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Sunday, November 20, 2005

Book Review: Road To Reality Roger Penrose



I've just completed "reading" Penrose's The Road to Reality. I use the quotes because I never got beyond high school algebra (and I'm not talking AP algebra, and I'm not even able to claim anything above a C in maths -AND- all that was about twenty years ago). So I was unable to make much use of about 35% of the characters
in the book. That said, I consider physics and cosmology a hobby and follow current developments to the best of my intuitive ability.

What did I get out of this book? I got a better understanding of what the higher maths are all about. It seems that math is about establishing and formalizing logical/proportional relationships. Penrose, in his final chapter, waxes on about the importance of math and the things math can reveal. From a non-math person's perspective I sensed a bit of hubris here. I think it's somewhat obvious that any number of aspects of reality can be formalized. The problem, as string theory is so pointedly illustrating, is finding the correct aspects to put in the correct relation to provide a useful result. To simply find beautiful relationships satisfies the definition of poetry as much as math. I would argue that excellent poetry is as instructive as excellent math in explaining reality. The common denominator here is excellence, not any specific formalism.

Penrose leads us through a progression of handpicked conventions and discoveries. The narrative does not come together in the way James Burke is able to establish "connections" in history. I think Penrose is a little bit more objective than Burke. As a mathematician Penrose is happy to maintain that the answers are out there, the undiscovered maths are waiting for a bright spark to get to them. And I'm sure he's right, but as he points out (but attempts to avoid, distancing himself from a strict Popperian view) science demands observation. Any theory that's not refutable, unless it somehow leads to a theory that is refutable, isn't worth much. On several occasions Penrose took time to talk about various constructs and mathematical tools that failed to prove useful towards the purposes for which they were developed (only to be revived later in a useful way for a totally unrelated theory).

As someone who's not nearly numerate enough to make this judgment, I found math to be too strict a tool to apply to reality. I found questions of "fine tuning", the problem of relative scale of forces and particles to be mildly offensive (anthropic). I'm starting find the assumption of "constants" to be a little hollow.
Plank units manage an attempt to establish an immutable frame of measurement, however I'm now questioning the relevance of that frame or the relevance of a frame at all. I have a similar difficulty with common accounting conventions that delineate quarters and make salesmen go crazy four times per year (trying to make
quota). I expect more than an accounting system from the people who propose to explain reality (I think Penrose fairly makes this same point in the last chapter (an embarrassing question for a physicist: what is an electron? or nearly any "why?" question). Physicists are making a good effort at accounting for reality, but I
think it makes a fair effort of accounting for itself.

I've always had a problem with string theory. That's one reason I wanted to read Penrose, and to that end I was not disappointed. He admits to the seductive mathematics of string theory, but turns that into a liability of the theory more than an asset. He manages to walk a diplomatic line while pretty well slamming
the viability of such a well funded theory that has produced bugger all in the way of results (sure some beautiful math has been created, but we still haven't been able to correlate relativity theory to quantum theory, and by golly we haven't gotten any warp engines or new doomsday devices out of it either).

I have to confess I left the book without any concept whatsoever regarding Twistor Theory, Penrose's pet theory. Penrose uses the bulk of the book to set up for his proposal of Twistor Theory, but I found that I'd come to my own conclusions before Penrose was able make his point. And I'm afraid it doesn't include Twistor Theory, which is why I think I wasn't too concerned with it. It struck me at some point that I was reading a very long version of the parable of the six blind men who authoritatively interpret an elephant from their individual perspectives: one touching the trunk, one the tail, one an ear, on the tusk, etc.

That's not to say I've abandoned all hope in physics. I still think it's at least as important as the written word, bread and wine. But no more so.

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