MetaFilter posts tagged with Mathematics
http://www.metafilter.com/tags/Mathematics
Posts tagged with 'Mathematics' at MetaFilter.Sat, 04 Oct 2014 15:38:13 -0800Sat, 04 Oct 2014 15:38:13 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Of 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 -0800kliulessmusical mathematical journeys
http://www.metafilter.com/140588/musical%2Dmathematical%2Djourneys
<a href="http://vimeo.com/channels/bkcfilms/98290488">Trio for Three Angles</a> (1968) is one of many beautiful acclaimed visually-oriented short films with music by <a href="http://www.afana.org/cornwell.htm">mathematical filmmakers Bruce and Katharine Cornwell</a>, some animated by hand and some using early digital technology. It inspired three sequels: <a href="http://vimeo.com/channels/bkcfilms/98290491">Similar Triangles</a> (1975), <a href="http://vimeo.com/channels/bkcfilms/98290485">Congruent Triangles</a> (1976), and <a href="http://vimeo.com/channels/bkcfilms/98297985">Journey to the Center of a Triangle</a> (1978) (<a href="http://www.metafilter.com/94416/Quasihypnotic-mathematical-construct">previously</a>). <a href="http://vimeo.com/channels/bkcfilms">Other extant films by the couple</a>, recently generously released by their sons Eric and Scott Cornwell under a Creative Commons license "to encourage artists, educators, and others to give these images new life", are:
<ul><li><a href="http://vimeo.com/channels/bkcfilms/98290486">The Seven Bridges of Königsberg</a> (1958), on Leonard Euler's famous solution to the topological problem</li>
<li><a href="http://vimeo.com/channels/bkcfilms/98297987">Possibly So, Pythagoras</a> (1963), using the patterns of a tile floor to demonstrate the Pythagorean Theorem</li>
<li><a href="http://vimeo.com/channels/bkcfilms/99488699">How Do You Count</a> (1963), on counting in bases 2, 3, 4, 10, 12, and more</li>
<li><a href="http://vimeo.com/channels/bkcfilms/98297986">Newton's Equal Areas</a> (1967), an elegant visual demonstration of Newton's proof of Kepler's Second Law</li>
<li><a href="http://vimeo.com/channels/bkcfilms/98501883">Circle Circus</a> (1978), featuring ten ways to draw a circle</li>
<li><a href="http://vimeo.com/channels/bkcfilms/98285334">Dragon Fold</a> (1978), on fractals</li></ul> tag:metafilter.com,2014:site.140588Sun, 06 Jul 2014 10:26:08 -0800berylliumI'm leaving my body to science, not medical but physics
http://www.metafilter.com/140487/Im%2Dleaving%2Dmy%2Dbody%2Dto%2Dscience%2Dnot%2Dmedical%2Dbut%2Dphysics
<a href="https://letstalkaboutscience.wordpress.com/">Let's Talk About Science</a> is a blog devoted to discussing the world of science and technology communication with clear, beginner-friendly language, written and compiled by <a href="http://www.physics.upenn.edu/~fairfia/">nanoscientist</a>/<a href="http://dartofphysics.ie/about">physicist</a> <a href="https://letstalkaboutscience.wordpress.com/author/jessamynfairfield/">Jessamyn Fairfield</a> and <a href="https://letstalkaboutscience.wordpress.com/2012/01/03/introductions-erin/">science educator</a> <a href="https://letstalkaboutscience.wordpress.com/author/erindubitably/">ErinDubitably</a>. <a href="https://letstalkaboutscience.wordpress.com/2013/10/07/topic-index/">Topics of discussion</a> at LTAS include physics and nanoscience (natch), along with mathematics, electronics and circuitry, quantum mechanics, and thermodynamics, all of which are covered in loving detail while remaining refreshingly free of intimidating jargon.
Intrigued? Let's talk about science!
<ul><li><a href="https://letstalkaboutscience.wordpress.com/2013/07/30/scientific-inquiry-and-critical-thinking/">Scientific inquiry and critical thinking</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2013/01/07/what-is-entropy/">What is entropy?</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2012/06/19/magnets-how-do-they-work/">Magnets, how do they work?</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2013/05/24/why-the-nanoscale-matters/">Why the nanoscale matters</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2012/07/30/understanding-deep-time/">Understanding 'deep time'</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2012/07/11/particles-field-theory-and-the-higgs-boson/">Particles, field theory, and the Higgs boson</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2014/04/23/quantum-worldview/">Quantum worldview</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2012/05/28/how-resistors-and-capacitors-work/">How resistors and capacitors work</a></li>
<li><a href="https://letstalkaboutscience.wordpress.com/2013/04/05/still-not-there-yet/">11 reasons we're still not there yet: Women in science</a></li></ul>
<small><strong>Fun fact</strong>: LTAS contributor ErinDubitably is <a href="http://www.manfeels-park.com/links/">also known</a> as one half of the dynamic duo responsible for <a href="http://www.manfeels-park.com/">Manfeels Park</a> (<a href="https://www.metafilter.com/140387/This-is-no-very-striking-resemblance-of-your-own-character-I-am-sure">previously</a>).</small> tag:metafilter.com,2014:site.140487Thu, 03 Jul 2014 10:16:14 -0800divined by radioFollowing your heart is another tolerable option
http://www.metafilter.com/140110/Following%2Dyour%2Dheart%2Dis%2Danother%2Dtolerable%2Doption
<a href="http://www.npr.org/blogs/krulwich/2014/05/15/312537965/how-to-marry-the-right-girl-a-mathematical-solution">How To Marry The Right Girl: A Mathematical Solution</a> tag:metafilter.com,2014:site.140110Sat, 21 Jun 2014 05:16:17 -0800paleyellowwithorangeMath or Maths?
http://www.metafilter.com/138740/Math%2Dor%2DMaths
<a href="http://www.numberphile.com/videos/math_maths.html">Math or Maths?</a> A few minutes with Dr Lynne Murphy (an American linguist in England) should clear this right up. Via <a href="http://www.numberphile.com/index.html">Numberphile</a>. tag:metafilter.com,2014:site.138740Wed, 30 Apr 2014 17:39:24 -0800R. MuttA SAT Attack on the Erdos Discrepancy Conjecture
http://www.metafilter.com/138247/A%2DSAT%2DAttack%2Don%2Dthe%2DErdos%2DDiscrepancy%2DConjecture
<a href="http://io9.com/computers-are-providing-solutions-to-math-problems-that-1525261141">Computers are providing solutions to math problems that we can't check</a> - "A computer has solved the longstanding <a href="http://arxiv.org/abs/1402.2184">Erdős discrepancy</a> problem! Trouble is, we have no idea what it's talking about — because the solution, which is <a href="http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html">as long as all of Wikipedia</a>'s pages combined, is far too <a href="http://mathbabe.org/2013/07/30/the-stacks-project-gets-ever-awesomer-with-new-viz/">voluminous</a> for us <a href="http://oliviacaramello.com/Unification/Unification.htm">puny humans</a> to confirm." (<a href="http://marginalrevolution.com/marginalrevolution/2014/04/are-computer-coming-up-with-answers-we-cannot-understand.html">via</a>; <a href="http://www.metafilter.com/126041/Computerized-Math-Formal-Proofs-andamp-Alternative-Logic">previously</a> ;) tag:metafilter.com,2014:site.138247Sat, 12 Apr 2014 08:55:27 -0800kliulessVisually stunning math concepts...
http://www.metafilter.com/138098/Visually%2Dstunning%2Dmath%2Dconcepts
<a href="http://math.stackexchange.com/questions/733754/visually-stunning-math-concepts-which-are-easy-to-explain">...which are easy to explain.</a> tag:metafilter.com,2014:site.138098Mon, 07 Apr 2014 14:36:40 -0800Foci for AnalysisDon't be gauche—guilloche!
http://www.metafilter.com/137833/Dont%2Dbe%2Dgauche%2Dguilloche
Did you know there's a direct correlation between the decline in Spirograph popularity and the rise in gang activity? Reverse this deplorable trend by playing around with the <a href="http://www.subblue.com/projects/guilloche">Guilloché spiral pattern generator</a>! (You may recognize the characteristic whorls of <a href="http://en.wikipedia.org/wiki/Guilloche#In_today.E2.80.99s_terminology">Guilloche</a> patterns from their use as <a href="http://ministryoftype.co.uk/words/article/one_hundred_dollars/">security features on bank notes</a>.) tag:metafilter.com,2014:site.137833Fri, 28 Mar 2014 13:24:56 -0800Iridicthere is no soundtrack
http://www.metafilter.com/137347/there%2Dis%2Dno%2Dsoundtrack
<a href="https://www.simonsfoundation.org/quanta/20140224-a-fluid-new-path-in-grand-math-challenge/">Finite time blowup for an averaged three-dimensional Navier-Stokes equation</a> - "[<a href="http://terrytao.wordpress.com/">Terence Tao</a>] has shown that in an alternative abstract universe closely related to the one described by the <a href="http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations">Navier-Stokes</a> equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, <a href="http://www.drseussart.com/details/illustration/littlecats.html">like the Cat in the Hat</a>, keeps transferring its energy to smaller and smaller copies of itself until the fluid '<a href="http://terrytao.wordpress.com/2014/02/04/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes-equation/">blows up</a>.' " [<a href="http://terrytao.wordpress.com/2014/02/25/conserved-quantities-for-the-euler-equations/">1</a>,<a href="http://terrytao.wordpress.com/2014/03/02/noethers-theorem-and-the-conservation-laws-for-the-euler-equations/">2</a>,<a href="http://terrytao.wordpress.com/2014/03/06/conserved-quantities-for-the-surface-quasi-geostrophic-equation/">3</a>] (<a href="http://www.metafilter.com/55295/Another-Clay-Institute-Millenium-Prize-Problem-Solved">previously</a>) tag:metafilter.com,2014:site.137347Sun, 09 Mar 2014 13:49:39 -0800kliulessJohn Baez on the maths of connecting everyone (and everything) on earth
http://www.metafilter.com/137105/John%2DBaez%2Don%2Dthe%2Dmaths%2Dof%2Dconnecting%2Deveryone%2Dand%2Deverything%2Don%2Dearth
<a href="http://johncarlosbaez.wordpress.com/2014/02/22/network-theory-overview/">Network Theory Overview</a> - "<a href="http://johncarlosbaez.wordpress.com/2014/02/07/network-theory-talks-at-oxford/">The idea</a>: nature and the world of human technology are <a href="http://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/">full of networks</a>! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using <a href="http://math.ucr.edu/home/baez/irvine/">category theory</a>. But why should <a href="http://www.perimeterinstitute.ca/videos/energy-and-environment-what-physicists-can-do">physicists have all the fun</a>? This is the century of <i><a href="https://plus.google.com/117663015413546257905/posts/e6stQjMvm3y">understanding living systems and adapting to life on a finite planet</a></i>. Math isn't the main thing we need, but it's got to be <a href="https://plus.google.com/117663015413546257905/posts/5gt7pfibYMg">part of the solution</a>... <a href="http://johncarlosbaez.wordpress.com/2014/03/02/network-theory-i/">so one thing we should do</a> is develop a unified and powerful <a href="http://math.ucr.edu/home/baez/networks/">theory of networks</a>." (<a href="https://plus.google.com/117663015413546257905/posts/SmWyn8HcDyW">via</a> ;) tag:metafilter.com,2014:site.137105Sun, 02 Mar 2014 09:06:38 -0800kliuless"What is...." from the Notices of the American Math Society
http://www.metafilter.com/137005/What%2Dis%2Dfrom%2Dthe%2DNotices%2Dof%2Dthe%2DAmerican%2DMath%2DSociety
Each month, the Notices of the American Math Society runs a column called "What is...." which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good undergrad math major. Armin Straub, a postdoc at Illinois, <a href="http://arminstraub.com/math/what-is-column">has collected them all in one place</a>. Some that I particularly like:
<a href="http://www.ams.org/notices/201204/rtx120400532p.pdf">"What is ... data mining?" by Mauro Maggioni</a>
<a href="http://www.ams.org/notices/201008/rtx100800976p.pdf">"What is ... a sandpile?" by Lionel Levine and James Propp</a>
<a href="http://www.ams.org/notices/200511/what-is.pdf">"What is ... a random matrix?" by Persi Diaconis</a>
If these are all too down-to-earth for you, feel free to head straight for Jacob Lurie's <a href="http://www.ams.org/notices/200808/tx080800949p.pdf">"What is ... an infinity-category?"</a> tag:metafilter.com,2014:site.137005Wed, 26 Feb 2014 19:15:42 -0800escabecheThe dangers of A/B testing
http://www.metafilter.com/136897/The%2Ddangers%2Dof%2DA%2DB%2Dtesting
A/B testing has become a familiar term for most people running web sites, especially e-commerce sites. Unfortunately, <a href="http://www.qubitproducts.com/sites/default/files/pdf/Plain%20whitepaper%20sans.pdf">most A/B test results are illusory (PDF, 312 kB)</a>. Here's <a href="http://www.evanmiller.org/how-not-to-run-an-ab-test.html">how not to run an A/B test</a>. Do use <a href="http://www.evanmiller.org/ab-testing/sample-size.html">this sample size calculator</a> or <a href="http://www.evanmiller.org/lazy-assignment-and-ab-testing.html">this weird trick</a>. tag:metafilter.com,2014:site.136897Sun, 23 Feb 2014 14:39:45 -0800Foci for Analysis