MetaFilter posts tagged with Mathematics
http://www.metafilter.com/tags/Mathematics
Posts tagged with 'Mathematics' at MetaFilter.Fri, 20 Feb 2015 18:05:13 -0800Fri, 20 Feb 2015 18:05:13 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60"You blew it, and you blew it big!"
http://www.metafilter.com/147228/You%2Dblew%2Dit%2Dand%2Dyou%2Dblew%2Dit%2Dbig
<a href="http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/">The Time Everyone “Corrected” the World’s Smartest Woman</a> tag:metafilter.com,2015:site.147228Fri, 20 Feb 2015 18:05:13 -0800brundleflyThe Man Who Tried to Redeem the World with Logic
http://www.metafilter.com/146921/The%2DMan%2DWho%2DTried%2Dto%2DRedeem%2Dthe%2DWorld%2Dwith%2DLogic
<a href="http://nautil.us/issue/21/information/the-man-who-tried-to-redeem-the-world-with-logic">Walter Pitts rose from the streets to MIT, but couldn’t escape himself.</a> Pitts was used to being bullied. He’d been born into a tough family in Prohibition-era Detroit, where his father, a boiler-maker, had no trouble raising his fists to get his way. The neighborhood boys weren’t much better. One afternoon in 1935, they chased him through the streets until he ducked into the local library to hide. The library was familiar ground, where he had taught himself Greek, Latin, logic, and mathematics—better than home, where his father insisted he drop out of school and go to work. Outside, the world was messy. Inside, it all made sense. Not wanting to risk another run-in that night, Pitts stayed hidden until the library closed for the evening. Alone, he wandered through the stacks of books until he came across Principia Mathematica, a three-volume tome written by Bertrand Russell and Alfred Whitehead between 1910 and 1913, which attempted to reduce all of mathematics to pure logic. Pitts sat down and began to read. For three days he remained in the library until he had read each volume cover to cover—nearly 2,000 pages in all—and had identified several mistakes. Deciding that Bertrand Russell himself needed to know about these, the boy drafted a letter to Russell detailing the errors. Not only did Russell write back, he was so impressed that he invited Pitts to study with him as a graduate student at Cambridge University in England. Pitts couldn’t oblige him, though—he was only 12 years old. But three years later, when he heard that Russell would be visiting the University of Chicago, the 15-year-old ran away from home and headed for Illinois. He never saw his family again. tag:metafilter.com,2015:site.146921Tue, 10 Feb 2015 18:13:50 -0800standardasparagusIslamic Astropolitik
http://www.metafilter.com/146640/Islamic%2DAstropolitik
<a href="http://thenewinquiry.com/essays/islamic-astropolitik/">Despite Western anxieties over Muslim conquest, traditions of Islamic astronomy and the portability of ritual space in Islam find Muslims at home among the stars.</a> Astrological and cosmological inquiry by medieval Muslim and Arabian scholars (that is, they wrote in Arabic) were concerned with the link that connected the earth and the night sky, and humankind’s place in it. The religious impulse to make sense of this “place” would animate scientific debates about the stars in the ninth to 14th centuries—the “golden age of Islam.” In turn, the legacy of Muslim scientists or natural philosophers of this period would inspire Islamic practice in outer space in the 21st century, with dubious results.
For centuries, the stars out in outer space provided humanity with a sense of wonder, mystery, and the divine. Through gazing upon the stars and stripping away their distant secret, a mastery of extraterrestrial worlds and dreams of conquest became inevitable. Thus in the present century, Islamic science and space exploration would together at last arrive at a spectacular conclusion: an achievement of greater proximity to the stars to better understand humankind’s place and space in the universe. Not only would Muslims arrive in outer space, but through techno-theological discourse, they would able to make space for Islam among the stars. tag:metafilter.com,2015:site.146640Sun, 01 Feb 2015 11:39:28 -0800standardasparagusThanks, Common Core.
http://www.metafilter.com/146159/Thanks%2DCommon%2DCore
<a href="http://scienceblogs.com/principles/2015/01/15/thanks-common-core/">Thanks, Common Core.</a> Physics blogger Chad Orzel writes about the way kids do math now. (Spoiler: he likes it.) Other math Common Core links:
<a href="http://mathbabe.org/2014/02/11/interview-with-bill-mccallum-lead-writer-of-math-common-core/">Interview with mathematician Bill McCallum</a>, leader of the working group that prepared the math Common Core standards.
<a href="http://www.ams.org/notices/201401/rnoti-p24.pdf">Conversations with Euclid</a>: an alternate pedagogical approach to the Common Core geometry standards.
The Common Core standards increase the emphasis on statistical and probabilistic ideas, even in the earliest grades. <a href="http://www.amstat.org/education/stn/pdfs/STN79.pdf">Statistics Teacher Network</a> walks you through the content. tag:metafilter.com,2015:site.146159Thu, 15 Jan 2015 16:28:08 -0800escabecheNo Pentagons
http://www.metafilter.com/146120/No%2DPentagons
<a href="http://gruze.org/tilings/">Imperfect Congruence</a> - <i>It is a curious fact that no edge-to-edge regular polygon tiling of the plane can include a pentagon ... This website explains the basic mathematics of a particular class of tilings of the plane, those involving regular polygons such as triangles or hexagons. As will be shown, certain combinations of regular polygons cannot be extended to a full tiling of the plane without involving additional shapes, such as rhombs. The site contains some commentary on Renaissance research on this subject carried out by two renowned figures, the mathematician-astronomer Johannes Kepler and the artist Albrecht Dürer.</i> Bonus link: <a href="http://plus.maths.org/content/trouble-five">The Trouble with Five</a> (by Craig Kaplan, at Plus magazine - a short, tantalizing article suitable for school-age readers...) tag:metafilter.com,2015:site.146120Wed, 14 Jan 2015 11:58:51 -0800WolfdogFake 3D Until You Make 3D
http://www.metafilter.com/145968/Fake%2D3D%2DUntil%2DYou%2DMake%2D3D
Louis Gorenfeld lovingly explores <a href="http://www.extentofthejam.com/pseudo/">the mathematics and techniques</a> behind early, pseudo-3D games. <blockquote>Now that every system can produce graphics consisting of a zillion polygons on the fly, why would you want to do a road the old way? Aren't polygons the exact same thing, only better? Well, no. It's true that polygons lead to less distortion, but it is the warping in these old engines that give the surreal, exhillerating sense of speed found in many pre-polygon games. Think of the view as being controlled by a camera. As you take a curve in a game which uses one of these engines, it seems to look around the curve. Then, as the road straightens, the view straightens. As you go over a blind curve, the camera would seem to peer down over the ridge. And, since these games do not use a traditional track format with perfect spatial relationships, it is possible to effortlessly create tracks large enough that the player can go at ridiculous speeds-- without worrying about an object appearing on the track faster than the player can possibly react since the physical reality of the game can easily be tailored to the gameplay style.</blockquote> tag:metafilter.com,2015:site.145968Fri, 09 Jan 2015 05:43:35 -0800gilrain"Science is when you think a lot."
http://www.metafilter.com/145704/Science%2Dis%2Dwhen%2Dyou%2Dthink%2Da%2Dlot
<a href="http://www.ams.org/bookstore/pspdf/mcl-5-prev.pdf">Two enjoyable chapters</a> [PDF, 33 pages] from the book <i><a href="http://www.ams.org/bookstore-getitem/item=MCL-5">Math from Three to Seven</a>: The Story of a Mathematical Circle for Preschoolers.</i> "This book does not purport to show you how to create precocious high achievers. It is just one person's story about things he tried with a half-dozen young children." tag:metafilter.com,2014:site.145704Mon, 29 Dec 2014 10:43:09 -0800WolfdogProfessor and the boomerang
http://www.metafilter.com/144799/Professor%2Dand%2Dthe%2Dboomerang
Professor Yutaka Nishiyama is a mathematician and a boomerang enthusiast. His <a href="http://www.kbn3.com/bip/index2.html">Boomerang International Project page</a> contains instructions in multiple languages for making your own paper boomerang and several videos of the boomerang in action. Furthermore, he has written books and articles about mathematics in daily life, with publications and links to his articles available on <a href="http://www.osaka-ue.ac.jp/zemi/nishiyama/index.html">his homepage</a> (in English too). There is <a href="http://www.moebiusnoodles.com/2014/09/1001-leaders-make-and-fly-boomerangs-with-yutaka-nishiyama/">a short interview</a> with him on Moebius Noodles. tag:metafilter.com,2014:site.144799Mon, 24 Nov 2014 10:13:04 -0800tykkyIt's pretty obscure, you probably haven't--wait, what?
http://www.metafilter.com/144537/Its%2Dpretty%2Dobscure%2Dyou%2Dprobably%2Dhavent%2Dwait%2Dwhat
<a href="http://www.washingtonpost.com/news/storyline/wp/2014/11/11/the-mathematician-who-proved-why-hipsters-all-look-alike/">The mathematician who proved why hipsters all look alike</a> <br><br>Jonathan Touboul is a mathematician and a neuroscientist. Recently, he has been thinking about hipsters. Specifically, why hipsters all seem to dress alike. In his line of work, there are neurons that also behave like hipsters. They fire when every neuron around them is quiet; or they fall silent when every neuron around them is chattering. Because he is a mathematician, Touboul began to look for a way to explore this idea using equations. In other words, he constructed a mathematical model. His key insight is that people (and neurons) do not instantly perceive what is mainstream. There’s a delay. And in situations where the delay is large enough, the contrarians can inadvertently synchronize with each other.
“In wanting to oppose the trends, there actually emerges some sort of hipster loop,” Touboul said. A day before Halloween, Touboul put a draft of his paper on the arXiv, calling it <a href="http://arxiv.org/abs/1410.8001">"The hipster effect: When anticonformists all look the same.”</a> tag:metafilter.com,2014:site.144537Sun, 16 Nov 2014 08:34:55 -0800Johnny WallflowerAlexander Grothendieck
http://www.metafilter.com/144475/Alexander%2DGrothendieck
Alexander Grothendieck, who brought much of contemporary mathematics into being with the force of his uncompromising vision, <a href="http://www.lemonde.fr/disparitions/article/2014/11/14/le-mathematicien-alexandre-grothendieck-est-mort_4523482_3382.html">is dead</a> at 86, some twenty-five years after leaving academic mathematics and retreating into a spiritual seclusion in the countryside. "As if summoned from the void," a two-part account of Grothendieck's life, from the Notices of the American Math Society: <a href="http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf">part I</a>, <a href="http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf">part II</a>. "Most mathematicians take refuge within a specific conceptual framework, in a “Universe” which seemingly has been fixed for all time – basically the one they encountered “ready-made” at the time when they did their studies. They may be compared to the heirs of a beautiful and capacious mansion in which all the installations and interior decorating have already been done, with its living-rooms , its kitchens, its studios, its cookery and cutlery, with everything in short, one needs to make or cook whatever one wishes. How this mansion has been constructed, laboriously over generations, and how and why this or that tool has been invented (as opposed to others which were not), why the rooms are disposed in just this fashion and not another – these are the kinds of questions which the heirs don’t dream of asking . It’s their “Universe”, it’s been given once and for all! It impresses one by virtue of its greatness, (even though one rarely makes the tour of all the rooms) yet at the same time by its familiarity, and, above all, with its immutability.....
I consider myself to be in the distinguished line of mathematicians whose spontaneous and joyful vocation it has been to be ceaseless building new mansions." (quoted in <a href="http://www.thebigquestions.com/2014/11/13/the-rising-sea/">a memorial blog post</a> by Steven Landsburg.)
<a href="http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf">"A country of which nothing is known but the name"</a>: Pierre Cartier remembers Grothendieck.
<a href="http://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Oort.pdf">"Did earlier ideas influence Grothendieck?"</a> Frans Oort traces the origins of Grothendieck's revolutionary way of approaching mathematics, and asks: did he <em>really</em> never work examples? (This one is a bit more technical than the others.)
<a href="http://webusers.imj-prg.fr/~leila.schneps/corr.pdf">"The Grothendieck-Serre correspondence"</a>: Leila Schneps reflects on the decades-long exchange of letters between Grothendieck and Jean-Pierre Serre.
Much more Grothendieckiana can be found at <a href="http://www.grothendieckcircle.org/">The Grothendieck Circle.</a> tag:metafilter.com,2014:site.144475Thu, 13 Nov 2014 19:56:44 -0800escabecheOne of these things is not like the others
http://www.metafilter.com/144444/One%2Dof%2Dthese%2Dthings%2Dis%2Dnot%2Dlike%2Dthe%2Dothers
US News and World Report (USNWR) ranking of the top ten universities in mathematics are:
1. Berkeley ;
2. Stanford ;
3. Princeton ;
4. UCLA ;
5. University of Oxford ;
6. Harvard ;
<a href="http://liorpachter.wordpress.com/2014/10/31/to-some-a-citation-is-worth-3-per-year/">
7. King Abdulaziz University</a> ;
8. Pierre and Marie Curie – Paris 6 ;
9. University of Hong Kong ;
10. University of Cambridge <a href="http://gulfnews.com/opinions/columnists/universities-unethical-race-to-the-top-1.965748">Article summarizing</a> the original <a href="http://www.sciencemag.org/content/334/6061/1344.summary">2011 Science article</a> (paywalled) which exposed the Saudi cash-for-citations system. The blog comments are worth reading. tag:metafilter.com,2014:site.144444Wed, 12 Nov 2014 23:49:35 -0800benzenedreamOf course, everyone knows about levers...
http://www.metafilter.com/143330/Of%2Dcourse%2Deveryone%2Dknows%2Dabout%2Dlevers
<a href="http://www.math.uga.edu/%7Eshifrin/Spivak_physics.pdf">Elementary Mechanics from a Mathematician's Viewpoint</a> [direct link to large PDF] by Michael Spivak - notes from his eight 2004 lectures (which eventually became a book). See the quote inside to get the flavor of it. <blockquote>These lectures are based on a book that I am writing, or at least trying to write. For many years I have been saying that I would like to write a book (or series of books) called Physics for Mathematicians. Whenever I would tell people that, they would say, Oh good, you're going to explain quantum mechanics, or string theory, or something like that. And I would say, Well that would be nice, but I can't begin to do that now; first I have to learn elementary physics, so the first thing I will be writing will be Mechanics for Mathematicians.
So then people would say, Ah, so you're going to be writing about symplectic structures, or something of that sort. And I would have to say, No, I'm not trying to write a book about <em>mathematics</em> for mathematicians, I'm trying to write a book about <em>physics</em> for mathematicians; of course, symplectic structures will eventually make an appearance, but the problem is that I could easily understand symplectic structures, it's elementary mechanics that I don't understand.
Then people would look at me a little strangely, so I'd better explain what I mean. When I say that I don't understand elementary mechanics, I mean, for example, that I don't understand this:
<pre>
:......,
:......,
:......,
:......,
:......,
:......, ;;;;
:......, ,..,
:......, ,..,
##########################################################
/\
. .
.... </pre>Of course, everyone knows about levers. They are so familiar that most of us have forgotten how wonderful a lever is, how great a surprise it was when we first saw a small body balancing a much bigger one. Most of us also know the law of the lever, but this law is simply a quantitative statement of exactly how amazing the lever is, and doesn't give us a clue as to why it is true, how such a small force at one end can exert such a great force at the other.
</blockquote> tag:metafilter.com,2014:site.143330Sat, 04 Oct 2014 15:38:13 -0800WolfdogTake that, Keanu Reeves.
http://www.metafilter.com/143228/Take%2Dthat%2DKeanu%2DReeves
<a href="http://www.autostraddle.com/rebel-girls-mapping-power-privilege-and-oppression-254794/">Privilege and oppression explained through math</a> - specifically, matrices and Venn diagrams. tag:metafilter.com,2014:site.143228Wed, 01 Oct 2014 10:05:31 -0800divabatTotally Freaking Out About Peg + Cat
http://www.metafilter.com/143036/Totally%2DFreaking%2DOut%2DAbout%2DPeg%2DCat
<a href="http://pbskids.org/peg/">Peg + Cat</a> is an <a href="http://www.awn.com/news/fred-rogers-cos-peg-cat-wins-3-daytime-emmys">Emmy award-winning</a> cartoon from PBS, featuring the adventures of a young girl and her feline friend, using the power of math to <a href="https://www.youtube.com/watch?v=e3mLoFndR6M">solve</a> Really Big Problems. The show, created by kid TV and Broadway veterans <a href="http://parade.condenast.com/255784/scottneumyer/peg-cat-creators-jen-oxley-billy-aronson-talk-making-math-fun-animation-inspiration/">Jen Oxley & Billy Aronson</a>, not only gives preschoolers an introduction to practical mathematics, it's also <a href="http://www.avclub.com/tvclub/empeg-catem-104101">surprisingly entertaining for adults</a>. tag:metafilter.com,2014:site.143036Wed, 24 Sep 2014 18:45:58 -0800murphy slawCalculus without limits
http://www.metafilter.com/142845/Calculus%2Dwithout%2Dlimits
<a href="https://plus.google.com/u/0/117663015413546257905/posts/14b9fdM62un">Hyperreal numbers: infinities and infinitesimals</a> - "In 1976, <a href="https://www.math.wisc.edu/~keisler/">Jerome Keisler</a>, a student of the famous logician <a href="http://johncarlosbaez.wordpress.com/2013/03/31/probability-theory-and-the-undefinability-of-truth/">Tarski</a>, published this <a href="http://www.vias.org/calculus/">elementary textbook</a> that <a href="http://en.wikipedia.org/wiki/Infinitesimal#History_of_the_infinitesimal">teaches calculus</a> using <a href="http://en.wikipedia.org/wiki/Hyperreal_number">hyperreal numbers</a>. <a href="https://www.math.wisc.edu/~keisler/calc.html">Now it's free</a>, with a Creative Commons copyright!" (pdf—<a href="https://www.math.wisc.edu/~keisler/keislercalc-12-27-13.pdf">25mb</a> :) also btw :P
<ul><li><a href="https://plus.google.com/u/0/117663015413546257905/posts/JHAku2S1KFw">The logic of real and complex numbers</a> - "The cool part is that in some ways the complex numbers are <i>simpler</i> than the real numbers! The <a href="http://johncarlosbaez.wordpress.com/2014/09/08/the-logic-of-real-and-complex-numbers/">ultimate reason</a> is that you can't talk about one complex number being greater than another. This avoids some nonstandard number systems where you have a number that's greater than all the ones you wanted to talk about."</li>
<li><a href="https://plus.google.com/u/0/117663015413546257905/posts/dZcXuyHj7LH">Science, models, and machine learning</a> - "<a href="http://johncarlosbaez.wordpress.com/2014/09/03/science-models-and-machine-learning/">Machine learning</a> is the art of <a href="http://www.newscientist.com/article/mg22329832.700-googles-factchecking-bots-build-vast-knowledge-bank.html?full=true">getting computers to learn, so you don't have to</a> explicitly tell them what to do. People use it in spam filters, search engines that guess what you're trying to find, optical character recognition, <a href="https://medium.com/aspen-ideas/robots-with-their-heads-in-the-clouds-e88ac44def8a">cars that drive themselves</a>, and <a href="https://plus.google.com/u/0/117663015413546257905/posts/SrQe3Bsd9kp">many other</a> things. <a href="http://www.metafilter.com/135046/Things-Dont-Make-Sense-Till-They-Make-Sense-to-a-Stupid-Robot">But how does it work?</a>"</li>
<li><a href="http://infoproc.blogspot.com/2014/08/neural-networks-and-deep-learning-2.html">Neural Networks and Deep Learning</a> - "Inspired by the topics discussed in this <a href="http://infoproc.blogspot.com/2014/08/neural-networks-and-deep-learning.html">earlier post</a>, I've been reading <a href="http://neuralnetworksanddeeplearning.com/">Michael Nielsen's online book</a> on neural nets and deep learning."</li>
<li><a href="http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/cat_statcomp.html">Introduction to Statistical Computing</a> - "At an intersection of <a href="http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/cat_enigmas_of_chance.html">Enigmas of Chance</a> and <a href="http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/cat_corrupting_the_young.html">Corrupting the Young</a>."</li>
<li><a href="http://www.math.columbia.edu/~woit/wordpress/?p=7172">Higher Algebra & Topos Theory</a> - "<a href="http://www.macfound.org/fellows/921/">Mathematician Jacob Lurie</a>, who was honored for redefining models in algebraic geometry, negotiated with his publisher to make his book on <a href="https://plus.google.com/u/0/117663015413546257905/posts/LX52bzbuWgH">math principles</a> available for <a href="http://www.math.harvard.edu/~lurie/">free download</a> on his personal website. While academics sometimes place papers online free, putting a whole book online isn't yet standard practice, according to the 36-year-old Harvard University professor. 'From my point of view, the benefit of writing a book is for people to look at it. I would like as many people as possible to look at it', he said."</li></ul> tag:metafilter.com,2014:site.142845Wed, 17 Sep 2014 17:23:34 -0800kliulessRing the bells that still can ring
http://www.metafilter.com/142347/Ring%2Dthe%2Dbells%2Dthat%2Dstill%2Dcan%2Dring
<blockquote><i><a href="http://www.cabinetmagazine.org/issues/53/hunt.php">How did something as loud as a bell</a>—something which is experienced so much more often, and more powerfully, by hearing than by sight—become dumb?</i></blockquote> A dumbbell <a href="http://en.wikipedia.org/wiki/Dumbbell#Etymology">originally</a> referred to equipment simulating a bell rope that did not make a noise, used for practicing bell ringing technique and developing strength.
<blockquote><i>[T]he possible combinations presented by eight bells (40,320 changes) would [...] have taken over thirty-seven hours to fully work through.</i></blockquote>
Katherine Hunt writes on the history of <a href="https://www.youtube.com/watch?v=3lyDCUKsWZs">change</a> ringing, in which multiple <a href="https://www.youtube.com/watch?v=G-yI6j7QPMQ">bells</a> are <a href="http://www.bellringing.org/">rung</a> in varying orders without repeating the same pattern. <small><a href="https://www.youtube.com/results?search_query=change+ringing">See more Youtube videos.</a></small> tag:metafilter.com,2014:site.142347Sat, 30 Aug 2014 00:05:08 -0800tykkyHidden patterns even in the most mundane of objects
http://www.metafilter.com/142344/Hidden%2Dpatterns%2Deven%2Din%2Dthe%2Dmost%2Dmundane%2Dof%2Dobjects
Mathematician Zachary Abel builds impressive <a href="http://zacharyabel.com/sculpture/">Mathematical Sculptures</a> from office supplies and other household objects. Via this mildlyimpressive reddit post: <a href="http://www.reddit.com/r/mildlyinteresting/comments/2dkd3g/i_made_a_ball_out_of_binder_clips/">I made a ball out of binder clips</a> (130 binder clips, "decently heavy") whose poster sadly has not yet followed up with instructions. Instructables has a less-impressive <a href="http://www.instructables.com/id/Binder-Clip-Ball/?ALLSTEPS">60-binder-clip ball</a>, which may still prove to be a challenging build: "My fingers have now just recovered to the point where I can post a comment", "O.M.G.!!!!! I am SO FRUSTRATED!!!!!!!!!!!!!!". tag:metafilter.com,2014:site.142344Fri, 29 Aug 2014 18:48:07 -0800We had a deal, KyleGeometry in motion
http://www.metafilter.com/142250/Geometry%2Din%2Dmotion
<a href="http://beesandbombs.tumblr.com/">Bees & Bombs</a> is a tumblr of hypnotic GIF animations programmed by Dublin-based physics student <a href="https://dribbble.com/beesandbombs">Dave Whyte</a> tag:metafilter.com,2014:site.142250Tue, 26 Aug 2014 14:34:50 -0800Mr. SixMiddle East Peace Potential through Dynamics in Spherical Geometry
http://www.metafilter.com/142097/Middle%2DEast%2DPeace%2DPotential%2Dthrough%2DDynamics%2Din%2DSpherical%2DGeometry
<a href="http://www.laetusinpraesens.org/docs10s/fivesix.php">Middle East Peace Potential through Dynamics in Spherical Geometry: Engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks</a>. <em> This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism...Mathematically these patterns cannot be readily combined. This issue is described in mathematics in terms of tiling...A set of hexagons and pentagons can however be uniquely fitted together as a particular three-dimensional polyhedron, namely the truncated icosahedron. </em> <em>"The key question for this argument -- given the truncated icosahedral pattern explored above -- is whether "resonance" in some form, and "cyclical edge-connectivity", have implications for the viability of structures reconciling the differences between the "hexagonal" and "pentagonal" mindsets assumed here to be fundamental to the dynamics in the Middle East. The challenge might well be framed as one of reframing the pattern of edges to form a larger whole...should the challenges of the Middle East be understood as a problem of resonance -- calling for the quality of thinking applied to resonant structures?...
Of particular interest to this approach is the use of a Schlegel diagram by those exploring resonance within the truncated icosahedron as the polyedral form of the basic fullerene C60."</em> tag:metafilter.com,2014:site.142097Thu, 21 Aug 2014 10:33:16 -0800leahwrennIt's just a jump to the ... well, in any legal direction really
http://www.metafilter.com/141947/Its%2Djust%2Da%2Djump%2Dto%2Dthe%2Dwell%2Din%2Dany%2Dlegal%2Ddirection%2Dreally
<a href="http://plus.maths.org/content/os/issue12/xfile/index">The Peg Solitaire Army</a> is a problem spun off from a classic recreation, and yet another example of the golden ratio turning up where you least expect it. If you want to look at the game more deeply, George Bell's solitaire pages are the ne plus ultra: There's <a href="http://recmath.org/pegsolitaire/army/index.html">more about the solitaire army (and variants)</a>, ... ... <a href="http://recmath.org/pegsolitaire/index.html">peg solitaire on all kinds of square-grid boards</a> and <a href="http://recmath.org/pegsolitaire/tindex.html">triangular peg solitaire</a>.
If you want to read more about why the traditional cross-shaped, 33-hole board is special, <a href="http://recmath.org/pegsolitaire/papers/Bell_AFreshLookatPegSolitaire_MathMag2007.pdf">A Fresh Look at Peg Solitaire</a> [PDF] explains its unique properties.
If you just want to solve puzzles, there are both <a href="http://recmath.org/pegsolitaire/index.html#games">square and triangular games</a> to play. The <a href="http://recmath.org/pegsolitaire/Tools/g4g7/index.htm">puzzles with diagonal moves allowed</a> are an especially fun variant if you're a jaded veteran of the usual game.
And if you want neat connection to formal languages, <a href="http://arxiv.org/abs/math/0008172">this short paper</a> gives a grammar for recognizing solvable positions in 1-dimensional peg solitaire. tag:metafilter.com,2014:site.141947Fri, 15 Aug 2014 08:49:44 -0800Wolfdogdo while !glory
http://www.metafilter.com/141913/do%2Dwhile%2Dglory
<a href="http://www.azspcs.net/">Welcome to Al Zimmermann's Programming Contests.</a> <em>You've entered an arena where demented computer programmers compete for glory and for some <abbr title="i.e., works from Bathsheba Sculpture">cool prizes</abbr>.</em> The current challenge is just about to come to an end, but you can peruse the previous contests and prepare for the new one starting next month. tag:metafilter.com,2014:site.141913Thu, 14 Aug 2014 05:18:26 -0800Wolfdog2014 Fields Medals
http://www.metafilter.com/141875/2014%2DFields%2DMedals
<a href="http://www.mathunion.org/general/prizes/2014/">The 2014 Fields Medals have been awarded</a> to Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani. Mirzakhani, a professor at Stanford, is the first woman to win math's highest prize, and Avila is the first South American. Erica Klarreich at Quanta Magazine has profiles of all four winners. <a href="http://www.simonsfoundation.org/quanta/20140812-a-brazilian-wunderkind-who-calms-chaos/">A Brazilian Wunderkind who Calms Chaos</a> (Avila)
<a href="http://www.simonsfoundation.org/quanta/20140812-the-musical-magical-number-theorist/">The Musical, Magical Number Theorist</a> (Bhargava)
<a href="http://www.simonsfoundation.org/quanta/20140808-in-mathematical-noise-one-who-heard-music/">In Noisy Equations, One Who Heard Music</a> (Hairer)
<a href="http://www.simonsfoundation.org/quanta/20140812-a-tenacious-explorer-of-abstract-surfaces/">A Tenacious Explorer of Abstract Surfaces</a> (Mirzakhani) tag:metafilter.com,2014:site.141875Tue, 12 Aug 2014 13:47:53 -0800escabecheOrchestrate Illusions (Superpermuter)
http://www.metafilter.com/141822/Orchestrate%2DIllusions%2DSuperpermuter
<a href="http://www.njohnston.ca/2013/04/the-minimal-superpermutation-problem/">The Minimal Superpermutation Problem</a> - <em>Imagine that there is a TV series that you want to watch. The series consists of n episodes, with each episode on a single DVD. Unfortunately, however, the DVDs have become mixed up and the order of the episodes is in no way marked (and furthermore, the episodes of the TV show are not connected by any continuous storyline – there is no way to determine the order of the episodes just from watching them). Suppose that you want to watch the episodes of the TV series, consecutively, in the correct order. The question is: how many episodes must you watch in order to do this?</em> There's relatively written about these but one of the most interesting places you can read about them is in <a href="http://chance.amstat.org/2012/11/interview-with-persi-diaconis/">Magical Mathematics</a> (that's a link to a very enjoyable interview about the book with Perci Diaconis, coauthor with Ron Graham). tag:metafilter.com,2014:site.141822Sun, 10 Aug 2014 16:19:40 -0800WolfdogThe Foehr Reef
http://www.metafilter.com/141813/The%2DFoehr%2DReef
The Foehr Reef is part of the worldwide Crochet Coral Reef Project. It was made by over 700 women and combines more than 4000 individual pieces of marine wonder. A short <a href="http://vimeo.com/45191819">video</a> shows its beauty [alternating English and German audio]. <a href="http://www.mkdw.de/uploads/media/Bilddokumentation_Teil_2.pdf">PDFs</a> with <a href="http://www.mkdw.de/uploads/media/Bilddokumentation_Teil_3.pdf">pictures</a>.
"The Crochet Coral Reef is <a href="http://www.crochetcoralreef.org/">a woolly celebration</a> of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world." It originated out of a desire to increase awareness of environmental threats to the world's reefs and is a conjunction of art, environmentalism, and geometry. Woolly reefs arise <a href="http://www.crochetcoralreef.org/satellite/index.php">around the world</a>, currently seeking crocheters for a project in <a href="http://community.sunshinecoast.qld.gov.au/news/help-create-sunshine-coast-satellite-reef">Australia</a>. An upcoming exhibit in <a href="http://nyuad.nyu.edu/en/research/nyuad-institute/institute-programs/AbuDhabi_Satellite-Reef.html">Abu Dhabi</a> will showcase the reefs of the Persian Gulf. The Foehr Reef is currently on <a href="https://www.krefeld.de/de/dtm/aktuelle-ausstellung/">display</a> in Krefeld.
Instructions on hyperbolic crochet basics for reef corals [<a href="http://crochetcoralreef.org/Content/makeyourown/IFF-CrochetReef-HowToHandout.pdf">PDF</a>]. More patterns <a href="http://themainereef.blogspot.de/p/patterns.html">here</a> and on <a href="http://www.ravelry.com/patterns/sources/the-maine-reef-crochet-patterns/patterns">ravelry</a> [<a href="http://www.ravelry.com/patterns/library/brittle-star">2</a>, <a href="http://www.ravelry.com/patterns/library/hyperbolic-crochet-motifs-coral-reef">3</a>].
<a href="http://www.pinterest.com/memiller123/amigurumi-coral-reef/">Pinterest board</a> [<a href="http://www.pinterest.com/ouidamac/crochet-coral-reef/">2</a>, <a href="http://www.pinterest.com/mainereef/the-maine-crochet-coral-reef-project/">3</a>]. tag:metafilter.com,2014:site.141813Sun, 10 Aug 2014 08:34:26 -0800travelwithcats21st Century Wiener
http://www.metafilter.com/140806/21st%2DCentury%2DWiener
<a href="http://www.theatlantic.com/technology/archive/2014/06/norbert-wiener-the-eccentric-genius-whose-time-may-have-finally-come-again/372607/">Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again)</a> - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named <a href="http://www.metafilter.com/6138/The-passing-of-a-giant">Claude Shannon</a>." <a href="http://tikalon.com/blog/blog.php?article=2014/Norbert_Wiener">Norbert Wiener</a>:
<blockquote>In his 1950 book, "<a href="http://en.wikipedia.org/wiki/The_Human_Use_of_Human_Beings">The Human Use of Human Beings</a>," [<a href="http://21stcenturywiener.org/wp-content/uploads/2013/11/The-Human-Use-of-Human-Beings-by-N.-Wiener.pdf">PDF</a>] Wiener <a href="http://www.forbes.com/sites/christopherhelman/2014/07/02/dean-kamen-thinks-his-new-stirling-engine-could-power-the-world/print/">envisioned</a> a <a href="https://medium.com/@AdamThierer/muddling-through-how-we-learn-to-cope-with-technological-change-6282d0d342a6">utopia</a> in which <a href="http://www.bloombergview.com/articles/2014-07-07/larry-page-s-slacker-utopia">automation</a> would relieve humanity of <a href="http://marginalrevolution.com/marginalrevolution/2014/07/the-decline-of-drudgery-and-the-paradox-of-hard-work.html">manual</a> <a href="http://crookedtimber.org/2014/07/10/in-search-of-search-theory/">labor</a> to allow more <a href="http://continuations.com/post/91111911845/more-on-basic-income-and-robots">creative</a> pursuits. Sixty years later, we have much automation, but <a href="http://www.economist.com/blogs/freeexchange/2014/07/thomas-piketty-history-money">income</a> <a href="http://boingboing.net/2014/06/24/thomas-pikettys-capital-in-t.html">inequality</a> rather than utopia. Wiener died in Stockholm, Sweden, at age 69.
The crater, <a href="http://en.wikipedia.org/wiki/Wiener_%28crater%29">Wiener</a>, on the far side of the Moon is named after him. I've always believed in "Wiener's Law of Libraries," "<a href="http://en.wikiquote.org/wiki/Norbert_Wiener">There are no answers, only cross references</a>". The IEEE is sponsoring a conference, <a href="http://21stcenturywiener.org/">Norbert Wiener in the 21st Century</a>, commemorating Norbert Wiener. </blockquote>
also btw...
<ul><li><a href="http://www.nytimes.com/2013/05/21/science/mit-scholars-1949-essay-on-machine-age-is-found.html?pagewanted=all">In 1949, He Imagined an Age of Robots</a>: " 'The Machine Age' (<a href="http://libraries.mit.edu/archives/mithistory/pdf/MC0022_MachineAgeV3_1949.pdf">pdf</a>) an essay written for <i>The New York Times</i> by Norbert Wiener, a visionary mathematician, languished for six decades in the M.I.T. archives, and now excerpts are being published."</li>
<li><a href="http://infoproc.blogspot.com/2014/06/theoreticians-as-professional-outsiders.html">Theoreticians as Professional Outsiders</a>: The Modeling Strategies of John von Neumann and Norbert Wiener (<a href="http://www.ehudlamm.com/outsiders.pdf">pdf</a>)</li>
<blockquote>Both von Neumann and Wiener were outsiders to biology. Both were inspired by biology and both proposed models and generalizations that proved inspirational for biologists. Around the same time in the 1940s von Neumann developed the notion of self reproducing automata and Wiener suggested an explication of teleology using the notion of negative feedback. These efforts were similar in spirit. Both von Neumann and Wiener used mathematical ideas to attack foundational issues in biology, and the concepts they articulated had lasting effect. But there were significant differences as well. Von Neumann presented a how-possibly model, which sparked interest by mathematicians and computer scientists, while Wiener collaborated more directly with biologists, and his proposal influenced the philosophy of biology. The two cases illustrate different strategies by which mathematicians, the "professional outsiders" of science, can choose to guide their engagement with biological questions and with the biological community, and <a href="http://www.metafilter.com/137105/John-Baez-on-the-maths-of-connecting-everyone-and-everything-on-earth">illustrate different kinds of generalizations</a> that mathematization can contribute to biology. The different strategies employed by von Neumann and Wiener and the types of models they constructed may have affected the fate of von Neumann's and Wiener's ideas – as well as the reputation, in biology, of von Neumann and Wiener themselves.</blockquote>
<li><a href="http://www.nytimes.com/2014/07/08/science/a-billionaire-mathematicians-life-of-ferocious-curiosity.html">A Billionaire Mathematician's Life of Ferocious Curiosity</a>: "Dr. Simons received his doctorate at 23; advanced code breaking for the National Security Agency at 26; led a university math department at 30; won geometry's top prize at 37; <a href="http://infoproc.blogspot.com/2014/07/james-simons-mathematics-common-sense.html">founded Renaissance Technologies</a>, one of the world's most successful hedge funds, at 44; and began setting up <a href="http://www.simonsfoundation.org/quanta/">charitable foundations</a> at 56."</li>
<li><a href="http://infoproc.blogspot.com/2014/07/physics-and-horizons-of-truth.html">Physics and the Horizons of Truth</a>: "mathematics without something like the 'axiom of infinity' might be well-defined..." [<a href="http://infoproc.blogspot.com/2013/06/horizons-of-truth.html">Horizons of Truth</a>: Kurt Gödel and the Foundations of Mathematics (<a href="http://f3.tiera.ru/2/M_Mathematics/MA_Algebra/MAml_Mathematical%20logic/Baaz%20M.,%20et%20al.%20(eds.)%20Kurt%20Goedel%20and%20the%20foundations%20of%20mathematics.%20Horizons%20of%20truth%20(CUP,%202011)(ISBN%200521761441)(O)(541s)_MAml_.pdf">pdf</a>)]</li>
<li><a href="https://www.youtube.com/watch?v=uh6GCY9i6tY">Sentences you never thought you'd hear in Congress</a>: "Madame Speaker, I would like to talk about <a href="http://www.metafilter.com/134338/binding-the-andat">twin prime numbers</a>..."</li></ul> tag:metafilter.com,2014:site.140806Fri, 11 Jul 2014 07:11:08 -0800kliuless