March 2016 - mathfun@mailman.xmission.com

[math-fun] conical fallacy
by Bill Gosper 10 Mar '16

10 Mar '16

Where is the misapplication of integral calculus in the following?: While preserving its edge, deform the base of a circular, say, cone to make it convex or concave, with area A. Then the volume formula should remain V = A h/3, because you can decompose it into a tapered series of curved plates dV = A (z/h)^2 dz. And I am the Virgin Mary. --rwg

7 9

[math-fun] More "morons-in-a-hurry" --- Maple UI
by Fred Lunnon 09 Mar '16

09 Mar '16

Maple's numerical equation solver does have some powerful features, available to any user equipped with persistance sufficient to battle through thickets of inconsistent user interface in order to access them. While aware of all this, my jaw still dropped at this latest specimen of machine intelligence: savour at leisure! fsolve({x^2 + y^2 = 1}, {x, y}); Error, (in fsolve) number of equations, 1, does not match number of variables, 2 [ The machine can count to two. Let us attempt to hoodwink it ... ] fsolve({x^2 + y^2 = 1, (x^2 + y^2)^2 = 1^2}, {x, y}); fsolve({(x^2+y^2)^2 = 1, x^2+y^2 = 1}, {x, y}) [ Sometimes it just repeats (a subtly re-interpreted version of) the input when it can't find a solution. Or instead returns a null result, and too bad if the user program guesses wrong. Whatever, we were evidently not devious enough ... ] fsolve({x^2 + y^2 = 1, x^4 + 2*x^2*y^2 + y^4 = 1}, {x, y}); {x = 0.9882233619, y = -0.1530182571} [ Wonderful --- so it could find an approximate numerical solution after all! Then why not just bl00dy well get on with the job first off, instead of wasting user time and temper with all the previous bullshit? ] Fred Lunnon

1 0

[math-fun] Sedol loses game 1: In defense of the final move
by Jim Gillogly 09 Mar '16

09 Mar '16

While I agree with Warren D. Smith's observation that game programs can have bugs that may be triggered by playing the game out (which I simplify to "You can't win by losing."), there are practical and abstract reasons that resigning a good move. On the practical side, go programs are best in the yose (end-game) phase, where plausible moves are much more limited than in the opening or middle game. As Michael Redmond (the 9-dan commentator on the YouTube stream) observed, there are programs on the go servers that can solve even very difficult life and death problems. In the end-game there's a dance between the players where they tidy up the boundaries between settled groups in an order determined by maximizing relative value and retaining initiative ("sente"). There's an optimal order, and Lee Sedol knew from AlphaGo's five published games that the program could handle it. Given that confidence (misplaced or not), tactically it made sense for Lee to save his energy for the next game in the match, which will start 24 hours after the first one. Playing tournament-length matches on subsequent days is hard -- it's rather like a baseball pitcher pitching two days in a row -- and Lee Sedol had just gotten off a grueling string of games in the Nongshim Cup where he'd played games on the 2nd, 3rd, 4th and 5th of March against top competition. My pitch for an abstract reason is more... abstract. He could read on the board that he had lost by a few points - less than the komi (the bonus given to the white player to make up for the advantage of black's first move) but still obvious to a top professional. All the top go players as well as duffers like me will be studying this game for generations. Playing it out and hoping for the box to blow a transistor would be like completing a masterpiece oil painting and then signing it across the center in red. To get a feel for this, read "The Master of Go" by Yasunari Kawabata. It's better to lose a uniquely ground-breaking game played brilliantly on both sides than win by a bug. Lee Sedol still has four games to go - it appears that they were evenly matched, so there's still a good chance that he can win the match -- especially if he wins in the middle-game, which is his forte. -- Jim Gillogly

2 1

[math-fun] A question about the "is this prime?" game
by Christian Lawson-Perfect 09 Mar '16

09 Mar '16

This week I made a game which has turned out to be like crack to maths fans - http://isthisprime.com/game/. You're shown a number, and you have to decide if it's prime or not. The aim is to correctly sort as many numbers as possible within a minute; the game ends as soon as you get one wrong. So, I thought that would appeal on its own merits to math-funsters, but I have a question which occurred to me while talking about it with Colin Wright: since primes become rarer the higher you go, at what point is just clicking "No" as good a strategy as doing any thinking? I suppose I could rephrase and slightly change the question to: if the maximum number you can be shown increases by a factor of X each time you make a correct decision, what's the expected score of a strategy that just clicks "no" every time? And finally, I'm collecting data on each attempt made at the game. I expect to be able to come up with some interesting statistics about people's intuitions on primality. So far, 51 seems to be by the far most "primey" composite, before factoring in the likelihoods of particular numbers being shown.

5 6

[math-fun] Packing a 2-by-n rectangle with disks
by James Propp 09 Mar '16

09 Mar '16

I'd like a mini-bibliography on the problem of packings disks of diameter 1 in a 2-by-n rectangle. So far all I've found is problem 211 in "The Inquisitive Problem Solver" (by Vanderlind, Guy, and Larson --- hi, Richard); those authors credit Eugene Luks for passing along the problem, but they don't say who first noticed/proved that you can fit more than 2n disks of unit diameter into a 2-by-n rectangle. In addition to seeking the original source for this paradox, I'd like to know of places that write about it clearly. (Is it somewhere in Gardner's works?) Also, the solution provided by Vanderlind et al. isn't the optimal packing; as was recently discussed in this forum (Bill Gosper being the discussant who comes to mind), one can do better with a pattern that repeats every 6 disks. Is that pattern published somewhere? For that matter, where is that picture? Someone posted a link to it, but Google won't help me find it. Thanks, Jim

4 4

[math-fun] Sedol loses game 1. Humankind=toast?
by Warren D Smith 09 Mar '16

09 Mar '16

Lee Sedol may be a great go player, but I don't think he's a very good software tester. Specifically, I criticize his last move -- resigning! I would advise playing it out well beyond where most humans would agree to stop play. Probably won't work, but you don't find bugs in software by just assuming it must be fine. You find bugs by pushing it. I think there is a consensus that no previous go program has managed to "solve" the problem of exactly when the game is over and even in positions where go masters resign, a player like me often cannot even tell who is ahead (!) and so even positions masters consider easy, are by no means easy. And it isn't so easy to write software like this without bugs. In the Kasparov-DeepBlue match #2, which K lost 3.5 to 2.5, Kasparov resigned one game in a position where he could have forced a draw. (Which would have changed match outcome to 3-3.) Even I, who was 800 elo dumber than Kasparov (if I'm generous to myself) saw the rough outlines of that draw line and would have gone for it instead of resigning. I quite likely would have failed (since it required some precise play, which I might not have been able to pull off) but it would have been better than resigning, and Kasparov should have been strong enough to find the right moves in that line. So why did he resign? He "explained" that the computer had outplayed him all game, was clearly super grandmaster, and therefore it was inconceivable the computer had missed that comparatively obvious draw line, so it wasn't even worth trying. Say WHAT? The reality, which Kasparov did not appreciate, is perpetual check draws were a fairly well known tough issue for computers. Hard for them to see. And in fact, the computer had not seen it. And what humans find are "easy" and "hard" and "obvious" positions to handle, are not necessarily the same as what computers find easy and hard and obvious to handle. And computers have in the past experienced hugely embarrassing bugs in matches with humans and with other computers, and alphago has been little tested by anybody external to google. Another game, Kasparov decided to play some opening he was not familiar with, and blundered in a book position into a book trap loss. Apparently K figured the computer knew his favorite openings since they'd input all or most of K's games and had the computer pre-analyse them. Also dumb choice. The truth was, computers at that time were known not to be as strong as correspondence chess masters, i.e. DeepBlue lost a correspondence match with Mike Valvo... the longer the time to think, the worse chess computers did versus humans; but in fast games the computers are supreme. Because the humans have (or anyhow certainly at that time had) effectively a smaller growth factor C in their exponential: TimeUsed=C^DepthSearched. So in my opinion, if K had not employed stupid anti-computer strategy, the truth was he probably still would have been a bit stronger than DeepBlue even in the 2nd match. It also is known that in at least one move of one of the K-D matches, D basically crashed due to a bug, and played a "safety move" due to some bug-recovery fallback routine, which luckily for it happened to be an acceptable move. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

1 0

[math-fun] math puzzles for very young enthusiasts
by Fred Kochman 08 Mar '16

08 Mar '16

One of my daughters writes, One of my co-workers recently bought Smullyan's Lady or the Tiger book for his daughters, but he said that it seems to be too difficult so far. (To be fair, his oldest daughter is only 8 years old.) His kids seem to love mind-bending puzzles though - do you know of any logic books that would be better for really young kids? Any suggestions? Probably "logic" could be broadly interpreted. Thanks, Fred Kochman

8 10

[math-fun] AlphaGo game time
by rcs＠xmission.com 08 Mar '16

08 Mar '16

Game 1 of the Go match starts tonight (Tuesday March 8, 9pm MST here in Utah). One link is https://www.youtube.com/c/DeepmindAI which points to the link below from Jim Gillogly. > The go match will be at 1300 KST on the 9th; that's 2300 EST today, 2000 PST, and 1800 HST (my current time zone). There's a countdown clock on https://www.youtube.com/watch?v=vFr3K2DORc8 that currently shows 10:18:50 before they start the live stream half an hour before the match. ---- Rich

1 0

Re: [math-fun] Ray Tomlinson, 74 (from Bill Ackerman)
by rcs＠xmission.com 08 Mar '16

08 Mar '16

[this is from Bill Ackerman --rich] Date: Tue, 8 Mar 2016 09:47:11 -0500 Subject: Re: [math-fun] Ray Tomlinson, 74 From: Bill Ackerman <wbackerman(a)gmail.com> rwg> I met him at the RLE PDP-1, mid 60s, where, I seem to remember, he worked on myoelectric prosthetics. He could chug a 16 oz Coke and and belch RensselaerPolytecnicInstitute. --rwg I remember when email was a disappointing outcome. :SEND <user> would interject (MAIL) when <user> was not logged in. Nowadays :send is called live chat. <wba> He was my mentor and fellow hacker at the PDP-1 in the late 60s. I don't remember myoelectric prosthetics; he was in the RLE Speech Group, working on speech synthesis. He had a hardware engine controlled by the computer. An early version was called POVO, I didn't know what that stood for. It wasn't very good. A later device was called SPASS, the last 4 letters of which stood for "pole-analog speech synthesizer". Its voice was quite realistic. It's standard demo said, in high-quality speech, "This ... is the voice of SPASS." That kind of voice quality was nearly unheard-of in the 60s. I asked him if he could make it say "foo", but he said that fricatives were very hard, and it would come out sounding like "voo". He also wrote a rats-eye-view maze game that was very sophisticated for the capabilities of the PDP-1.

1 0

[math-fun] UK GCHQ finally declassifies Ellis papers on public key crypto
by Henry Baker 08 Mar '16

08 Mar '16

FYI -- Q: So when will NSA declassify the rest of Shannon's WWII work? The Ellis papers The possibility of secure non-secret digital encryption (PDF, 3.51MB) http://www.gchq.gov.uk/SiteCollectionDocuments/CESG_Research_Report_No_3006… The possibility of secure non-secret analogue encryption (PDF, 5MB) http://www.gchq.gov.uk/SiteCollectionDocuments/CESG_Research_Report_No_3007…

2 1