Re: Guest Post - What is...

1

The first one I clicked on ["What is a building?" . . . I know what a building is, right? I mean, I'm in one now. Oh, ok, you math types speak a whole different language. But I digress . . .] opens with this sentence:

Buildings were introduced by Jacques Tits to provide a geometric framework for understanding certain classes of groups.

Everything beyond the first paragraph is gibberish to me, but no matter, for I was presented with a philosophical question: Can fruit that hangs so low that it is actually resting on the ground still be called "low-hanging?"


Posted by: MAE | Link to this comment | 10-27-14 8:43 AM
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Are you suggesting that there's something comical about the man to whom we credit the Tits group and the Tits alternative?


Posted by: snarkout | Link to this comment | 10-27-14 8:46 AM
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Are you suggesting that there's something comical about the man to whom we credit the Tits group and the Tits alternative?

This whole "invent your own gender pronouns" thing really has gone too far.


Posted by: MAE | Link to this comment | 10-27-14 8:48 AM
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The linked one ("infinite swindle"), despite the encouraging title, manages to lose me pretty quickly: "Let f be a hyperbolic diffeomorphism". what does "hyperbolic" mean in this context? We must be talking about something with more structure than just a smooth manifold, but what is that structure? I would venture to guess that if they lose me in the first paragraph they're probably losing a large fraction of mathematics graduate students.


Posted by: essear | Link to this comment | 10-27-14 8:52 AM
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They just mean they're exaggerating.


Posted by: heebie-geebie | Link to this comment | 10-27-14 8:56 AM
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1,2: Hmm, maybe there's a deep linkage to the beautiful building blog we've discussed here before.


Posted by: JP Stormcrow | Link to this comment | 10-27-14 8:57 AM
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I liked the Quasicrystal and Strange Attractor articles, both topics I know something about. Being editor to get people to write good intros or overviews must be pretty thankless. Snark about some of these aside, I'm grateful for the effort.


Posted by: lw | Link to this comment | 10-27-14 8:57 AM
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8

ITERATE ALL THE DIFFEOMORPHISMS!


Posted by: JP Stormcrow | Link to this comment | 10-27-14 9:00 AM
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9

They're sort of like colloquium-level talks: no matter how much you tell someone they're supposed to be pitching their talk at a broad audience including people from different subfields and students, three quarters of them are going to dive right into technical mumbo-jumbo and not notice that everyone hates them for it. But maybe a quarter of them turn out to be accessible and then they're usually fascinating.


Posted by: essear | Link to this comment | 10-27-14 9:00 AM
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These should exist in my field, replacing some of the review articles containing single-sentence summaries of 300 different citations.

"What is TGF-Beta signaling?"


Posted by: Cryptic ned | Link to this comment | 10-27-14 9:03 AM
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"What is...a grope?"

No! Bad mathematician!


Posted by: essear | Link to this comment | 10-27-14 9:03 AM
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7: Only snarking because most of us (well me anyways) are just playing the 2001 apes prancing around in front of the big black thing we don't understand. But at some point one of us will be inspired to use a rhetorical jawbone to verbally slay another commenter and then (with a few mere "engineering" problems solved) SINGULARITY! Or maybe Star Child... hard to predict these things.


Posted by: JP Stormcrow | Link to this comment | 10-27-14 9:06 AM
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From the quasicrystal article:

Penrose tilings, the Drosophila of aperiodic order, don't tell us what the structures of real aperiodic crystals are, but they do tell us what aperiodic order can look like.

Hee.


Posted by: heebie-geebie | Link to this comment | 10-27-14 9:09 AM
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I know the background necessary to understand what buildings are for (the p-adics, reductive groups), and yet I have no fucking idea what they are or what they're for.

essear: I don't actually know what a hyperbolic diffeomorphism is, but I think they mean hyperbolic in this sense.


Posted by: Walt Someguy | Link to this comment | 10-27-14 9:13 AM
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9: Mathematicians are the goddamn worst at this. It's a disgrace. What's the point of a talk where maybe one person in the audience can follow it?


Posted by: Walt Someguy | Link to this comment | 10-27-14 9:14 AM
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Motivating statements like the one in 13, explaining why something simplified and unusual is worth noticing, are gold to me. They're more common in talks than in written overviews, leading to the paradox that youtube is actually a good way for me to browse math. Maybe there's a prejudice among some against writing clearly. Oh the person who writes motivation and explanation that I can manage is John Baez.


Posted by: lw | Link to this comment | 10-27-14 9:16 AM
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16: it runs against the glory of being as concise as possible.


Posted by: heebie-geebie | Link to this comment | 10-27-14 9:22 AM
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15: I'd say that's the point. The relationship of the thing signed to the signifier is mediated by the social context. As a side effect some new math might get stumbled upon from time to time.


Posted by: JP Stormcrow | Link to this comment | 10-27-14 9:23 AM
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16: I think that basically mathematicians don't really know why they study the things they study, anymore than chess players know why the horsey makes an L move. Half the time if you ask, you'll get some terrible reason that wouldn't interest anybody, while if you go back and check the history it's actually pretty natural.


Posted by: Walt Someguy | Link to this comment | 10-27-14 9:25 AM
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15. What's the point of a middle aged schlub on a $9000 bicycle? I got the seatpost problem on the nice (but reasonably proced) 2nd hand frame I bought mostly resolved, by the way.


Posted by: lw | Link to this comment | 10-27-14 9:25 AM
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I skimmed a few that I knew would be incomprehensible to me and those I knew I'd understand (the more comp-sci ones). It's nice to see that those entries (natural proof, Turing reducibility, halting probability, data mining, JPEG) are very communicative. This is probably mostly due to the fact that it's a young field and there's less background to be compressed in Magick Runes, but I think the culture of computer science research also emphasizes communicability a bit more, though this can lead to the dual problem - I've listened to several talks and come away with the impression that I pretty much understood the important bits, only to realize later that I didn't - I was just fooled by their good use of analogies.


Posted by: Awl | Link to this comment | 10-27-14 9:26 AM
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18: but it's also a whole lot of cluelessness. A lot of mathematicians truly aren't self-reflective as to whether what they're saying will be comprehensible to their audience.


Posted by: heebie-geebie | Link to this comment | 10-27-14 9:27 AM
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I was just fooled by their good use of analogies

I think you mean "skilled yet evil use of analogies"


Posted by: peep | Link to this comment | 10-27-14 9:29 AM
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20: The same as people who bike leisurely to work on racing bikes wearing fancy racing gear: LARPing.


Posted by: MHPH | Link to this comment | 10-27-14 9:33 AM
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22: I think it's partially a cultural norm. I was told as a grad student that a good seminar talk was comprehensible to a general mathematical audience for 10-15 minutes. It just seemed accepted as normal that seminars were a waste of time for almost everybody in the audience.


Posted by: Walt Someguy | Link to this comment | 10-27-14 9:35 AM
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We're warned to never use equations in talks. This is fairly ridiculous given the current content of the field, but is an interesting and usually rewarding exercise when making a talk.


Posted by: Sifu Tweety | Link to this comment | 10-27-14 9:40 AM
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Yeah, I was told that too. Everyone should understand the first five minutes, half should understand the next thirty minutes, 2-3 should get the next ten minutes, and no one should get the very end.


Posted by: heebie-geebie | Link to this comment | 10-27-14 9:42 AM
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25, 27: that seems absurd.


Posted by: Sifu Tweety | Link to this comment | 10-27-14 9:43 AM
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Now I don't feel bad that I never tried to listen in seminars anyway.


Posted by: Moby Hick | Link to this comment | 10-27-14 9:47 AM
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27: Just as an exercise, you could try putting together a talk that reverses the order.


Posted by: AcademicLurker | Link to this comment | 10-27-14 9:49 AM
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Everyone should understand the first five minutes, half should understand the next thirty minutes, 2-3 should get the next ten minutes, and no one should get the very end.

Jesus.


Posted by: essear | Link to this comment | 10-27-14 10:00 AM
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32

31: On a much larger scale, but I believe David Chase used the same proportions in putting together The Sopranos.


Posted by: peep | Link to this comment | 10-27-14 10:04 AM
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33

I mean, the bit about the end is intended with a wink.


Posted by: heebie-geebie | Link to this comment | 10-27-14 10:05 AM
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34

In my academic neighborhood I've concluded that there's a basic disconnect in what people understand science to be, which disturbingly many people are on the wrong side of. They've internalized some grade-school notion of "science" which says that the goal is to have a theory, by which they mean some set of procedures they can follow to produce a number predicting an experimental result, and if that number matches what is measured you have a party and then go home. My version of what a theory is is that it should give us some understanding, not just some procedure to follow that generates numbers. But there's a surprising amount of hostility toward that viewpoint; some people even go so far as to argue explicitly that "understanding" is meaningless, that if you can calculate a number that's the best possible objective outcome, and that talking in words about what these numbers mean is a pointless thing to do.


Posted by: essear | Link to this comment | 10-27-14 10:05 AM
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In fact I've been strongly warned that if I bring up, in the context of a job interview, the notion that I think we should be uncomfortable with a theory in which some numbers have to cancel to a part in ten to the fifteen for no apparent reason, it would seriously damage my chances at getting the job.


Posted by: essear | Link to this comment | 10-27-14 10:08 AM
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Anyway, in that kind of environment I think the awful talks that are ninety slides of lengthy equations rushed through in sixty minutes are more a symptom of a basic failure to understand what their job is than an independent problem.


Posted by: essear | Link to this comment | 10-27-14 10:09 AM
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They've internalized some grade-school notion of "science" which says that it's all about building death rays.

More seriously, what you're describing in 34 sounds like instrumentalism. I didn't know that it was so popular.


Posted by: AcademicLurker | Link to this comment | 10-27-14 10:12 AM
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Instrumentals are the best.


Posted by: Opinionated Kenny G | Link to this comment | 10-27-14 10:15 AM
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Everyone should understand the first five minutes, half should understand the next thirty minutes, 2-3 should get the next ten minutes, and no one should get the very end.

"Everybody understands Mickey Mouse. Few understand Hermann Hesse. Hardly anyone understands Albert Einstein. And nobody understands Emperor Norton."


Posted by: MAE | Link to this comment | 10-27-14 10:18 AM
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I forget, is that Illuminatus! or the Principia Discordia?


Posted by: Ginger Yellow | Link to this comment | 10-27-14 10:25 AM
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The former.


Posted by: Awl | Link to this comment | 10-27-14 10:30 AM
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I believe it is Illuminautus! quoting one of the authors of the Principia Discordia.


Posted by: MAE | Link to this comment | 10-27-14 10:30 AM
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I haven't clicked on all of the "What is . . ." links yet, but do any of them answer the question "What is the ideal number of cats to have?" I maintain that c = 2. Mrs. E., on the other hand, is proposing that c ≥ 4. I counter that that is crazy talk. She counters that I am an insensitive lout who just doesn't understand.


Posted by: MAE | Link to this comment | 10-27-14 10:44 AM
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That's definitely crazy talk.


Posted by: Ginger Yellow | Link to this comment | 10-27-14 10:47 AM
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45

Mrs. E = c^4?


Posted by: heebie-geebie | Link to this comment | 10-27-14 10:49 AM
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46

The answer is obviously c = no get a dog.


Posted by: MHPH | Link to this comment | 10-27-14 10:49 AM
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47

1-2 cats is the right number to start with. But then you're allowed to recklessly fall in love with individual cats and acquire them, so that the total gets arbitrarily large.


Posted by: heebie-geebie | Link to this comment | 10-27-14 10:50 AM
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48

Nobody wants a damn dog, MHPH.


Posted by: heebie-geebie | Link to this comment | 10-27-14 10:50 AM
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49

Only people who hate love and joy don't want dogs.


Posted by: MHPH | Link to this comment | 10-27-14 10:56 AM
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Mrs. E = c^4?

At times, yes.

For a long time we had two cats, and then we had one cat, and for the past year or so we've had no cats. And now we're planning on ending our period of catlessness. Based on prior experience with two cats, I think two is the Goldilocks number. But Mrs. E is (in my opinion) currently like the proverbial hungry person at the grocery store. (And I mean that in the analogy-ban-violating way; Mrs. E. is not contemplating eating any cats.)


Posted by: MAE | Link to this comment | 10-27-14 11:00 AM
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47.last: You should run any proposed sequence of cat ownership against the Kitty Convergence Test.


Posted by: JP Stormcrow | Link to this comment | 10-27-14 11:31 AM
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Mrs. E needs to be allowed the space of future acquisitions. You win currently - get two cats. Then adopt those adorable, purring, strays as they show up and adopt you.


Posted by: heebie-geebie | Link to this comment | 10-27-14 11:33 AM
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Mrs E = Catless Everdeen?


Posted by: Ginger Yellow | Link to this comment | 10-27-14 11:35 AM
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The ellipsis in the post title are kind of driving me crazy in the side bar. I keep having the passing thought that it's truncated because I need to widen my browser.


Posted by: heebie-geebie | Link to this comment | 10-27-14 11:46 AM
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I was once going on about Marx somewhere on the Internet, and somebody probably much more radical than me asked me why the transformation problem was important. I said that, since we were discussing the theory of value, I did not need an answer. That was a focus of academic attention for over a century. Somehow this was not considered an acceptable answer.

I am amazed at those who can explain deep ideas to popular audiences.


Posted by: Robert | Link to this comment | 10-27-14 1:17 PM
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My takeaway from these is that no matter how much math I learn, it isn't enough. I'm fractally ignorant.


Posted by: Eggplant | Link to this comment | 10-27-14 1:17 PM
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57

Adult cats generally don't get along with each other and stress each other out. If you have 3+ cats it should be ones that knew each other as young kittens. Especially if your cats are inside all day. They would prefer to each have a territory.

I have been converted to this way of thinking by this interesting book.


Posted by: Cryptic ned | Link to this comment | 10-27-14 1:45 PM
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The "What is..." format is often just too short to explain what they're setting out to explain.

I don't understand why the swindle article doesn't start out with the easiest application, which is that if you tie a knot in a rope which cannot be untied (without pulling the ends back through the knot) then there's no way to tie a second knot later in the rope such that the combined knot can be untied. Suppose you can cancel out knot A by tying knot B next to it. Then look at the infinite knot where you tie knot A then B then A then B etc. On the one hand, by canceling each A with the next B, this knot is trivial. On the other hand, by canceling each A with the preceding B, this knot is the same as A. But since A can't be untied that's a contradiction. So there's no way to cancel knots.


Posted by: Unfoggetarian: "Pause endlessly, then go in." (9) | Link to this comment | 10-27-14 1:47 PM
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I would have never even considered that as a question that could or should be asked.


Posted by: Moby Hick | Link to this comment | 10-27-14 1:48 PM
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I completely agree that just dropping in "hyperbolic diffeomorphism" with no explanation is ridiculous. I *think* what they mean is that you realize your surface as a quotient of the upper half-plane, so you realize your diffeomorphism as a diffeomorphism of the upper half-plane. That's just a two-by-two real matrix. Such a nontrivial matrix either has two distinct complex conjugate eigenvalues (elliptic), a repeated eigenvector (parabolic), or two distinct inverse real eigenvalues (hyperbolic).

http://en.wikipedia.org/wiki/SL2(R)


Posted by: Unfoggetarian: "Pause endlessly, then go in." (9) | Link to this comment | 10-27-14 1:52 PM
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58: Is there a version of that proof that doesn't appeal to infinite numbers of knots? I'm suspicious (unjustifiably, I'm sure) of a proof that depends on the order of summation of an infinite series


Posted by: Eggplant | Link to this comment | 10-27-14 1:54 PM
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57.1 is not my experience, but ours are roughly the same age. They're unrelated and were acquired a year apart.

2 pets per adult, 1 pet per child is my personal household limit. With more, I feel like there's not enough lap space or attention to go around.


Posted by: ydnew | Link to this comment | 10-27-14 1:58 PM
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The Projective Structure article seems interesting to me, but I can get through about the first page before there's a cascade of unfamiliar terms that render it unreadable.


Posted by: Eggplant | Link to this comment | 10-27-14 2:13 PM
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61: The infiniteness is the entire point of the swindle. A "swindle" is a situation where the argument 1 = 1-1+1-1 \ldots =0 makes sense. You're right to be skeptical, there's a reason it's called a "swindle." In the case of knots one needs to take care to see that infinite knots make sense and that the notion of untying carries over nicely.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 10-27-14 2:24 PM
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60: a diffeomorphism of the upper half-plane. That's just a two-by-two real matrix.

I'm confused. Aren't you assuming it's an isometry, not just a diffeomorphism, when you say that?


Posted by: essear | Link to this comment | 10-27-14 2:49 PM
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66

Assume a spherical knot....


Posted by: Moby Hick | Link to this comment | 10-27-14 2:53 PM
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Also, if we're to assume our space can be realized as a quotient of the upper half plane, that puts some restrictions on the closed surface S we started with, no? Genus 2 or higher spaces can inherit a metric from the upper half plane, but spheres and tori don't.


Posted by: essear | Link to this comment | 10-27-14 2:56 PM
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This would seem to be the relevant definition. It does seem to require a metric.


Posted by: essear | Link to this comment | 10-27-14 3:38 PM
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65: I meant to say that the diffeomorphism is somehow automatically isotopic to an isometry (I'm not sure if that's true, but it's the kind of thing that's true in these settings).

66: That's a good point, the image is a torus. On the other hand, 68 contradicts 67. As you say, the torus doesn't have a hyperbolic structure in that sense.

I think what the author means is what's more commonly called an Anosov diffeomorphism.


Posted by: Unfoggetarian: "Pause endlessly, then go in" (9) | Link to this comment | 10-27-14 5:04 PM
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Speaking of mathy things I enjoyed this recent article about the Tracy-Widom distribution in Quanta Magazine, although I'm a little wary because the Quanta articles about things I know well generally seem to be subtly but importantly wrong about things.


Posted by: essear | Link to this comment | 10-27-14 5:18 PM
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When I got to the part about third-order phase transitions I had a brief moment of thinking "maybe no one's gotten around to connecting it to the Gross-Witten transition at large N?" but of course that was a few paragraphs later.


Posted by: essear | Link to this comment | 10-27-14 5:19 PM
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