July 2018 - mathfun@mailman.xmission.com

[math-fun] Is zero “weakly positive”?
by James Propp 27 Jul '18

27 Jul '18

f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0? Does anyone use the phrase “weakly positive” in this way? Jim Propp

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[math-fun] Deep learning vs deep positions
by Bill Gosper 27 Jul '18

27 Jul '18

Does anybody know how Alpha Zero would fare on RKG's endgame composition in https://en.wikipedia.org/wiki/Richard_K._Guy ? Put another way, how would RKG's intended solution fare against Alpha Zero? Similarly, can Alpha Zero win those computer-generated "hundred move rule" positions? https://www.chess.com/forum/view/fun-with-chess/longest-mate-official---mat… --rwg

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[math-fun] Worm warning & Netiquette
by Keith F. Lynch 27 Jul '18

27 Jul '18

Fred Lunnon <fred.lunnon(a)gmail.com> wrote: > Further observation suggests that this particular `worm' is growing > only linearly rather than exponentially. However, the potential > for exponential growth --- eg. where some mail-server replaces an > unrecognised character code by two copies of the same --- remains > when users attempt to employ rich codes, and might quickly bring > down large parts of the list network, particularly if the bug lurks > on the central list server. > [Two characters may not be a long string by itself; but after (say) > 30 replies, a billion characters concealed beneath your top posting > becomes bad news!] The longest I've seen in the wild is the following: =C3=83=C2=83=C3=82=C2=83=C3=83=C2=82=C3=82=C2=A2=C3=83=C2=83=C3=82=C2=A2=C3=83=C2=82=C3=82=C2=82=C3=83=C2=82=C3=82=C2=AC=C3=83=C2=83=C3=82=C2=A2=C3=83=C2=82=C3=82=C2=84=C3=83=C2=82=C3=82=C2=A2 That started as a single character. Puzzles: What character? What are the transition rules? How many levels deep was it quoted? I haven't seen anything like that on this list. Instead, non-ASCII characters get turned into question marks. However, occasionally someone quotes, not just all of a message, but all of a multi-message digest. If the average digest contained more than one message that quotes all of a recent previous digest, then messages would indeed grow exponentially in size. This is not a new problem. The first email lists to be digestified were SF-Lovers and Human-Nets, 38 years ago. Within a month, the problem of people quoting whole previous digests when replying to one message was solved by placing a line in the header of the digest that nobody would be have a legitimate reason to quote, and rejecting any submission that contained that line. Perhaps our moderator could start doing that. By 37 years ago, text email was pretty well figured out. And it, along with other "netiquette," stayed figured out for more than a decade. Unfortunately, the net was then flooded with newbies who arrived more quickly than they could assimilate into Internet culture, and the result was chaos. (Look up "Eternal September.") The purpose of quoting is to establish context for your reply. A good rule of thumb is to never quote more than you would retype or paraphrase if the automatic quoting function was broken. Quoting all of a message is like soaking a textbook in highlighter ink. Especially if it's a very recent message, which everyone has recently read. Also, since in English we read top to bottom, your response should come after what you're quoting, not before it. It should seldom be necessary to quote more than two levels deep. And of course you should always use angle brackets to make it clear what is and isn't being quoted. I recently posted a denunciation of IQ. I argued that just because someone is very smart in one field doesn't mean they aren't much less smart in another. I was thinking of (among other things) this list at the time. To put it bluntly, there are lots of brilliant mathematicians here who are so bad at writing readable non-bloated emails that they may qualify as idiot savants (idiots savant?).

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Re: [math-fun] Deep learning v deep positions
by Guy Haworth 27 Jul '18

27 Jul '18

I didn't see the start of this thread so don't know if it's just about Go or just about Alpha<x>. However, we have the advent of chess engines which rely more (than traditionally) on intelligent rather than deep search. Neural networks are challenging traditional 'alpha-beta cut-off' search, not just with AlphaZero but with LeelaChess and one other engine, making its first appearance in TCEC, Season 13. TCEC13, http://tcec.chessdom.com/live.php , should have kicked off on or before August 3rd according to my latest advice. The two engines above will be using 2x GTX 1080ti GPUs but not Google's TPUs. The improving LeelaChess may arguably be 'better than human' at chess but has not yet been competitive with TCEC engines in its lowest division. g

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Re: [math-fun] Is zero “weakly positive”?
by Dan Asimov 27 Jul '18

27 Jul '18

"We" *who* says that? I don't recall hearing it. ----- we sometimes say that a is strictly positive as a way of saying a>0 ----- —Dan

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Re: [math-fun] Equation plotter
by Dan Asimov 27 Jul '18

27 Jul '18

So little time, so many solutions. —Dan ----- ... but x = x throws it for a loop. -----

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[math-fun] Equation plotter
by David Wilson 27 Jul '18

27 Jul '18

Just so you knows, I get a lot of mileage out of this on-line equation plotter: http://www.cs.cornell.edu/w8/~andru/relplot/

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[math-fun] Machinoid π formulas
by Bill Gosper 26 Jul '18

26 Jul '18

Fooling with pslq (again) In[1209]:= 3 ArcTan[1/7] + 2 ArcTan[2/11] // FullSimplify (or ArcTan[1/5.5]) Out[1209]=π/4 Holy cow! Isn't that slightly better (at least for a true binary computation) than In[1208]:= 4 ArcTan[1/5] - ArcTan[1/239] // FullSimplify Out[1208]= π/4 with which all the old decimalization records were set? Then I stumbled upon In[1210]:= 5 ArcTan[1/7] + 2 ArcTan[3/79] // FullSimplify Out[1210]=π/4 (in http://www.cs.utsa.edu/~wagner/pi/ruby/pi_atan.html ) Euler was inhuman. I suspect the adherence to Machin was because, even on binary machines, people did the whole computation base 10^10 to avoid a big conversion later. Decimal. Feh. --rwg

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[math-fun] photomath
by Thane Plambeck 26 Jul '18

26 Jul '18

i suppose i'm last person to know about this, but .... i wrote this on an index card https://www.flickr.com/photos/thane/28755638457/in/dateposted-public/ then took a photo of it using an iphone app i just installed called photomath and got this (fragment of a) detailed solution in less than a second https://www.flickr.com/photos/thane/41835897350/in/dateposted-public/ don't ask me what this thing can do....i just heard about it just now. -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] was: 3D printers & musical instruments; now is: formerly 3D printers & musical instruments
by Dan Asimov 26 Jul '18

26 Jul '18

----- Airplanes don't have feathers. ----- It's interesting that, mathematically, this is just the dual of ----- Down pillows don't fly. ----- —Dan

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