MetaFilter posts tagged with philosophy and mathematics
http://www.metafilter.com/tags/philosophy+mathematics
Posts tagged with 'philosophy' and 'mathematics' 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 -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 -0800kliulessnoncommutative balls in boxes
http://www.metafilter.com/118119/noncommutative%2Dballs%2Din%2Dboxes
<a href="http://golem.ph.utexas.edu/category/2012/07/morton_and_vicary_on_the_categ.html">Morton and Vicary on the Categorified Heisenberg Algebra</a> - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." <blockquote>This insight, that funny facts about quantum mechanics are related to simple facts about balls in boxes, allows us to 'categorify' a chunk of quantum mechanics—including the Heisenberg algebra, which is the algebra generated by the position and momentum operators. Now is not the time to explain what that means. The important thing is that Mikhail Khovanov figured out a seemingly quite different way to categorify the same chunk of quantum mechanics, so there was a big puzzle about how his approach relates to the one I just described. Jeffrey Morton and Jamie Vicary have solved that puzzle.
The big spinoff is this. Khovanov's approach showed that in categorified quantum mechanics, a bunch of new equations are true! These equations are 'higher analogues' of Heisenberg's famous formula
<center><i>pq − qp = −i</i></center>
So, these new equations should be important! ... Now Jeffrey and Jamie have shown how to get these equations just by thinking about balls in boxes... The important thing is this: those equations are not something we get to choose, or make up. They are what they are, and they're just sitting there waiting for us to discover them.</blockquote>btw <a href="https://plus.google.com/u/0/117663015413546257905/posts/7ovL7oxoV5Z">John Baez sez</a>: "<a href="http://arxiv.org/abs/1207.2054">Don't even look at it</a> unless you're an expert in mathematical physics, but it's important - and I think someday it could change our understanding of quantum mechanics." :P (I didn't; I know next to nothing about this stuff, but I found it interesting so I thought I'd share ;) tag:metafilter.com,2012:site.118119Sat, 21 Jul 2012 09:42:04 -0800kliulessThe Strangest Man
http://www.metafilter.com/115403/The%2DStrangest%2DMan
<i>The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject, a method which has not yet been applied successfully, but which I feel confident will prove its value in the future. The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by <a href="http://www.damtp.cam.ac.uk/events/strings02/dirac/speach.html" title="The Relation between Mathematics and Physics">considerations of mathematical beauty</a>.</i> [1939] The physicist <a href="http://www.pparc.ac.uk/frontiers/archive/feature.asp?id=13F4&style=feature" title="Dirac's legacy">Paul Dirac</a> had a passion for mathematical beauty. The talk quoted above, <i>The Relation between Mathematics and Physics</i>, was given in 1939 and is available as part of the material posted from the <a href="http://www.damtp.cam.ac.uk/events/strings02/dirac.html">Dirac Centennial Celebration</a> at the University of Cambridge in 2002. More about his life is available in the (long) <a href="http://www.aip.org/history/ohilist/4575_1.html" title="Oral History Transcript - Paul Adrien Maurice Dirac">transcripts of his oral history interviews</a> with the American Insitute of Physics.
Via <a href="https://twitter.com/grahamfarmelo">Graham Farmelo</a>, author of <a href="http://www.thestrangestman.com/">The Strangest Man</a>, a biography of Dirac. tag:metafilter.com,2012:site.115403Sat, 28 Apr 2012 02:51:22 -0800smcgG.H. Hardy reviews Principia Mathematica
http://www.metafilter.com/107360/GH%2DHardy%2Dreviews%2DPrincipia%2DMathematica
<a href="http://www.cl.cam.ac.uk/~ns441/files/hardy-principia.pdf">"Perhaps twenty or thirty people in England may be expected to read this book."</a> G.H. Hardy's review of Whitehead and Russell's <em>Principia Mathematica</em>, published in the Times Literary Supplement 100 years ago last week. "The time has passed when a philosopher can afford to be ignorant of mathematics, and a little perseverance will be well rewarded. It will be something to learn how many of the spectres that have haunted philosophers modern mathematics has finally laid to rest." tag:metafilter.com,2011:site.107360Mon, 12 Sep 2011 14:37:37 -0800escabecheWhat is the title of this post?
http://www.metafilter.com/104970/What%2Dis%2Dthe%2Dtitle%2Dof%2Dthis%2Dpost
92 years young, the delightful <a href="http://raymond-smullyan.co.tv/">Raymond Smullyan</a> is a mathematician, logician, magician, <a href="http://www.youtube.com/watch?v=hrgYFHZGZ3c">concert pianist</a>, and <a href="http://www.mit.edu/people/dpolicar/writing/prose/text/godTaoist.html">Taoist philosopher</a> - who also pioneered <a href="http://blog.chess.com/kurtgodden/the-chess-mysteries-of-professor-smullyan">retrograde chess problems</a>. tag:metafilter.com,2011:site.104970Sun, 26 Jun 2011 19:42:55 -0800TrurlHe laughed like an irresponsible foetus
http://www.metafilter.com/82283/He%2Dlaughed%2Dlike%2Dan%2Dirresponsible%2Dfoetus
<b>Parts <a href="http://www.youtube.com/watch?v=OziPcicgmbw">1</a>, <a href="http://www.youtube.com/watch?v=TedtMmUq8ig">2</a>, <a href="http://www.youtube.com/watch?v=L7I9pgqiLo0">3</a> of a 1959 interview</b> with <a href="http://plato.stanford.edu/entries/russell/">philosopher</a>, <a href="http://fair-use.org/bertrand-russell/the-principles-of-mathematics/">mathematician</a> and <a href="http://www.russfound.org">peace campaigner</a> <a href="http://en.wikipedia.org/wiki/Bertrand_Russell">Bertrand</a> <a href="http://www.britannica.com/EBchecked/topic/513124/Bertrand-Russell">Russell</a> (1872-1970). <a href="http://www.users.drew.edu/~jlenz/brtexts.html">Works</a> and <a href="http://www.humanities.mcmaster.ca/~bertrand/">pictures</a> online include <a href="http://www.users.drew.edu/~jlenz/br-suffrage.html">Anti-suffragist Anxieties</a>, <a href="http://users.drew.edu/~jlenz/whynot.html">Why I am not a Christian</a>, the <a href="http://www.pugwash.org/about/manifesto.htm">Russell-Einstein Manifesto</a> against nuclear weapons and the book <a href="http://russell.cool.ne.jp/beginner/COH-TEXT.HTM">The Conquest of Happiness</a>. Russell is also known for his pithy <a href="http://en.wikiquote.org/wiki/Bertrand_Russell">quotes</a>, his <a href="http://en.wikipedia.org/wiki/Russell's_teapot">teapot</a> and was the subject of poem <a href="http://www.bartleby.com/198/9.html">Mr Apollinax</a> by T.S. Eliot. tag:metafilter.com,2009:site.82283Mon, 08 Jun 2009 02:30:17 -0800TheophileEscargotThe Spherical Wave Structure of Matter in Space
http://www.metafilter.com/78755/The%2DSpherical%2DWave%2DStructure%2Dof%2DMatter%2Din%2DSpace
<a href="http://www.spaceandmotion.com/">On Truth and Reality.</a> Despite several thousand years of failure to correctly understand physical reality (hence the current <a href="http://www.spaceandmotion.com/Philosophy-Postmodernism.htm">postmodern view that this is impossible</a>) it is actually very simple to work out how matter exists and moves about in Space. The rules of <a href="http://www.spaceandmotion.com/Ockhams-Razor.htm">Science (Occam's Razor / Simplicity)</a> and <a href="http://www.spaceandmotion.com/metaphysics.htm">Metaphysics (Dynamic Unity of Reality)</a> require that reality be described from only one single source existing, as Leibniz wrote: <em>"because of the interconnection of all things with one another."</em> <strong>The Four Main Purposes of this Website</strong>
1. To help people understand truth and reality
2. To realize that we are structures of the universe
3. To solve the central problems of knowledge
4. To share this knowledge with others
Deduce the most <a href="http://www.spaceandmotion.com/Most-Simple-Scientific-Theory-Reality.htm">simple science theory of reality</a>, the wave structure of matter in Space, then deduce from this to show that it works. There is no opinion involved - it shows that science does work - we just needed the correct (most simple) foundations.
Given the Wave Structure of Matter in Space it is now possible to explain what mathematics is, how it can exist in the universe, and thus why it is so well suited for describing physical quantities (<a href="http://www.spaceandmotion.com/mathematical-physics/logic-truth-reality.htm">mathematical physics</a>).
We can simplify Einstein's foundations of representing matter as <a href="http://www.spaceandmotion.com/Physics-Albert-Einstein-Theory-Relativity.htm">continuous fields in space-time, to waves in continuous space</a>. It does lead to a very simple, sensible foundation for understanding physical reality, and thus how you exist in the universe.
This article basically explains the main subjects of quantum theory from a <a href="http://www.spaceandmotion.com/Physics-Quantum-Theory-Mechanics.htm">Wave Structure of Matter foundation</a> (wave mechanics). If you prefer shorter summaries just browse the quantum physics links on either side of the page.
The purpose of the Cosmology page is to simply explain the <a href="http://www.spaceandmotion.com/Cosmology.htm">two cosmology theories that are consistent with current observations</a>. You will need a basic understanding of the Wave Structure of Matter (WSM) before you read it. This WSM cosmology is actually describing what you really are, how you exist in this space of the universe and interact with everything around you.
There is a revolution coming in the foundations of our knowledge because we have solved the central problem of metaphysics, of what exists (space) that causes and connects the many things we experience (waves in space that form matter, the discrete and separate particle an illusion of our limited senses). Matter is large, a structure of space, and <a href="http://www.spaceandmotion.com/Philosophy.htm">this truth about reality will change humanity</a>.
If we are to discuss <a href="http://www.spaceandmotion.com/theology-morality-god-world-religions.htm">God and Religion</a>, it is obvious that we must clearly define the meaning of these words (as all words are human constructions). In Philosophy God is generally referred to as the One thing that exists, infinite and eternal, that causes and connects the many things. Likewise, Religion, from Latin 'religare' meaning 'to bind', describes our connection to God as the One thing which exists. From this foundation we then see the clear connection between the sciences of philosophy, physics, metaphysics, and theology, as they are all founded on this Reality of One thing existing.
As humans have <a href="http://www.spaceandmotion.com/evolution-ecology-nature-culture-society.htm">evolved from Nature</a> they ultimately depend upon Nature for their survival. Until we understand what we are as humans (what matter is) and how we are connected to the universe (reality), it is impossible for humanity to be wise, and to be able to evolve cultural knowledge that enables us to live in harmony with Nature.
It is well known that our senses are deceptive, that when we see things as being separate and discrete bodies this is an illusion. Using science terminology then all we are really talking about is <a href="http://www.spaceandmotion.com/health/index.htm">evolution and ecology</a>. That all things in the universe (including life on earth) are interconnected and changing (the dynamic unity of reality).
Teaching people how to think correctly and to use language carefully (to work out the truth for themselves) is a pretty <a href="http://www.spaceandmotion.com/Philosophy-Education.htm">good start for education</a> (i.e. by teaching philosophy to students from a young age).
If we are to improve human societies (which has become an urgent problem) we must consider the forces that determine their evolution. And four of the most significant factors are <a href="http://www.spaceandmotion.com/society/politics-economics-truth-utopia.htm">market economics, politics</a>, education (the knowledge foundations of the people) and Nature. tag:metafilter.com,2009:site.78755Fri, 30 Jan 2009 16:05:00 -0800netbrosReality
http://www.metafilter.com/72280/Reality
<a href="http://www.seedmagazine.com/news/2008/06/the_reality_tests_1.php">The Reality Tests.</a> "A <a href="http://www.quantum.at/">team of physicists</a> in Vienna has devised experiments that may answer one of the enduring riddles of science: Do we create the world just by looking at it?" tag:metafilter.com,2008:site.72280Wed, 04 Jun 2008 23:40:09 -0800homunculusart with a lot of concept
http://www.metafilter.com/64328/art%2Dwith%2Da%2Dlot%2Dof%2Dconcept
Fate, Absolute Life and Death, the Aleph, the Zeitgeist, the sinking of the Atlantis, the <a href="http://www.kentgallery.com/lafbio.htm">World Trade Center</a>, the formation of the universe...what more could you want from art? There's probably already been a been a post on this guy, Paul Laffoley, but I should hope more people could get a glance at some of <a href="http://www.laffoley.com/">this man's work</a>. Crazy or brilliant, you make your decision. A <a href="http://laffoley.com/sample/index.html">video </a>from his website. tag:metafilter.com,2007:site.64328Fri, 31 Aug 2007 13:57:47 -0800moonbizcutNullity and Perspex Machines
http://www.metafilter.com/56810/Nullity%2Dand%2DPerspex%2DMachines
Dr James Anderson, from the University of Reading's computer science department, claims to have defined what it means to divide by zero. It's so simple, he claims, that he's even <a href="http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml">taught it to high school students</a> [via Digg]. You just have to work with a new number he calls <a href="http://www.bbc.co.uk/berkshire/features/divide_zero_sum.ram">Nullity</a> (RealPlayer video). According to Anderson's site <a href="http://www.bookofparagon.com/ ">The Book of Paragon</a>, the creation, innovation, or discovery of nullity is a step toward describing a "perspective simplex, or perspex [ . . . ] a simple physical thing that is both a mind and a body." Anderson claims that Nullity permits the definition of <a href="http://www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf">transreal arithmetic</a> (pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue <a href="http://www.bookofparagon.com/News/News_00002.htm">No Zombies, Only Feelies?</a> identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined. tag:metafilter.com,2006:site.56810Thu, 07 Dec 2006 12:07:57 -0800treepourNegative knowledge (or more precisely negative information)
http://www.metafilter.com/44136/Negative%2Dknowledge%2Dor%2Dmore%2Dprecisely%2Dnegative%2Dinformation
<a href="http://www.damtp.cam.ac.uk/user/jono/negative-information.html">Know less than nothing!?</a> <i>What could negative knowledge possibly mean? In short, after I tell you negative information, you will know less...</i> <small>"In <a href="http://www.nature.com/nphys/journal/vaop/nprelaunch/full/nphys104.html">this week's issue of Nature</a>, however, Michal Horodecki and colleagues present <a href="http://physics.bu.edu/~youssef/quantum/quantum_refs.html">a fresh approach</a> to <a href="http://arxiv.org/abs/quant-ph/0209082">understanding quantum phenomena</a> that <a href="http://www.spectrum.ieee.org/WEBONLY/wonews/jul03/lhand.html" title="nothing at all">cannot</a> <a href="http://www.eetimes.com/showArticle.jhtml?articleID=47902254" title="to do with negative quantum information">be</a> <a href="http://physicsweb.org/articles/world/17/5/3" title="i don't think">grasped</a> simply by <a href="http://physicsweb.org/articles/world/15/10/7">considering their classical counterparts</a>." [<a href="http://science.slashdot.org/science/05/08/08/222245.shtml">via slashdot</a> :]</small> tag:metafilter.com,2005:site.44136Mon, 08 Aug 2005 22:40:50 -0800kliulessNature of Mathematical Truth
http://www.metafilter.com/43828/Nature%2Dof%2DMathematical%2DTruth
<a href="http://www.edge.org/3rd_culture/vhd05/vhd05_index.html">Gödel and the Nature of Mathematical Truth</a> : A Talk with Verena Huber-Dyson tag:metafilter.com,2005:site.43828Fri, 29 Jul 2005 10:24:24 -0800GyanYou can't prove this title wasn't an attempt to illustrate Godel
http://www.metafilter.com/43130/You%2Dcant%2Dprove%2Dthis%2Dtitle%2Dwasnt%2Dan%2Dattempt%2Dto%2Dillustrate%2DGodel
Godel's theorems have been used to extrapolate a great <a href="http://www.sm.luth.se/~torkel/eget/godel.html">many</a> "truths" about the world. <a href="http://www.sm.luth.se/%7Etorkel/">Torkel Franzen</a> sets the record <a href="http://www.ucalgary.ca/~rzach/logblog/2005/06/franzn-on-use-and-abuse-of-gdels.html">straight</a> in his new book <a href="http://www.amazon.com/exec/obidos/ASIN/1568812388/metafilter-20/ref=nosim/">Godel's Theorem: An Incomplete Guide to Its Use and Abuse</a>. Read the <a href="http://www.sm.luth.se/~torkel/eget/tic.html">introduction</a> (PDF). If you want, check out his <a href="http://www.sm.luth.se/~torkel/eget/godel/theorems.html">explanation</a> of the theorems. tag:metafilter.com,2005:site.43130Wed, 29 Jun 2005 02:59:04 -0800GyanMeaning of Life
http://www.metafilter.com/35981/Meaning%2Dof%2DLife
<a href="http://www.meaningoflife.tv/">The Meaning of Life</a> according to various rather famous people (Dennett, Fukuyama, etc). I'm watching the Dennett video at the moment and it starts rather weakly, but, by midway through, is rolling along nicely. With topics like "being good without god" and "the anthropic principle" it struck me as relevant to a couple of recent <a href="http://ask.metafilter.com/mefi/10596">askmefi</a> <a href="http://metatalk.metafilter.com/mefi/8295">threads</a>.
<small><br />
Dennett: [pause] i guess i'll say it again, more slowly...</small><br />
(oh, and the player interface is rather delicate - give it time to load and click play a few times...) tag:metafilter.com,2004:site.35981Fri, 01 Oct 2004 17:29:27 -0800andrew cookeG. Spencer Brown & The Laws of Form
http://www.metafilter.com/12260/G%2DSpencer%2DBrown%2DThe%2DLaws%2Dof%2DForm
<a href="http://www.rgshoup.com/lof/lof.html">Laws of Form</a> In 1969, George Spencer-Brown published a mathematical book called <i>Laws of Form</i>, which has inspired explorations in philosophy, cybernetics, art, spirituality, and computation. The work is powerful and has established a passionate following as well as harsh critics. This web site explores these people, their ideas and history, and provides references for further exploration. I read this then, didn't understand much of the math due to my innumeracy, but was struck by a passage in passing... I especially am curious to see what the numerate in MetaFilter have to say. tag:metafilter.com,2001:site.12260Sun, 11 Nov 2001 13:50:09 -0800y2karl