Logic hacking - "Writing shorter and shorter computer programs for which it's unknowable whether these programs run forever, or stop... the winner of the Busy Beaver Game for N-state Turing machines becomes unknowable using ordinary math - somewhere between N = 5 and N = 1919." [more inside]
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 ;)
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]
In the early 1960s, actor/comedian/writer/composer/TV-star Steve Allen recorded How to Think, an educational album about the brain and the mind. [more inside]
How to Talk to a Climate Sceptic: "...a handy one-stop shop for all the material you should need to rebut the more common anti-global warming science arguments constantly echoed across the internet."
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.
In a breathless, passionate, yet level-headed 15 part series, YouTube user, paleontologist, ex-Christian, and potential Space Coyote impersonator AronRa presents an uncommonly well-written and presented argument against what he identifies as the 14 "Fundamental Falsehoods of Creationism." [more inside]
Parmenides. "The pre-Socratic philosopher sparked an intellectual revolution that still echoes today. Yet for philosophy and science to continue to progress in the 21st century, we may need to embark on an entirely new cognitive journey ."
Gödel and the Nature of Mathematical Truth : A Talk with Verena Huber-Dyson
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.
The Logic of Diversity "A new book, The Wisdom of Crowds [..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)