March 2015 - mathfun@mailman.xmission.com

Re: [math-fun] Computational effort
by Henry Baker 20 Mar '15

20 Mar '15

Some non floating point units of computational effort: Bitcoin POW (SHA-256 hashes/second) Other POW's https://en.wikipedia.org/wiki/Proof-of-work_system Password cracking Most of these problems are "embarrassingly parallel". Perhaps someone here has some ideas for a non-embarrassingly-parallel unit of computational effort. At 07:16 AM 3/20/2015, James Propp wrote: >I don't know what the relevant units of computation are --- floating-point >operations are the ones I've heard about most, but what if you're not using >floating point? --- but I'm wondering if anyone has tried to quantify "how >much computing" took place in (a) code-breaking at Bletchley Park, (b) the >Manhattan Project, and (c) the Apollo space program. > >It seems likely to me that my laptop, running some silly number-crunching >problem in Mathematica and returning an answer after six hours that I could >probably have figured out in my head if I'd thought a little bit more >before jumping in to write some code, has them all beat. > >What do you think? > >(And while we're on the subject: What's the canonical example of wasted >computational effort? Isn't there some well-known old story of someone who >had an early computer calculate the determinant of a singular matrix?) > >Jim Propp

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[math-fun] Fwd: pentagram snowflakes in a pentagram
by Bill Gosper 20 Mar '15

20 Mar '15

An attachment for the lucky nonvictims of xmission.com: [The mere presence of this attachment violated the idiot xmission.com byte limit, even though it would delete it no matter what size. Hence, this duplicate mailing.] Else gosper.org/pentarast.png In Minskys and Trinskys, Jack Holloway calls these figures rastermen. Rorschach: Do you see fat guys leaning left, or skinny guys leaning right? If you see fat guys leaning right, you're too empathetic--they're actually facing away from you. --rwg

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[math-fun] Resistence is futile
by Bill Gosper 19 Mar '15

19 Mar '15

It is absolutely ridiculous to impose both "irresistible" and "irresistance". The former is consistent with Latin resistere, so I am irresistent to some orthographic civil disobedience. --rwg

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[math-fun] a self-affine 3-dimensional tile
by Joerg Arndt 19 Mar '15

19 Mar '15

After some considerable fighting I managed to obtain a few rules to generate tilings of the cubic 3D grid with tiles that are up to (one) rotation and shifts copies of themselves. (Think of Gosper's island in 3D). Terminology: is "rep-tile" the proper term for these things? Here is one such rule. Let {D = [ [ 0, 0, 0]~, [ 0, 0, 2]~, [ 0, 1, 1]~, [ 0, 1, -1]~, [ 1, 1, 0]~, [ 1, 1, 2]~, [ 1, 2, 1]~, [ 1, 2, -1]~ ]; } (this is a little parallelepiped out of 8 points, only even coordinates are used). Set S = [ [0,0,0]~ ]; (just the origin). Now we need a matrix M with determinant 8. Repeatedly set S = M * (s - d) for all s \in S and d \in D Our set S grows by a factor of 8 with each such step. As a Pari fragment: map( S, D, M )= { my( T=vector(#D * #S), ct=0 ); for (j=1, #D, my(d=D[j]); for (k=1, #S, my(s=S[k]); ct += 1; T[ct] = M * (s - d); ); ); return( T ); } Using M = 2 * (identity matrix) gives bigger and bigger parallelepipeds (not really a surprise). Now set { M = 2 * [ 0, 0, 1; 1, 0, 0; 0, 1, 0]; } (rotation by 120 degrees around the vector [1, 1, 1]) and you DO get a surprise, a very nontrivial 3D tile. I can only render the thing as point cloud and so have no useful images to offer. Maybe some computerhead on this list can do better. I can email the point cloud (full or just the hull) if anybody wants the data. Apparently the problem "point cloud --> closed shape" is nontrivial, and made even harder by the fractal-ish nature of the surfaces we have here. If the rendering turns out to be too nasty I can give a systems with card(D) = 27 that at least as a point cloud looks much easier to grasp. Bonus track: Three more variations. Do the rotation by 60 degrees. Do both above with the following (compacted) parallelepiped {D = [ [ 0, 0, 0]~, [ 1, 0, 0]~, [ 0, 1, 0]~, [ 1, 1, 0]~, [ 1, 1, 1]~, [ 1, 2, 1]~, [ 2, 1, 1]~, [ 2, 2, 1]~ ]; } Best regards, jj

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[math-fun] An enigma solved!
by Christian Boyer 19 Mar '15

19 Mar '15

After two enigmas solved in 2010 by Japanese Toshihiro Shirakawa, a third enigma is now solved! The first 7x7 magic square of cubes has been built by Sébastien Miquel, a French student at Ecole Normale Supérieure Paris. This is now the SMALLEST known magic square of cubes, smaller than the previous record, 8x8 by German Walter Trump... but 6x6, 5x5 and 4x4 being still unknown (among other enigmas). Sébastien Miquel won the prizes of this problem: €200 and a bottle of champagne. But there remain nine unsolved enigmas for winning €6,700 (~$7,000) and nine bottles of champagne! These news, and others, are detailed in the update of March 2015 of www.multimagie.com Old press release of 2010 announcing the twelve enigmas: www.multimagie.com/English/MagicSquaresEnigmasE.pdf Only #3a, #5, and now #4c, are solved. Christian Boyer.

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[math-fun] Adam's Life census
by Bill Gosper 19 Mar '15

19 Mar '15

APG>Speaking of appeasing Wolfram, I recently launched a distributive search of random initial configurations in lifelike cellular automata. In order to contribute, it's as simple as running the Python script in Golly (preferably n instances if your computer has n cores). We're at 66 billion objects so far for the most popular search (Conway's Game of Life with no symmetry), which is satisfying given that it's only been running for 11 days: http://catagolue.appspot.com/census/b3s23/C1 (At the moment I'm running the script on 44 CPUs to attempt to reclaim my position as most prolific contributor, after it was stolen from me by my trans-Atlantic friend Dave Greene. He's only got 12 CPUs at his disposal, but they can run 24/7 rather than just overnight when no-one's looking!) Sincerely, Adam P. Goucher ---------- I expected little more from this effort than some tedious statistics. Instead, this search is turning up new and interesting stuff: oscillators, puffertrains, improved syntheses, a period 24(!) that should have been found by Conway and Guy decades before mine, a period 3 oscillator that cannot be stabilized by other than a (central) period 2. ...ooo.....ooo . ......o...o o.......o.......o o....ooooooo....o o...o.......o...o ..o.o..ooo..o.o ....o.o...o.o ...oo.o...o.oo ....o.o...o.o ..o.o..ooo..o.o o...o.......o...o o....ooooooo....o o.......o.......o ......o...o . ...ooo.....ooo Is this a period 6?? Even more fun: The long awaited invulnerable fighting gun-- a puffertrain that shoots gliders backwards. When two ordinary guns "cross swords", retaliatory gliders and stalagmites soon end the experiment (unless it loops quickly). But these babies are invulnerable. My very first "war" lasted nearly 40000000, gosper.org/invulgun.png , while doing remarkable things. --rwg

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[math-fun] Intel STS awards (they sent me this spam)
by Warren D Smith 18 Mar '15

18 Mar '15

Noah Golowich, Andrew Jin and Michael Hofmann Winer each received first-place awards of $150,000 at the Intel Science Talent Search 2015, a program of Society for Science & the Public. First through third place awards were provided in three different categories for the first time ever this year. Noah Golowich, 17, of Lexington, Mass. won the Medal of Distinction for Basic Research, for developing a proof in the area of Ramsey theory, a field of mathematics based on finding types of structure in large and complicated systems. Andrew Jin, 17, of San Jose, Calif. won the Medal of Distinction for Global Good, for using machine learning algorithms to identify adaptive mutations across the full human genome. After he "taught" the computer how to recognize adaptive mutations, his system discovered more than 100 of them in real-life DNA sequences. Michael Winer, 18, of North Bethesda, Md. won the Medal of Distinction for Innovation, for studying how fundamental quasi-particles of sound called phonons interact with electrons. --all 3 sound interesting, but very vaguely described... -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Interactive polyhedron viewer
by Bill Gosper 18 Mar '15

18 Mar '15

Sorry if this is a duplicate. First try three hrs ago seems to have disappeared. --rwg On 2015-03-18 08:31, rwg wrote: > Alternatively, e.g., > In[130]:= PolyhedronData[{"Prism", 7}, "NetImage"] > <Deleted attachment> > > (But not, e.g., {"Prism", 11}.) > > In[132]:= PolyhedronData["PentagonalGyrocupolarotunda", "NetGraph"] > <Deleted attachment> > > In[133]:= PolyhedronData[{"Prism", 3}, "NetCoordinates"] > > Out[133]= {{0, Sqrt[3]/2}, {0, 1/2 (2 + Sqrt[3])}, {1, Sqrt[3]/2}, {1, > 1/2 (2 + Sqrt[3])}, {3/2, 0}, {3/2, 1 + Sqrt[3]}, {2, Sqrt[3]/ > 2}, {2, 1/2 (2 + Sqrt[3])}, {3, Sqrt[3]/2}, {3, 1/2 (2 + Sqrt[3])}} > > --rwg > > On 2015-03-17 15:14, Tom Karzes wrote: >> Hi Tom, >> >> I agree it would be nice to be able to save snapshots as files, >> particularly of the unfolded forms. Ideally it would pop up a little >> "save as" window which would let you enter a file path to save to, but >> I don't know of any way to generate an in-memory file in JavaScript >> and then allow the user to save it locally. >> >> I can privately generate GIF files directly from the polyhedron data, >> but I agree that a scalable format is preferable. SVG may in fact be >> ideal for this. One advantage to SVG is that it's a text format, so I >> suppose I could create a text window and write the SVG content into >> it, which the user could then manually copy/paste into a local file. >> It's ugly, but I think it would work as long as the content isn't too >> large. >> >> The only other thing I can think of would be to set up a server app >> that would accept client requests and then generate temporary server >> files which the client could open and save. It seems silly to have >> to do it that way though, and I'm not sure I want to open up the >> server to that extent. >> >> If anyone has a better idea for how to do this, I'd love to hear it. >> >> Tom >> >> Tom Knight writes: >> > That’s very nice! >> > >> > It would be great if there were an easy way to get a PDF of the >> unfolded version, which could then be scaled and used to make models. >> > >> > > On Mar 17, 2015, at 1:32 AM, Tom Karzes <karzes(a)sonic.net> wrote: >> > > >> > > Hi folks, >> > > >> > > I've put together a simple interactive polyhedron viewer which might >> > > be of interest. It requires a web browser that's current enough to >> > > support html5, and JavaScript has to be enabled, but that's pretty >> > > much it. >> > > >> > > Here's the URL: >> > > >> > > http://karzes.best.vwh.net/polyhedra/polyhedron.html >> > > >> > > You can click-and-drag the individual polyhedra to rotate them, or you >> > > can make them spin around automatically. >> > > >> > > Some filters are available at the top, based on classification and >> > > on rotational symmetry. Please note that the rotational symmetry >> > > designations are deliberately broad and imprecise, so please don't >> > > flame me for their lack of specificity; it's intentional. >> > > >> > > I should add that the click-and-drag functionality won't work with a >> > > touch screen, so you'll want to use a real mouse to use the full >> > > interface. >> > > >> > > Anyway, let me know what you think. >> > > >> > > Tom >> > >

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[math-fun] Interactive polyhedron viewer
by Tom Karzes 18 Mar '15

18 Mar '15

Hi folks, I've put together a simple interactive polyhedron viewer which might be of interest. It requires a web browser that's current enough to support html5, and JavaScript has to be enabled, but that's pretty much it. Here's the URL: http://karzes.best.vwh.net/polyhedra/polyhedron.html You can click-and-drag the individual polyhedra to rotate them, or you can make them spin around automatically. Some filters are available at the top, based on classification and on rotational symmetry. Please note that the rotational symmetry designations are deliberately broad and imprecise, so please don't flame me for their lack of specificity; it's intentional. I should add that the click-and-drag functionality won't work with a touch screen, so you'll want to use a real mouse to use the full interface. Anyway, let me know what you think. Tom

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[math-fun] Simple stereoscopic polyhedron demo page
by Tom Karzes 17 Mar '15

17 Mar '15

For those who are interested, I put together a very simple stereoscopic polyhedron demo page. The scene consists of two independently rotating (and changing) polyhedra orbiting each other (non-Newtonian; there's no valid physics here at all). The URL is: http://karzes.best.vwh.net/polyhedra/stereo.html It displays small left and right views of the scene. In order to view it as a stereoscopic scene, one must "un-cross" one's eyes so that each one sees a different image (the left eye seeing the left image and the right eye seeing the right image). Not everyone can do this, so I also included a "cross-eyed" option which reverses the two images, with the left-eye image appearing to the right of the right-eye image. To view the cross-eyed version, one must cross one's eyes (so the left eye sees the right image and the right eye sees the left image). You can switch between the two modes via a little menu in the lower-left. Tom

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