30. First, the seeker for reality should be told that everything exists. Later, when he has understood things and is free from desire, he should be told that everything is vacuous.
— Nagarjuna
31. Those inferior people who do not understand the meaning of vacuity and accept merely the verbal sense do not accomplish merit and are lost.
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? [...]
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 [...]
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 [...]
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
Maths as it should be taught: a video intuitively explaining the turning of a sphere inside/out. Beautiful. Outside In Technorati Tags: mathematics
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 [...]
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
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 [...]
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 [...]
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 [...]
