Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid has been recorded as a series of video lectures for MIT's Open Courseware project.
posted by loquacious on May 30, 2009 - 74 comments

Correlative Analytics -- or as O'Reilly might term the Social Graph -- sort of mirrors the debate on 'brute force' algorithmic proofs (that are "true for no reason," cf.) in which "computers can extract patterns in this ocean of data that no human could ever possibly detect. These patterns are correlations. They may or may not be causative, but we can learn new things. Therefore they accomplish what science does, although not in the traditional manner... In this part of science, we may get answers that work, but which we don't understand. Is this partial understanding? Or a different kind of understanding?" Of course, say some in the scientific community: hogwash; it's just a fabrication of scientifically/statistically illiterate pundits, like whilst new techniques in data analysis are being developed to help keep ahead of the deluge...
posted by kliuless on Jul 21, 2008 - 40 comments

Open Text Book: a blog which lists freely-available online textbooks. [more inside]
posted by Upton O'Good on Oct 25, 2007 - 12 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

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

Crispin Sartwell is a cryptic and sensational man. The Chair of Humanities and Sciences at the Maryland Institute College of Art, he has translated the Tao Te Ching, published philosophy papers and books, maintained pages on hip hop, founded the American Nihilist Party (and gave a speech to young Democrats urging them to reconsider their votes for John Kerry), taught courses on conjuring and illusion, etc. etc. See also his essay on the pagan cult of mathematics and his thought experiment on music.
posted by painquale on Mar 26, 2005 - 17 comments

Mathematical beauty in science (NYTimes) Though I can't say I've seen a moment of God's glory in finding a balanced checkbook (on the first go), I have been in academia in physics and math enough to know the almost mystical pleasure its practitioners get from the "unreasonable effectiveness of mathematics", and the simplicity and elegance of the equations at its core. I was wondering -- are there other fields where this occurs, where people get the feeling they've tapped into some bare beauty of nature? Philosophy? Art? Architecture?
posted by meep on Mar 26, 2002 - 24 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