Incompleteness, Uncertainty, Relativity and the Universe

Been a month of heavy reading for me with two books of tremendous and mind-bending scope.

First was Simon Singh's latest 'The Big Bang'. I'm a huge fan of his sort of 'popularized history of science' kind of writing. His first book 'Fermat's Enigma' floored me with its engaging histories of insane mathematicians from Pythagoras (a^2+b^2=c^2) to Fermat (for n>2 there are no whole number solutions for a^n+b^n=c^n) to Wiles - the dude who proved Fermat's theorem in '91 or '92. I should link that book in the list on the right, but the only image I have of the cover is too big to fit in the column.

Singh also wrote 'The Code Book' - another excellent romp through mathematical history, this time as relates not to one of the great riddles of our time, but as relates to the people whose livelihood lies in creating and solving riddles themselves. Crypto is cool... and a naturally engaging topic for a history-of-science writer because it's all full of intrigue and war. I highly recommend it - especially if you're borderline OCD like me and have a dangerous fascination with that stuff. Of course - if you actually are OCD - stay the fuck away from it because it will make you go batty for real.

So his latest book - which I think is more than a year old now - is 'The Big Bang' and he veers away from the purer mathematicians toward the theoretical physicists and cosmologists who have been trying to explain the shape of the universe (spatially and temporally speaking) for a few thousand years. He starts with Aristarchus measuring the distance to the Sun using wells in Africa and the Stade as a unit of measurement and runs all the way up to the late 20th century, covering everyone from Ptolemy to Copernicus and Galileo to Hubble and Einstein. He doesn't go into the real up-to-date stuff like string theory and M-space though.

Anyway, I really enjoyed the book because I think Singh has a knack for finding the human stories and for making characters out of these names that you've been reading in textbooks since high-school. Science is so much more engaging when it's about people instead of just about ideas and numbers... kind of like games in a way. Unfortunately, my own appreciation of the book was hobbled a bit by the fact that I had covered the vast majority of the material in a 'Stars for Rockstars' course at UBC - one of those mandatory science courses for folks in the humanities.

So if you didn't take Astronomy For Arts Students Who Don't Understand Calculus 101 while in school - and you wanna know about more about the stars, planets, galaxies and universe itself so you'll have that information when you need it... I suggest picking it up.

The other book I read was the at turns tear-jerking, at turns punishing 'Incompleteness' by Rebecca Goldstein. It's about Kurt Godel, his life and his work. It's pretty short, but in some places trying to finish the page is akin to having a tooth extracted. I suspect that trying to put together a layman's description of Godel's Incompleteness theorems is a next-to-impossible task and it sure turned my brain into glue as I tried to read it. I'm very glad I pushed through though, because the last couple of chapters of the book are amazing. I cried at the end even, at how sad it is that someone as earth-shakingly brilliant as Godel can just kind of fall between the cracks of society - even in a place like the Institute for Advanced Study at Princeton.

What is great about the book though, aside from the touching perspectives on Godel himself, is the assertion that guys like Godel and Einstein - who us post-modernists most commonly take to be relativists - were in fact the purest of Platonists. Doubly weird when you consider that the term 'relativist' probably gets the majority of its current strength from Einstein himself.

How can Einstein and Godel - the two guys who (along with Heisenberg) probably dealt the most serious blows to any notion of objectivity - be Platonists? I think the argument goes something like this: (and I'll come at it from the Relativity side because it's less abstract and less full of self-referential statements than if I try to come from the Incompleteness side)

Time is relative to the observer and there is no preferred - or objective - frame of reference (duh). But in a sense, what that ends up meaning - or at least this is what I read Goldstein as claiming it meant to Einstein and Godel - is that the General Relativity equations themselves are an absolute and objective description of time. Time literally is the mathematics that describes it - and all of the infinitude of subjective frames of reference are just data-points in the system of time as is defined by General Relativity. Thus - in defining the system that encompasses subjective time, we have a new objective measure of what time is. I think that's kind of cool.

To put it in a context that anyone likely on this site might be more comfortable with... there are an infinite number of possible experiences for a player of Mario Bros. Every single play experience is unique, and none of them are 'preferred' - so if I've played it, I can say 'Mario Bros is X' and if you've played it, you can say 'No, Mario Bros is Y' - each of us is essentially describing his linear experience of the game. We are both right from our own perspective, but also we are both wrong in a sense. Neither of those singular experiences is Mario Bros. Mario Bros - in the Einstein-and-Godel-are-Platonists-sense - is the code. It is the all-encompassing truth that describes all the possible individual, subjective experiences and is itself an absolute. It is because of the code that both of our unique experiences can exist. Each unique experience becomes one of an infinity of solutions for the algorithm that is Mario Bros.

It goes back to the Allegory of the Cave (which I ironically used to help define the role of the Level Designer here). Einstein shows that each reference - each instance of subjective time is just a shadow on the wall, a projection of the Form of his equations... it shows rather irrefutably that there exist objective - though intangible - things... and you can't be much more Platonic than that.

Anyway - if you can tough out the math and can hold onto your marbles through highly self-referential sentences broken down into formal logic, then I'd recommend it. It'll be a breeze if you're a programmer, because the symbolic logic and equations aren't hard, they're just self-referential which sends the mind spinning a bit.

Comments

[Darius K.]

The equations-themselves-are-the-Platonic-ideals way of looking at things is interesting, but to me it stinks of confusing the map with the territory.

My other problem with equating laws of physics with Platonic forms is the inherent morality of the forms. Plato believed that everything in the ordinary world strives to attain its perfect form. This is sort of a judgement: if something is identical to its Platonic form, then it is the best at being itself that it can possibly be. Does this mean that subjective reality needs to strive to be something more than subjective? To bring back your Mario analogy, does it mean we're somehow imperfect Mario fans because we only experience one (or several) linear playthroughs of Mario Bros?

I guess what I'm saying is this: to believe in Platonic forms, even as laws of physics, is to pass judgement on the material world as imperfect in a grand moral sort of sense. And I don't think that this vibes with the spirit of science.

(Oh, and hi, Clint. We met very briefly through Randy at GDC this year. I like your blog so far.)

[andrew stern]

oh cool, I happen to be in the middle of reading Incompleteness right now. I too recommend it.

Just curious, have you read Richard Powers' fiction? Your post somehow made me think of that. His novels are good, and his short story "Literary Devices" was particularly excellent.

The server is currently down, but that story can be found here:
http://www.all-story.com/issues.cgi?tImage=back&action=show_story&story_id=174

[Patrick Dugan]

Sure, Einstein and Godel were platonists, but in an imperfect sense. Once you become the perfect platonist you give up on the notion of ideal forms and embrace the eternal recurrence. Or start making indie games.