MetaFilter posts tagged with Math
http://www.metafilter.com/tags/Math
Posts tagged with 'Math' at MetaFilter.Sat, 14 Mar 2015 11:50:26 -0800Sat, 14 Mar 2015 11:50:26 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60I got cosines / on a cloudy day
http://www.metafilter.com/147940/I%2Dgot%2Dcosines%2Don%2Da%2Dcloudy%2Dday
The goofy, lofi math music of Al G. Bra and friends: <a href="https://www.youtube.com/watch?v=yCe1G0LuHKs">Pi Girl</a> — <a href="https://www.youtube.com/watch?v=Qs464DqnPTo">Say That Funky Number, Math Guy</a> — Mathonna's <a href="https://www.youtube.com/watch?v=pS8b2ZHz4yw">Mathematical Girl</a>. Plus: a trailer for math thriller <a href="https://www.youtube.com/watch?v=qRiaSzfSBsU">Live and Let Pi</a>, featuring the title track by Paul DesCartney. tag:metafilter.com,2015:site.147940Sat, 14 Mar 2015 11:50:26 -0800cortexCelebrate Vi day.
http://www.metafilter.com/147933/Celebrate%2DVi%2Dday
<a href="https://www.youtube.com/watch?v=2E9m6yDEIj8">Vi Hart rants about what day today is.</a> <a href="http://www.metafilter.com/59428/Heres-a-slice-of-pi">(previous</a> <a href="http://www.metafilter.com/24292/Happy-Pi-Day">celebrations)</a> tag:metafilter.com,2015:site.147933Sat, 14 Mar 2015 06:53:20 -0800Obscure Reference"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 -0800brundleflyThey evolved. They rebelled. There are many copies. And they have a plan
http://www.metafilter.com/147082/They%2Devolved%2DThey%2Drebelled%2DThere%2Dare%2Dmany%2Dcopies%2DAnd%2Dthey%2Dhave%2Da%2Dplan
The Philadelphia 76ers are currently the worst team in basketball, but in terms of expected value, they are <a href="http://espn.go.com/nba/story/_/id/12318808/the-philadelphia-76ers-radical-guide-winning">crushing</a>. This <a href="http://philadelphia.cbslocal.com/2015/02/15/boyd-why-winning-will-matter-to-the-sixers-in-2015-16/">analytics-based approach to tearing down and rebuilding a team</a> is spearheaded by former Rockets VP <a href="http://thesixersense.com/2015/01/24/sixers-gm-sam-hinkie-teaches-life-lessons/">Sam Hinkie</a>. His plan is <a href="http://www.si.com/nba/2014/11/20/76ers-tanking-building-sam-hinkie-michael-carter-williams">not</a> <a href="http://www.philly.com/philly/sports/sixers/20150210_Sixers_have_nobody_but_Hinkie_to_blame.html">popular</a> in <a href="http://www.philly.com/philly/sports/sixers/20150215_Expect_more_tank_maneuvers_from_Hinkie.html">some places</a> (<a href="http://www.libertyballers.com/2015/2/11/8016823/the-sixers-like-their-mascot-lack-substance">guess which places!</a>) tag:metafilter.com,2015:site.147082Mon, 16 Feb 2015 10:08:38 -0800Potomac Avenue"Where is the door?"
http://www.metafilter.com/146501/Where%2Dis%2Dthe%2Ddoor
<a href="http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty">Profile: Breaking down the problem of bound gaps [New Yorker]:</a> After graduating with a Ph.D. in algebraic geometry from Purdue in 1991, Yiting Zhang kept the books for a friend's Subway franchise and found other odd jobs before taking up a part-time calculus teaching position at the University of New Hampshire in 1999.
<blockquote>“For years, I didn’t really keep up my dream in mathematics,” he said.<br><br>
“You must have been unhappy.”<br><br>
He shrugged. “My life is not always easy,” he said.</blockquote>
He published one paper in 2001. Then, in 2013, he submitted "<a href="http://ir.nmu.org.ua/bitstream/handle/123456789/23842/c18a29be5bb5b86f1bbeaa8616a7fe42.pdf?sequence=1">Bounded Gaps Between Primes</a>" to <i>Annals of Mathematics</i>, one of the most prestigious journals in the field, which contained a proof for a finite bound within which there exist an infinite number of pairs of primes. It was a stunning mathematical breakthrough. An excerpt on the many interesting types of primes:
<blockquote>Prime numbers have so many novel qualities, and are so enigmatic, that mathematicians have grown fetishistic about them. Twin primes are two apart. Cousin primes are four apart, sexy primes are six apart, and neighbor primes are adjacent at some greater remove. From “Prime Curios!,” by Chris Caldwell and G. L. Honaker, Jr., I know that an absolute prime is prime regardless of how its digits are arranged: 199; 919; 991. A beastly prime has 666 in the center. The number 700666007 is a beastly palindromic prime, since it reads the same forward and backward. A circular prime is prime through all its cycles or formulations: 1193, 1931, 9311, 3119. There are Cuban primes, Cullen primes, and curved-digit primes, which have only curved numerals—0, 6, 8, and 9. A prime from which you can remove numbers and still have a prime is a deletable prime, such as 1987. An emirp is prime even when you reverse it: 389, 983. Gigantic primes have more than ten thousand digits, and holey primes have only digits with holes (0, 4, 6, 8, and 9). There are Mersenne primes; minimal primes; naughty primes, which are made mostly from zeros (naughts); ordinary primes; Pierpont primes; plateau primes, which have the same interior numbers and smaller numbers on the ends, such as 1777771; snowball primes, which are prime even if you haven’t finished writing all the digits, like 73939133; Titanic primes; Wagstaff primes; Wall-Sun-Sun primes; Wolstenholme primes; Woodall primes; and Yarborough primes, which have neither a 0 nor a 1.</blockquote>
<a href="http://www.metafilter.com/128049/Quite-a-day-for-analytic-number-theory">Previously on Metafilter.</a> tag:metafilter.com,2015:site.146501Tue, 27 Jan 2015 08:29:12 -0800ilicetArithmeticfilter
http://www.metafilter.com/146474/Arithmeticfilter
<a href="http://www.momonix.com/calc/">Nothing but an endless supply of mental arithmetic problems.</a> Five levels of difficulty, from "10 - 6" to "√370881." You can find slightly more granular training <a href="http://windhoff.net/mental_arithmetic/#Addition">here</a>. See <a href="http://en.wikipedia.org/wiki/Mental_calculation">Wikipedia</a> for a survey of mental methods, or read <a href="http://www-history.mcs.st-and.ac.uk/HistTopics/Mental_arithmetic.html">A.C. Aitken's</a> <a href="http://stepanov.lk.net/mnemo/aitkene.html">explanation</a> of his Art of Calculation. tag:metafilter.com,2015:site.146474Mon, 26 Jan 2015 08:41:53 -0800IridicStephen Hawking is not part of the solution, he is part of the problem.
http://www.metafilter.com/146251/Stephen%2DHawking%2Dis%2Dnot%2Dpart%2Dof%2Dthe%2Dsolution%2Dhe%2Dis%2Dpart%2Dof%2Dthe%2Dproblem
<a href="http://bryanappleyard.com/physics-superstitions-and-allegories/">The equations on the blackboard may be the problem. Mathematics, the language of science, may have misled the scientists.</a> “The idea,” says physicist Lee Smolin, “that the truth about nature can be wrestled from pure thought through mathematics is overdone… The idea that mathematics is prophetic and that mathematical structure and beauty are a clue to how nature ultimately works is just wrong.” Lee Smolin thinks that <a href="http://www.theawl.com/2014/05/who-will-rescue-time-from-the-physicists">time is real</a>. If that strikes you as unusual, you haven’t spent much time with theoretical physicists, who tend to think that the passing of time is either an emergent property of the universe, or, perhaps, an illusion.
And in an <a href="http://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535">essay</a> published last week in the science journal Nature astrophysicists George Ellis and Joe Silk say that the wild claims of theoretical physicists are threatening the authority of science itself. tag:metafilter.com,2015:site.146251Mon, 19 Jan 2015 07:32:15 -0800leotrotskyThanks, 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 -0800WolfdogAdditive-noise methods
http://www.metafilter.com/146055/Additive%2Dnoise%2Dmethods
<a href="http://qz.com/316826/mathematicians-have-finally-figured-out-how-to-tell-correlation-from-causation/">How to tell correlation from causation</a> - "The <a href="https://medium.com/the-physics-arxiv-blog/cause-and-effect-the-revolutionary-new-statistical-test-that-can-tease-them-apart-ed84a988e">basic intuition</a> behind the <a href="http://arxiv.org/abs/1412.3773">method demonstrated</a> by Prof. Joris Mooij of the University of Amsterdam and his co-authors is surprisingly simple: if one event influences another, then the random noise in the causing event will be reflected in the affected event." tag:metafilter.com,2015:site.146055Mon, 12 Jan 2015 19:42:22 -0800kliulessFake 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 -0800gilrainSacred Typography
http://www.metafilter.com/145943/Sacred%2DTypography
<a href="http://www.lindaalila.com/lettering-around">Lettering Around</a> :mandalas for all you font-fetishes out there. From <a href="http://www.lindaalila.com/">Linda Alila</a>. tag:metafilter.com,2015:site.145943Thu, 08 Jan 2015 09:25:16 -0800es_de_bah"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 -0800WolfdogStill Combining Numbers On A Grid To Get Bigger Numbers, But Different
http://www.metafilter.com/145164/Still%2DCombining%2DNumbers%2DOn%2DA%2DGrid%2DTo%2DGet%2DBigger%2DNumbers%2DBut%2DDifferent
<a href="http://www.veewo.com/games/get10/">Get 10</a> is a new browser game from veewo, creators of <em>1024</em>. tag:metafilter.com,2014:site.145164Tue, 09 Dec 2014 00:12:41 -0800RinkuIt's too early on a Monday morning for this hot math nonsense, come on
http://www.metafilter.com/145146/Its%2Dtoo%2Dearly%2Don%2Da%2DMonday%2Dmorning%2Dfor%2Dthis%2Dhot%2Dmath%2Dnonsense%2Dcome%2Don
<a href="http://www.numberphile.com/videos/three.html">Numberphile demonstrates that the digit three is in almost all integers.</a> tag:metafilter.com,2014:site.145146Mon, 08 Dec 2014 09:12:40 -0800boo_radleyThe Saddest Thing I Know about the Integers
http://www.metafilter.com/144958/The%2DSaddest%2DThing%2DI%2DKnow%2Dabout%2Dthe%2DIntegers
The integers are a unique factorization domain, so we can’t tune pianos. <a href="http://blogs.scientificamerican.com/roots-of-unity/2014/11/30/the-saddest-thing-i-know-about-the-integers/">That is the saddest thing I know about the integers.</a> I talked to a Girl Scout troop about math earlier this month, and one of our topics was the intersection of math and music. I chose the way we perceive ratios of sound wave frequencies as intervals. We interpret frequencies that have the ratio 2:1 as octaves. (Larger frequencies sound higher.) We interpret frequencies that have the ratio 3:2 as perfect fifths. And sadly, I had to break it to the girls that these two facts mean that no piano is in tune. In other words, you can tuna fish, but you can’t tune a piano. tag:metafilter.com,2014:site.144958Mon, 01 Dec 2014 12:52:44 -0800jenkinsEarRainy Day
http://www.metafilter.com/144841/Rainy%2DDay
<a href="http://www.papg.com/">Pencil and Paper Games</a> <i>is devoted to games you can play with nothing more than a pencil and a piece of paper</i> (some of which can be played on the site, for those who do not have access to a pencil and paper, or remember what those are.) All the games are worth a look, but their implementation of the <a href="http://www.papg.com/show?2XLM">Countdown Numbers Game</a> is a particularly nice one because you play against a computer opponent that is constrained to a short solve time, so you have a fighting chance of winning. If you want, though, there's a <a href="http://www.crosswordtools.com/numbers-game/">perfect Numbers Game solver at crosswordtools</a> that will show multiple solutions according to the computer's estimate of their difficulty.
Some amusing Numbers Game videos from Countdown:
<a href="https://www.youtube.com/watch?v=pfa3MHLLSWI">Difficult Numbers Game</a>
<a href="https://www.youtube.com/watch?v=MelAwcjxMug">Somewhat Less Difficult Numbers Game</a> tag:metafilter.com,2014:site.144841Wed, 26 Nov 2014 05:02:07 -0800WolfdogVisualisations: oh, I get it now!
http://www.metafilter.com/144514/Visualisations%2Doh%2DI%2Dget%2Dit%2Dnow
<a href="http://setosa.io/ev/">Explained Visually</a> (EV) is an experiment in making hard ideas intuitive <small>[source: <a href="https://news.ycombinator.com/item?id=8608358">hackernews</a>]</small> There are plenty more <a href="http://math.stackexchange.com/questions/733754/visually-stunning-math-concepts-which-are-easy-to-explain">mathematical visualisations</a> around, too... tag:metafilter.com,2014:site.144514Sat, 15 Nov 2014 08:01:44 -0800katrielalexAlexander 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 -0800escabeche√2N
http://www.metafilter.com/143992/2N
<a href="http://www.quantamagazine.org/20141015-at-the-far-ends-of-a-new-universal-law/">At the Far Ends of a New Universal Law</a> <blockquote>The law appeared in full form two decades later, when the mathematicians Craig Tracy and Harold Widom proved that the critical point in the kind of model May used was the peak of a statistical distribution. Then, in 1999, Jinho Baik, Percy Deift and Kurt Johansson discovered that the same statistical distribution also describes variations in sequences of shuffled integers — a completely unrelated mathematical abstraction. Soon the distribution appeared in models of the wriggling perimeter of a bacterial colony and other kinds of random growth. Before long, it was showing up all over physics and mathematics.
“The big question was why,” said Satya Majumdar, a statistical physicist at the University of Paris-Sud. “Why does it pop up everywhere?”</blockquote> tag:metafilter.com,2014:site.143992Tue, 28 Oct 2014 12:59:35 -0800the man of twists and turns100 Years of Martin Gardner!
http://www.metafilter.com/143854/100%2DYears%2Dof%2DMartin%2DGardner
<a href="http://www.celebrationofmind.org/OCTOBER.html">In Honor of the Centennial of Martin Gardner's birth (October 21, 1914),</a> <em>we've lined up Thirty-One Tricks and Treats for you: Magazine articles, new and classic puzzles, unique video interviews, and lots more.</em> ✤ <a href="http://vimeo.com/7176521">The Nature of Things / Martin Gardner</a> [46min video] ✤ <a href="http://www.maa.org/publications/periodicals/college-mathematics-journal/college-mathematics-journal-contents-january-7">The College Mathematics Journal, January 2012</a> dedicated to Gardner with all articles readable online. tag:metafilter.com,2014:site.143854Thu, 23 Oct 2014 08:19:37 -0800WolfdogThe Math Behind the Rolling Shutter Effect.
http://www.metafilter.com/143561/The%2DMath%2DBehind%2Dthe%2DRolling%2DShutter%2DEffect
Here's a pair of blog posts explaining the math behind the "<a href="https://www.youtube.com/watch?v=ecV7oo68vAc">Rolling Shutter Effect</a>":
<a href="http://danielwalsh.tumblr.com/post/54400376441/playing-detective-with-rolling-shutter-photos">Playing Detective with Rolling Shutter Photos</a> and <a href="http://jasmcole.com/2014/10/12/rolling-shutters/">Rolling Shutters</a>. tag:metafilter.com,2014:site.143561Mon, 13 Oct 2014 07:33:35 -0800empathзапомнить практики запоминать практика запоминать практику
http://www.metafilter.com/143285/fluency
<a href="http://nautil.us/issue/17/big-bangs/how-i-rewired-my-brain-to-become-fluent-in-math-rd">Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their succes</a> Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency. tag:metafilter.com,2014:site.143285Fri, 03 Oct 2014 06:24:33 -0800sammyoTake 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 -0800divabatCalculus 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 -0800kliuless