MetaFilter posts tagged with universality
http://www.metafilter.com/tags/universality
Posts tagged with 'universality' at MetaFilter.Sat, 12 Apr 2014 08:55:27 -0800Sat, 12 Apr 2014 08:55:27 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60A 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 -0800kliulessbinding the andat
http://www.metafilter.com/134338/binding%2Dthe%2Dandat
<a href="http://www.wired.com/wiredscience/2013/11/prime/all/">Closing in on the twin prime conjecture</a> (<a href="https://www.simonsfoundation.org/quanta/20131119-together-and-alone-closing-the-prime-gap/">Quanta</a>) - "Just months after <a href="http://www.metafilter.com/128049/Quite-a-day-for-analytic-number-theory">Zhang</a> announced his result, <a href="http://arxiv.org/abs/1311.4600">Maynard</a> has presented an independent proof that pushes the gap down to 600. A <a href="http://terrytao.wordpress.com/tag/polymath8/">new Polymath project</a> is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." <a href="https://plus.google.com/u/0/117663015413546257905/posts/LxR23RdyvuF">also btw</a> :P (<a href="https://plus.google.com/u/0/117663015413546257905/posts/jd5K4jBKRYP">for fun</a>!)
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/Z4cUWGQp8Ar">Schröder–Hipparchus numbers</a> (<a href="http://golem.ph.utexas.edu/category/2013/04/permutations_polynomials_and_p.html">The Hipparchus Operad</a>)
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/WoXqXCzkc9S">Quasi</a>-<a href="http://golem.ph.utexas.edu/category/2013/06/quasicrystals_and_the_riemann.html">crystals</a> (<a href="https://plus.google.com/u/0/117663015413546257905/posts/j4Xxg44n1t6">quantum physics and number theory</a>)
-<a href="https://www.simonsfoundation.org/quanta/20131126-to-settle-infinity-question-a-new-law-of-logic/">To Settle Infinity Question, a New Law of Mathematics</a>
oh and <a href="https://www.simonsfoundation.org/quanta/20131107-physicists-eye-quantum-gravity-interface/">perhaps</a> more practically...
-<a href="http://www.thephysicsmill.com/2013/10/13/causal-dynamical-triangulations/">Quantum Geometry: Causal Dynamical Triangulations</a> (<a href="https://plus.google.com/u/0/117663015413546257905/posts/ATg9EwD5CJy">via</a>)
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/9HeN1sSQztA">Quantropy</a>
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/51Gd5adQZNM">Petri nets</a> (<a href="http://johncarlosbaez.wordpress.com/2013/04/19/petri-net-programming-part-3/">programming</a> <a href="http://www.metafilter.com/134300/ASCII-fluid-simulator">water</a>)
-<a href="http://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/">Network theory</a>
-<a href="https://plus.google.com/u/0/117663015413546257905/posts/SrQe3Bsd9kp">The network of mathematics</a>
-<a href="http://math.ucr.edu/home/baez/irvine/">The Foundations of Applied Mathematics</a> (<a href="https://plus.google.com/u/0/117663015413546257905/posts/LX52bzbuWgH">topos theory</a>)
-<a href="http://www.wired.com/wiredscience/2013/10/topology-data-sets/all/">Topological Data Analysis</a> tag:metafilter.com,2013:site.134338Sun, 01 Dec 2013 16:19:50 -0800kliulessComputerized Math, Formal Proofs and Alternative Logic
http://www.metafilter.com/126041/Computerized%2DMath%2DFormal%2DProofs%2Dandamp%2DAlternative%2DLogic
<a href="http://www.wired.com/wiredscience/2013/03/computers-and-math/all/">Using computer systems for doing mathematical proofs</a> - "With the proliferation of <a href="http://en.wikipedia.org/wiki/Computer-assisted_proof">computer-assisted proofs</a> that are all but impossible to check by hand, Hales thinks computers must become the judge." <blockquote>Three years ago, Vladimir Voevodsky, one of the organizers of a new program on the foundations of mathematics at the Institute for Advanced Study in Princeton, N.J., discovered that a formal logic system that was developed by computer scientists, called "<a href="http://en.wikipedia.org/wiki/Type_theory">type theory</a>" could be used to re-create the entire mathematical universe from scratch. Type theory is consistent with the mathematical axioms, but couched in the language of computers. Voevodsky believes this alternative way to formalize mathematics, which he has renamed the <a href="http://video.ias.edu/univalent/voevodsky">univalent foundations of mathematics</a>, will streamline the process of formal theorem proving. Voevodsky and his team are adapting a <a href="https://plus.google.com/u/0/117663015413546257905/posts/4BZRibN6iKQ">program named Coq</a>, which was designed to formally verify computer algorithms, for use in abstract mathematics.</blockquote>
also btw, speaking of mathematical revolutions, from a historical perspective, check out <a href="http://www.scientificamerican.com/article.cfm?id=the-man-of-numbers-fibona&print=true">The Man of Numbers: Fibonacci's Arithmetic Revolution</a> - "Before the 13th century Europeans used Roman numerals to do arithmetic. Leonardo of Pisa, better known today as Fibonacci, is largely responsible for the adoption of the Hindu–Arabic numeral system in Europe, which revolutionized not only mathematics but commerce and trade as well. How did the system spread from the Arab world to Europe, and what would our lives be without it?" tag:metafilter.com,2013:site.126041Sat, 16 Mar 2013 15:33:01 -0800kliulessthe power and beauty of mathematics
http://www.metafilter.com/124535/the%2Dpower%2Dand%2Dbeauty%2Dof%2Dmathematics
<a href="http://blogs.scientificamerican.com/the-curious-wavefunction/2013/01/22/an-eternity-of-infinities-the-power-and-beauty-of-mathematics/">An eternity of infinities</a> (<a href="http://economistsview.typepad.com/economistsview/2013/01/links-for-01-23-2013.html">via</a>) "The comparison of infinities is simple to understand and is a fantastic device for introducing children to the wonders of mathematics. It drives home the essential weirdness of the mathematical universe and raises penetrating questions not only about the nature of this universe but about the nature of the human mind that can comprehend it. One of the biggest questions concerns the nature of reality itself. Physics has also revealed counter-intuitive truths about the universe like the curvature of space-time, the duality of waves and particles and the spooky phenomenon of entanglement, but these truths undoubtedly have a real existence as observed through exhaustive experimentation. But what do the bizarre truths revealed by mathematics actually mean? Unlike the truths of physics they can't exactly be touched and seen. Can some of these such as the perceived differences between two kinds of infinities simply be a function of human perception, or do these truths point to an objective reality 'out there'? If they are only a function of human perception, what is it exactly in the structure of the brain that makes such wondrous creations possible? In the twenty-first century when neuroscience promises to reveal more of the brain than was ever possible, the investigation of mathematical understanding could prove to be profoundly significant." tag:metafilter.com,2013:site.124535Sat, 02 Feb 2013 09:14:26 -0800kliulessdirect realism
http://www.metafilter.com/122400/direct%2Drealism
<a href="http://dannyreviews.com/h/Nature_Computation.html">The Nature of Computation</a> - <a href="http://masi.cscs.lsa.umich.edu/~crshalizi/reviews/nature-of-computation.html">Intellects Vast and Warm and Sympathetic</a>: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/weblog/algae-2011-10.html">via</a>) <blockquote>This is, simply put, the best-written book on the theory of computation I have ever read; one of the best-written mathematical books I have ever read, period... from beginning to end, and all the 900+ pages in between, this was lucid, insightful, just rigorous enough, alive to how technical problems relate to larger issues, and above all, passionate and human.</blockquote>also btw...<ul><li><a href="http://infoproc.blogspot.com/2011/10/on-origin-of-probability-in-quantum.html">On the origin of probability in quantum mechanics</a> - "Because the wave function evolves entirely deterministically in <a href="http://infoproc.blogspot.com/2012/11/schwinger-on-quantum-foundations.html">many worlds</a>, all probabilities are necessarily subjective and the interpretation does not require <a href="http://www.metafilter.com/contribute/search.mefi?q=chaitin&tab=comments&site=mefi&sort=date">true</a> <a href="http://www.metafilter.com/122256/The-Royal-Society-Winton-Prize-2012">randomness</a>, thereby preserving Einstein's requirement that outcomes have causes."
<li><a href="http://johncarlosbaez.wordpress.com/2012/10/08/the-mathematical-origin-of-irreversibility/">The Mathematical Origin of Irreversibility</a> - "The key to this rather profound connection resides in a universal property of Markov processes discovered recently in the context of non-equilibrium statistical mechanics, and known as the '<a href="https://plus.google.com/u/0/117663015413546257905/posts/cLjAKybxWR8">fluctuation theorem</a>'. Typically stated in terms of '<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/notebooks/prigogine.html">dissipated work</a>' or '<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/notebooks/tsallis.html">entropy production</a>', this result can be seen as an extension of the Second Law of Thermodynamics to <i>small</i> systems, where thermal fluctuations cannot be neglected. But <i>it is actually much more than this</i>: it is the mathematical underpinning of irreversibility itself, be it thermodynamical, evolutionary, or else. To make this point clear, let me start by giving a general formulation of the fluctuation theorem that makes no reference to physics concepts such as 'heat' or 'work' "
<li><a href="https://plus.google.com/u/0/117663015413546257905/posts/jYw1fnVTFbY">A nice easy explanation</a> of the <a href="http://www.metafilter.com/119847/Mathematics-world-abuzz-with-a-proof-of-the-ABC-Conjecture">abc</a> <a href="https://plus.google.com/u/0/117663015413546257905/posts/Npu7xDniXMS">conjecture</a> [also btw <a href="http://www.metafilter.com/121668/Grahams-Number">1</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/VLkhD7NBAb3">2</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/6pbLR5Yyf8h">3</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/cqMha2Lz5gr">4</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/cLjAKybxWR8">5</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/4BZRibN6iKQ">6</a>,<a href="https://plus.google.com/u/0/117663015413546257905/posts/DdA4HkKfMiL">7</a>,<a href="http://www.metafilter.com/107661/Counting">8</a>]
<li><a href="http://en.wikipedia.org/wiki/Hilary_Putnam">An argument for the reality of mathematical entities</a> [<a href="http://en.wikipedia.org/wiki/Max_Tegmark">1</a>,<a href="http://masi.cscs.lsa.umich.edu/~crshalizi/reviews/ballard-natural/">2</a>,<a href="http://andrewsullivan.thedailybeast.com/2012/08/ask-jim-holt-anything-your-favorite-philosopher-and-why.html">3</a>]
<li><a href="http://blogs.discovermagazine.com/cosmicvariance/2012/10/22/from-particles-to-people-the-laws-of-nature-and-the-meaning-of-life/">From Particles to People: The Laws of Nature and the Meaning of Life</a> [<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/04/24/the-particle-at-the-end-of-the-universe/">1</a>,<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/11/13/a-book-full-of-particles/">2</a>,<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/10/11/moving-naturalism-forward/">3</a>,<a href="http://blogs.discovermagazine.com/cosmicvariance/2012/10/18/feynman-on-initial-conditions-evolving-laws-and-what-we-consider-physics/">4</a>,<a href="http://science.slashdot.org/story/12/08/01/2127225/entangled-particles-break-classical-law-of-thermodynamics-say-physicists">5</a>]</li></li></li></li></li></ul><a href="http://www.hpcwire.com/hpcwire/2012-10-10/could_the_universe_reveal_itself_as_a_computer_simulation_.html">Could the Universe Reveal Itself as a Computer Simulation?</a> (<a href="http://www.metafilter.com/119883/WHOA-DUDE-ARE-WE-INSIDE-A-COMPUTER-RIGHT-NOW">previously</a>) tag:metafilter.com,2012:site.122400Sat, 01 Dec 2012 00:12:10 -0800kliulessThe Iranian revolution in its singularity
http://www.metafilter.com/98024/The%2DIranian%2Drevolution%2Din%2Dits%2Dsingularity
<a href="http://www.wumingfoundation.com/english/wumingblog/?p=1394">Foucault in Iran: Revolution, Entropy and Equality</a> By way of introduction to the <a href="http://www.wumingfoundation.com/english/biography.html">Wu Ming Foundation</a>'s (<a href="http://www.metafilter.com/32191/Luther-Blissett-taking-revenge-on-stupidity">previously</a>) re-vamped <a href="http://www.wumingfoundation.com/english/wumingblog/">blog</a>, one of their more substantive essays re-assessing Foucault's <a href="http://www.newpol.org/node/327">notorious</a> enthusiasm for the Iranian revolution. tag:metafilter.com,2010:site.98024Tue, 30 Nov 2010 09:48:48 -0800AbiezerLike Democracy Itself, It Needs Defending
http://www.metafilter.com/97767/Like%2DDemocracy%2DItself%2DIt%2DNeeds%2DDefending
<a href="http://www.scientificamerican.com/article.cfm?id=long-live-the-web&print=true">Long Live the Web</a> — An impassioned plea to actively support openness on the Web from <a href="http://www.w3.org/People/Berners-Lee/">Tim Berners-Lee</a>. <em>"The principle of universality allows the Web to work no matter what hardware, software, network connection or language you use and to handle information of all types and qualities. This principle guides Web technology design.
Technical standards that are open and royalty-free allow people to create applications without anyone’s permission or having to pay. Patents, and Web services that do not use the common URIs for addresses, limit innovation.
Threats to the Internet, such as companies or governments that interfere with or snoop on Internet traffic, compromise basic human network rights.
Web applications, linked data and other future Web technologies will flourish only if we protect the medium’s basic principles."</em> tag:metafilter.com,2010:site.97767Fri, 19 Nov 2010 15:54:37 -0800netbrosfrom complexity, universality
http://www.metafilter.com/96954/from%2Dcomplexity%2Duniversality
<a href="http://terrytao.wordpress.com/2010/09/14/a-second-draft-of-a-non-technical-article-on-universality/">A brief tour of the mysteriously universal laws of mathematics and nature.</a> BONUS
- <a href="http://www.americanscientist.org/issues/id.9346,y.2010,no.3,content.true,page.1,css.print/issue.aspx">The Bootstrap</a> [<a href="http://cscs.umich.edu/~crshalizi/notebooks/bootstrap.html">1</a>,<a href="http://bactra.org/weblog/652.html">2</a>]
- <a href="http://delong.typepad.com/sdj/2010/10/the-physics-of-wet-dogs.html">The Physics of Wet Dogs</a> tag:metafilter.com,2010:site.96954Sun, 24 Oct 2010 07:11:27 -0800kliuless