Wednesday, June 01, 2005

From the archives of timeless truths

In the previous post, we talked about John Baez, who hosts the column this week's finds in mathematical physics on his website. Seeing his name in Brad's post reminded me of something that I wrote a while ago elsewhere.

In the past, there have been many attempts to explain all physical phenomena -- why, Nature herself -- using One Big Idea: unified field theory, universality, self-organized criticality, and so on. I just became aware of a meme that goes even further.

Take a look at a milder version of this meme (emphasis added by me):

If we think of the universe as passing through the course of history from simplicity to complexity, from neutrinos to nematodes to humans, it's natural to wonder what's at the bottom, where things get very simple, where physics blurs into pure logic.... far from the "spires of form". (emphasis added by me) -- John Baez

Now, this second quote, a rather extended one, is from the book "The Large, the Small and the Human Mind" by none other than Roger Penrose:

...I shall also have [something to say] about another world, the Platonic world of absolutes, in its particular role as the world of mathematical truth. One can well take the view that the 'Platonic world' contains other absolutes, such as the Good and the Beautiful, but I shall be concerned here only with the Platonic concepts of mathematics. Some people find it hard to conceive of this world as existing on its own. They may prefer to think of mathematical concepts merely as idealizations of our physical world -- and, on this view, the mathematical world would be thought of as emerging from the world of physical objects.

Now, this is not how I think of mathematics, nor, I believe, is it how most mathematicians or mathematical physicists think about the world. They think about it in a rather different way, as a structure precisely governed according to timeless mathematical laws. Thus, they prefer to think of the physical world, more appropriately, as emerging out of the ('timeless') world of mathematics. [...]

Here we were, living with this comfortable notion that mathematics is such a nice tool -- rather like a key -- for unlocking and understanding physics. We were even willing (well, sort of) to concede the possibility that mathematics may exist all by itself and be its own master, without being burdened by having to explain anything. Now, along come these wise men, telling us that we got it all backwards. "It is all just mathematics", they seem to suggest, "from whose timeless depths the physical world 'emerges', and into which it 'blurs' when it has done its job".

Fabulous, i'nnit?


  1. Anonymous said...

    Abi, I've always thought mathematics is at the core of pretty much everything. It's why I think nobody should ever give up studying maths; preferably all through an education, but at any rate certainly not in school. Taught well, I venture to say there is no more delightful subject.