complexitystudies

Bee over at Backreaction had a post last week on Max Tegmark: Discover Interview with Tegmark, and I would like to respond to some things said there and in a previous post by Bee on the topic.
(The Tegmark paper on “The Mathematical Universe” can be found on arxiv.org.)

Does the theory warrant further scrutiny?
First of all [...]

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One of the most interesting topics in the philosophy of mathematics is the Axiom of Choice. Here is a nice page with a little intro to the topic and also lots of links for further reading.
For the philosophical relevancy, this quote is a nice demonstration:
Jerry Bona once said,
The Axiom of Choice is obviously [...]

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I guess this is the same idea I presented a couple of days ago in this post (which incidentally was also inspired by an Overcoming Bias blogpost):
Overcoming Bias: The Simple Math of Everything
I called it a concept hierarchy of science; and mathematics is nothing else than concepts in relation. (the uninterpreted equations are only meaningless [...]

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An experiment showing how number symbols and abstract quantities are processed in the prefontal cortex (in monkeys). Of interest to anybody interested in a naturalized mathematics/logic (of course, this is just the beginning…).
How the Brain Maps Symbols to Numbers: Scientific American

Technorati Tags: cognitive science, mathematics

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Maths as it should be taught: a video intuitively explaining the turning of a sphere inside/out.
Beautiful.
Outside In

Technorati Tags: mathematics

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Tim Gowers, a Field’s medalist, has now entered the blogosphere, cool! He has an interesting post on the advantage of teaching syntactically versus semantically. I don’t know if I quite agree, as I have received a largely syntactical education and had to strive for the semantics myself. I would have appreciated more semantics in my [...]

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I posted some of my views on math on the FRIAM list - maybe also of interest to my blog readers.
Re: [FRIAM] math and the mother church
I can recommend the FRIAM list very much - always interesting discussions going on there.

Technorati Tags: mathematics, philosophy of science

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Good Math Bad Math talks about how order arises naturally out of disorder and a simple way of seeing it via Ramsey’s Theorem. He uses the Theorem as an argument against creationism. As good a refutation of creationism as one can desire, I would say, as it is really evident and nicely transferable to the [...]

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Ony of my favorite topics in mathematics is infinity and it’s diverse forms. A nice result is that the Continuum Hypothesis (the hypothesis that there is no infinity between aleph_zero of the integers and aleph_1 of the reals) is independent of the currently accepted/used Axioms of set theory (ZFC) - which form the basics of [...]

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Here in quick succession another fractal link: I am especially fascinated by this, because ever since seeing the picture by Escher I have wondered why he didn’t fill in the middle and that there must be a way to do this. This site has all the details.

In 1956, Maurits Cornelis Escher completed a drawing called [...]

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