18 posts tagged with Mathematics *and* philosophy. (View popular tags)

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Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)

posted by kliuless on Apr 12, 2014 - 24 comments

posted by kliuless on Apr 12, 2014 - 24 comments

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]

posted by kliuless on Mar 16, 2013 - 25 comments

posted by kliuless on Mar 16, 2013 - 25 comments

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "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?" (via) [more inside]

posted by kliuless on Dec 1, 2012 - 19 comments

posted by kliuless on Dec 1, 2012 - 19 comments

Morton and Vicary on the Categorified Heisenberg Algebra - "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..." [more inside]

posted by kliuless on Jul 21, 2012 - 78 comments

posted by kliuless on Jul 21, 2012 - 78 comments

posted by smcg on Apr 28, 2012 - 8 comments

"Perhaps twenty or thirty people in England may be expected to read this book." G.H. Hardy's review of Whitehead and Russell's *Principia Mathematica*, 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."

posted by escabeche on Sep 12, 2011 - 29 comments

posted by escabeche on Sep 12, 2011 - 29 comments

92 years young, the delightful Raymond Smullyan is a mathematician, logician, magician, concert pianist, and Taoist philosopher - who also pioneered retrograde chess problems.

posted by Trurl on Jun 26, 2011 - 22 comments

posted by Trurl on Jun 26, 2011 - 22 comments

posted by TheophileEscargot on Jun 8, 2009 - 59 comments

On Truth and Reality. Despite several thousand years of failure to correctly understand physical reality (hence the current postmodern view that this is impossible) it is actually very simple to work out how matter exists and moves about in Space. The rules of Science (Occam's Razor / Simplicity) and Metaphysics (Dynamic Unity of Reality) require that reality be described from only one single source existing, as Leibniz wrote: *"because of the interconnection of all things with one another."* [more inside]

posted by netbros on Jan 30, 2009 - 46 comments

posted by netbros on Jan 30, 2009 - 46 comments

The Reality Tests. "A team of physicists 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?"

posted by homunculus on Jun 4, 2008 - 82 comments

posted by homunculus on Jun 4, 2008 - 82 comments

Fate, Absolute Life and Death, the Aleph, the Zeitgeist, the sinking of the Atlantis, the World Trade Center, 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 this man's work. Crazy or brilliant, you make your decision. A video from his website.

posted by moonbizcut on Aug 31, 2007 - 24 comments

posted by moonbizcut on Aug 31, 2007 - 24 comments

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 taught it to high school students [via Digg]. You just have to work with a new number he calls Nullity (RealPlayer video). According to Anderson's site The Book of Paragon, 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 transreal arithmetic (pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue No Zombies, Only Feelies? identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined.

posted by treepour on Dec 7, 2006 - 63 comments

posted by treepour on Dec 7, 2006 - 63 comments

Know less than nothing!? *What could negative knowledge possibly mean? In short, after I tell you negative information, you will know less...* "In this week's issue of Nature, however, Michal Horodecki and colleagues present a fresh approach to understanding quantum phenomena that cannot be grasped simply by considering their classical counterparts." [via slashdot :]

posted by kliuless on Aug 8, 2005 - 26 comments

posted by kliuless on Aug 8, 2005 - 26 comments

Gödel and the Nature of Mathematical Truth : A Talk with Verena Huber-Dyson

posted by Gyan on Jul 29, 2005 - 77 comments

posted by Gyan on Jul 29, 2005 - 77 comments

Godel's theorems have been used to extrapolate a great many "truths" about the world. Torkel Franzen sets the record straight in his new book Godel's Theorem: An Incomplete Guide to Its Use and Abuse. Read the introduction (PDF). If you want, check out his explanation of the theorems.

posted by Gyan on Jun 29, 2005 - 65 comments

posted by Gyan on Jun 29, 2005 - 65 comments

The Meaning of Life 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 askmefi threads.

Dennett: [pause] i guess i'll say it again, more slowly...

(oh, and the player interface is rather delicate - give it time to load and click play a few times...)

posted by andrew cooke on Oct 1, 2004 - 17 comments

Dennett: [pause] i guess i'll say it again, more slowly...

(oh, and the player interface is rather delicate - give it time to load and click play a few times...)

posted by andrew cooke on Oct 1, 2004 - 17 comments

Laws of Form In 1969, George Spencer-Brown published a mathematical book called *Laws of Form*, 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.

posted by y2karl on Nov 11, 2001 - 18 comments

posted by y2karl on Nov 11, 2001 - 18 comments

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