Nov 18, 2006

NewScientist at 50: Roger Penrose describes reality

In his entry, Roger Penrose argues that a Platonic world of mathematical truths coexists with the world of molecules and molehills. Penrose's argument, in short [sub. req.]:
Our mathematical models of physical reality are far from complete, but they provide us with schemes that model reality with great precision - a precision enormously exceeding that of any description that is free of mathematics. There seems every reason to believe that these already remarkable schemes will be improved upon and that even more elegant and subtle pieces of mathematics will be found to mirror reality with even greater precision. Might mathematical entities inhabit their own world, the abstract Platonic world of mathematical forms? It is an idea that many mathematicians are comfortable with. In this scheme, the truths that mathematicians seek are, in a clear sense, already "there...." To a mathematical Platonist, it is not so absurd to seek an ultimate home for physical reality within Plato's world.

This is not acceptable to everyone. Many philosophers, and others, would argue that mathematics consists merely of idealised mental concepts, and, if the world of mathematics is to be regarded as arising ultimately from our minds, then we have reached a circularity: our minds arise from the functioning of our physical brains, and the very precise physical laws that underlie that functioning are grounded in the mathematics that requires our brains for its existence. My own position is to avoid this immediate paradox by allowing the Platonic mathematical world its own timeless and locationless existence, while allowing it to be accessible to us through mental activity. My viewpoint allows for three different kinds of reality: the physical, the mental and the Platonic-mathematical, with something (as yet) profoundly mysterious in the relations between the three.
What Penrose doesn't acknowledge is that some convergences are coincidences--and that mathematics can be entirely internally consistent, yet need not map onto any external reality, or are adaptable to entirely variable realities. (The gaping holes in the middle of math brought by Gödel go completely unmentioned.)

In other words, math would be an epiphenomenon: predictable, and predictive, but not on its own level of existence--like a literary character in the pages of a novel.

As a bonus, the article offers Nick Bostrom's simulation argument. If we grant that a sufficiently advanced civilization could create a workable simulation of existence, we have every right to suspect we inhabit that simulation.

3 comments:

JEFM said...

jan_fernandezAThotmail.com

:)

Andrew Thomas said...

I agree with what you say: "mathematics can be entirely internally consistent, yet need not map onto any external reality, or are adaptable to entirely variable realities."

Here's a quote from my own blog The Mathematical Universe: "The discovery of some logical paradoxes involving circular reasoning would also appear unable to correspond to any situation in the real world."

However, when you say Penrose ignores Godel that's a bit unfair - Penrose's "Emperor's New Mind" was all about Godel. He just didn't think it was relevant for this particular discussion.

I agree entirely with this: "In other words, math would be an epiphenomenon: predictable, and predictive, but not on its own level of existence."

You might enjoy the sections at the bottom of my Mathemtical Universe page (link given earlier).

Jim Anderson said...

Andrew,

I'll take back what I said about Godel. (It's been a very long time since I read "The Emperor's New Mind"--I discovered it as an undergrad, when I should have been studying Beowulf.)

Thanks for the informative and accessible link.