March 2017 - mathfun@mailman.xmission.com

[math-fun] Strange Gasket Sums
by Bill Gosper 19 Mar '17

19 Mar '17

I've just been reminded that Julian and I wrote them up about four years ago for G4G10: gosper.org/Article.pdf If you don't like seriously freaky formulas, just look at the pictures. --rwg

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[math-fun] http://www.conwaylife.com/wiki/R-pentomino
by Bill Gosper 19 Mar '17

19 Mar '17

relates how it led our RKG to discover the glider. I just added a line explaining why it SHOULD have led the MIT AILab group to discover the glider gun. --rwg

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[math-fun] Panel puzzle
by James Propp 18 Mar '17

18 Mar '17

You can join four isosceles right triangles along hinges (I use tape) to form a square, and then join four such square panels (again with tape) to form a long rectangle, and lastly join the first and last panels together with tape to form a closed band. If you color the two sides of the band with different colors, it's a fun puzzle to turn the band inside out, exchanging the colors. I learned about this in the 80s, and amused myself by learning how to do the moves behind my back. Does anyone know the name and/or provenance of this puzzle? Jim

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[math-fun] OECP? music-fun?
by James Propp 16 Mar '17

16 Mar '17

This is off-topic but since so many mathematicians love music I thought some of you might be able to provide useful leads: Is there anything like an Online Encyclopedia of Chord Progressions and/or a forum for "recreational musicology"? Of course, trying to list occurrences of IV - V - I in Western music would be as impossible as listing occurrences of 1,3,5,7,9,... in the mathematical literature, but less common chord progressions might be trackable. For instance, if you listen to the "Blazing Saddles" theme ( https://m.youtube.com/watch?v=hzRmp-O496Y ; 00:41-00:42 and elsewhere) and the "Big Country" theme (https://m.youtube.com/watch?v=AQTH3a0mjR8 ; 00:04-00:05 and 00:44-00:45 and elsewhere) you'll hear an C-major chord going to an A-major chord with a suspended E in the melody (before the song goes back to the D major tonic). How did VII-flat - V - I become a cowboy movie cliche? Does it trace back to actual cowboy music, or is it purely a Hollywood creation? And what are the antecedents in classical music? There may be a fun story here, but how would one search the internet to find it? Jim Propp

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[math-fun] 3rd Law of Thermodynamics proved mathematically
by Henry Baker 16 Mar '17

16 Mar '17

FYI -- "[We] place ultimate bounds on the ***speed*** at which information can be erased." "This tape with self-destruct in five seconds. Good luck, Jim." -- Mission Impossible TV series. We should now be able to determine an upper bound on how much information was stored on the tape. http://www.nature.com/articles/ncomms14538 http://www.nature.com/articles/ncomms14538.pdf A general derivation and quantification of the third law of thermodynamics LluÃs Masanes & Jonathan Oppenheim Nature Communications 8, Article number: 14538 (2017) doi:10.1038/ncomms14538 Quantum information Thermodynamics Received: 31 March 2016 Accepted: 09 January 2017 Published online: 14 March 2017 Abstract The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased.

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Re: [math-fun] OECP? music-fun?
by Henry Baker 14 Mar '17

14 Mar '17

I've always wanted to use Google to search for pieces of melodies as well as chords. The idea would be to type in a short midi sequence, and Google would find it (or a close match) in another midi file. More advanced: Google would find the sequence in mp3 files, mp4 files, etc. Perhaps Google has already done this? Perhaps Google has been screwed by the music industry? After all, who wants to make it trivial for copyright lawyers to find musical precedents for every big hit song? --- Another thought that's been in the back of my mind for at least 20 years: *midi sound "compression"*. The idea isn't to get the greatest compression, but to get the best musical approximation from a .wav file. As you know, a digital midi player basically cues up a finite-length "sound" from a "sound font" to be added into the output at the time and volume specified by the midi note. There are additional complexities, but this gives you a minimal midi player. [Mathematically, the sound output .wav file is a *polynomial*, where the sample "A" is the coefficient of A*x^t, and the sample A appears at time t. A midi score of one octave is a polynomial in 13 variables: 12 notes and the time "t". A sound font contains 12 polynomials in "t" which provide the samples for that particular note. The score is "played" by evaluating the score at the 12 different note polynomials. Note variables are C,B,B_,A,A_,G,G_,F,E,E_,D,D_; time variable is t. (%i1) a; 2 (%o1) a2 T + a1 T + a0 [rather short 440 A sample] (%i2) b; 2 (%o2) b2 T + b1 T + b0 [rather short B sample] (%i3) c; 3 (%o3) c2 T + c1 T + c0 [rather short C sample] (%i4) LittleLamb; 9 8 7 6 5 4 3 2 (%o4) B T + B T + B T + C T + C T + C T + B T + A T + B T + C (%i5) LittleLamb,A=a,B=b,C=c; 6 3 5 3 4 3 3 (%o5) T (c2 T + c1 T + c0) + T (c2 T + c1 T + c0) + T (c2 T + c1 T + c0) + c2 T 9 2 8 2 7 2 + T (b2 T + b1 T + b0) + T (b2 T + b1 T + b0) + T (b2 T + b1 T + b0) 3 2 2 2 2 + T (b2 T + b1 T + b0) + T (b2 T + b1 T + b0) + T (a2 T + a1 T + a0) + c1 T + c0 (%i6) ratsimp(%,T); 11 10 9 8 (%o6) b2 T + (b2 + b1) T + (c2 + b2 + b1 + b0) T + (c2 + b1 + b0) T 7 6 5 4 + (c2 + c1 + b0) T + (c1 + c0) T + (c1 + c0 + b2) T + (c0 + b1 + a2) T 3 2 + (c2 + b2 + b0 + a1) T + (b1 + a0) T + (c1 + b0) T + c0 (%i7) ] A Midi sound compression algorithm would be given an a priori "sound font" file which is an a priori "dictionary" of sounds. The sound compression algorithm would be charged with figuring out which sequence of these sounds at what volumes would produce the closest sound to the given sound file. Does this program exist? At 08:54 AM 3/14/2017, James Propp wrote: >This is off-topic but since so many mathematicians love music I thought >some of you might be able to provide useful leads: Is there anything like >an Online Encyclopedia of Chord Progressions and/or a forum for >"recreational musicology"? > >Of course, trying to list occurrences of IV - V - I in Western music would >be as impossible as listing occurrences of 1,3,5,7,9,... in the >mathematical literature, but less common chord progressions might be >trackable. For instance, if you listen to the "Blazing Saddles" theme ( >https://m.youtube.com/watch?v=hzRmp-O496Y ; 00:41-00:42 and elsewhere) and >the "Big Country" theme (https://m.youtube.com/watch?v=AQTH3a0mjR8 ; >00:04-00:05 and 00:44-00:45 and elsewhere) you'll hear an C-major chord >going to an A-major chord with a suspended E in the melody (before the song >goes back to the D major tonic). How did VII-flat - V - I become a cowboy >movie cliche? Does it trace back to actual cowboy music, or is it purely a >Hollywood creation? And what are the antecedents in classical music? There >may be a fun story here, but how would one search the internet to find it? > >Jim Propp

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[math-fun] Acta Mathematica
by Hans Havermann 12 Mar '17

12 Mar '17

It appears that since the end of January, by arrangement with the Institut Mittag-Leffler, International Press now provides fully open online access to the entire content of Acta Mathematica — from its first issue of 1882 to the most recent: http://projecteuclid.org/all/euclid.acta

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[math-fun] Draft of my March 2017 blog post
by James Propp 11 Mar '17

11 Mar '17

I started writing a new draft titled "Band saw blades, bedbug zappers, rubber bands and me" and would love to get your feedback. I plan on publishing it on March 17. Suggestions for references, and comments of all kinds, are welcome. I appreciate candid criticism from people who are sympathetic to my aims but think I've fallen short of them. My prose style is designed to make the material accessible, but my breeziness should not be interpreted as indicating indifference to scholarly correctness. Keep in mind that all math-fun feedback goes into one mail-feed, so I won't know whose feedback is whose unless you sign your comment. Also, all substantive suggestions that I use will be acknowledged (unless you specifically ask me not to do this). Please leave your feedback here: https://mathenchant.wordpress.com?p=1521&shareadraft=58c45d5546f5a Title: Bandsaw blades, bedbug zappers, rubber bands and me Beginning: I have trouble getting a feeling for what it's like to live in three-dimensional space. I mean, I do live in three-dimensional space, and I get by without hurting myself too badly too often, but I feel like I'm missing a lot of what's going on. ... Read more: https://mathenchant.wordpress.com?p=1521&shareadraft=58c45d5546f5a Thanks, jamespropp

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Re: [math-fun] Ag, a scriptable anagram generator
by Tomas Rokicki 08 Mar '17

08 Mar '17

Boy, Andrew, if you called me any of those names I don't think I'd continue to read the rest of your message! Very well done. On Wed, Mar 8, 2017 at 3:08 PM, Andrew Trevorrow <andrew(a)trevorrow.com> wrote: > Mostly to GERBIL SLOP, DIVA MOANS, ELDER NOB, NUN FONDLER, > and any other keen anagram fans... > > You might like to try out Ag, my scriptable anagram generator: > > http://ag1.sourceforge.net/ > > It's free, open source and runs on Win/Mac/Linux. Scripting is > supported via an embedded Lua interpreter. There are example > scripts for generating conundrums, word ladders, palindromes, > and crosswords. > > Have fun, > Andrew Trevorrow (aka OVERT WORD WARREN) > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > -- -- http://cube20.org/ -- [ <http://golly.sf.net/>Golly link suppressed; ask me why] --

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[math-fun] Ag, a scriptable anagram generator
by Andrew Trevorrow 08 Mar '17

08 Mar '17

Mostly to GERBIL SLOP, DIVA MOANS, ELDER NOB, NUN FONDLER, and any other keen anagram fans... You might like to try out Ag, my scriptable anagram generator: http://ag1.sourceforge.net/ It's free, open source and runs on Win/Mac/Linux. Scripting is supported via an embedded Lua interpreter. There are example scripts for generating conundrums, word ladders, palindromes, and crosswords. Have fun, Andrew Trevorrow (aka OVERT WORD WARREN)

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