this NYT article Why We Love Beautiful Things might invoke the Golden Ratio. Whaddya know:
For more than 2,000 years, philosophers, mathematicians and artists have marveled at the unique properties of the "golden rectangle": subtract a square from a golden rectangle, and what remains is another golden rectangle, and so on and so on -- an infinite spiral. These so-called magical proportions (about 5 by 8) are common in the shapes of books, television sets and credit cards, and they provide the underlying structure for some of the most beloved designs in history: the facades of the Parthenon and Notre Dame, the face of the "Mona Lisa," the Stradivarius violin and the original iPod.
The iPod! And credit cards!
112: so you are down to 2+2/3 bits of information which is just enough for 6 possibilities.
Yes, I was viewing that there was a 3-bit encoding as being a necessary but not sufficient condition for it being solvable. I do like trying to analyze puzzles like this from an informational viewpoint* but am often not sure I am really doing it right. For instance, I can intuitively see why the first ask with 1/3 chance of hitting the worthless whatever person would be 2/3 of a bit, but not sure I could demonstrate it (nor am I even sure that it is "linear" like that). But I do think a similar analysis indicates that my attempt in 99 (find a solution starting with "Are you the whatever?" to #1) is doomed to fail. Like the solution it also cuts out 2 scenarios so there are 4 left, but it does not eliminate the possibility of any of them being the whatever person (reduces it to 1/4 for 2 & 3), so you basically only have 1+3/4 bits to distinguish between 4 scenarios. And indeed, everything seems to lead to a dead end.
I didn't actually run the numbers, but that the golden mean isn't found in any of the mattress sizes I can think of off the top of my head proves to me that it's not so cosmically wonderful. (And that's supposed to be a sleep reference, not a sex reference, now that I suddenly feel vaguely dirty about it.)
117*: One that I've tried to analyze that way is one of my favorite heavy/light ball-weighing* problems. It is 12 balls, 1 is either heavier or lighter than the rest, 3 weighs on a balance scale to determine which it is and whether it is heavier or lighter. So 12x2=24 states which is ~4.6 bits. At first blush it seems as though you are doomed with only 3 weighings, but a weighing is not simply y/n so it can work. Just looking at the first weighing you reduce the 24 cases to the following (unbalanced/balance) for all 6 possible starts:
1x1 2/20
2x2 4/16
3x3 6/12
4x4 8/8
5x5 10/4
6x6 12 -
So after 4x4 weighing you are left with 8 possibilities with either result and (need 3 bits) and you've reduced it by 1.6 bits. It works from there, but it is not clear to me whether or not you could predict that you would be able average a small amount more than 1.5 bits /weighing (more than 1 because you can generally both eliminate some balls and also learn whether others would need to be heavy or light). When I first heard this one in high school I initially started 3x3 and got what I thought was tantalizingly "close" and wasted a lot of time trying to close the gap. This type of analysis would have saved that exploring that particular blind alley.
*Or low-hanging fruit weighing.
... but not sure I could demonstrate it ...
Yes, it is possible to get carried away and start asserting things that are plausible but not actually correct.
Another way of looking at it is you have 8 possible answer patterns but the two cases where you ask the whatever person the first question must get at least two patterns each so you can't afford any more wastage.
119: It works from there, but it is not clear to me whether or not you could predict that you would be able average a small amount more than 1.5 bits /weighing
Continuing my discussion with myself (and possibly James), thought about this a bit more and realized that it is in fact pretty easy to "predict". For any given weighing there are 3 possible outcomes* (left side higher, left side lower, balanced)--which is ~1.6 bits. And ignoring the "bit" talk, with 3 weighings you can theoretically distinguish 33=27 different states, so 24 is at least feasible**.
*And my table in 119 would have been much clearer if I had used that scheme since it always shows all 24 states:
1x1 2/2/20
2x2 4/4/16
3x3 6/6/12
4x4 8/8/8
5x5 10/10/4
6x6 12/12 -
**But 13 balls is also "feasible"--26 states--but it does not work since any initial weighing leaves you with at least on result with 10 or more possibilities (9 would be doable). However, if you allow a modification that the balls can be split in half, you can do it with an initial weighing of 4x4 where one of the "balls" is in fact the halves of two different balls. You then end up with 9/9/8 possibilities and can proceed from there to the solution with no further chicanery needed.
And a final note, this kind of analysis is probably as interesting to me in relation to creating puzzles as it is for solving puzzles. Generally, but not necessarily always*, the better puzzle is one which pushes everything to the limit. In contrast to, say, the LSAT logic section (IIRC) where there is often more information than needed to solve and where it is sometimes wasteful to overthink (but which is probably in fact a better representation of the way "logic" problems tend to confront one in real life).
*For instance, I was thinking that given neb's 106 solution you could add a constraint to the truther puzzle that although they have perfect awareness of the other two people's strategy they are unable to articulate their own. A nice variation. It makes it a bit more difficult at question 2, but the constraint probably actually helps with coming up with the right first question since it eliminates the blind alley I went down (and that type of "self" question is of course a very common trope in the solutions to such problems).
121
... However, if you allow a modification that the balls can be split in half, ...
Or perhaps add another ball known to be good.
Continuing the James/JP puzzle dialogue: I was thinking about how to set it up to "use" all of the 27 possible states. And d'oh, of course, just add the possibility that there is no heavy or light ball--adds one more state and it turns out that for either the 13-ball or the original 12-ball puzzle you literally do nothing differently other than note that you pick it up if the 3rd weighing in the branch where the 1st two weighings balance (the only remaining potentially anomalous ball against a known good one) balances. (In the "must be heavy or light" version it cannot balance.)
The 13-ball puzzle is maybe a bit hokie (or maybe not), but I think for either of them adding that possibility makes for a stronger puzzle. I must admit I am finding this quite satisfying.