On reality

18Jul06

I just finished reading The Fabric of the Cosmos by Brian Greene. I’m no phystronomer, but I do have thoughts on the book.

I generally dislike attempts to make metaphors out of mathematical conclusions. They never really convey the correct message, and especially, they don’t convey the consequences of the relationships involved. That being said, I think that Greene does a fantastic job of creating the right metaphors; he finds the pithy abstract lesson to be taken from the mathematics and brings it out. And in cases where one metaphor doesn’t suffice, he uses two, so you can look at his point from both views. At the end of the book this all gets a bit confusing, since you’re not sure which part of the metaphors are to be taken at face value, and which are glossed-over details introduced to ease comprehension. But, by the end of the book, you have learned so much that you already owe yourself a second reading, so that’s no huge complaint. (Sometimes I’m tempted to drop everything and study mathematics, just so I can better understand physics, which I find so interesting, yet so impenetrable when written in prose.)

Otherwise, the book is very interesting. Since my formal physics education really stopped when I was in high school, Higgs fields, gravitons, M-theory, the idea that there may be essential units of spacetime, etc. were all very new to me. I’d read snippets here and there about probability waves, “spooky action at a distance,” and the like, but I had never seen all of the relevant material presented accessibly and in-depth.

My favorite idea from the book is the notion that the disconnect between the world on classical and quantum scales may be akin to the difference between looking at TV screen up close and looking at it from a distance — up close, you can see the pixels, but when you step back, you can’t see it with the same resolution. So, if you could get “close” enough, you’d see all of the quantum uncertainty — particles in multiple places, etc. Wouldn’t that be fun? (No, it wouldn’t, but it would be massively interesting.)

The discussion of how quantum uncertainty disagrees with the way the world seems to us reminds me of the philosophical discussions of empiricists. We perceive the world through our senses, and we have no guarantee that the representation is a high-fidelity one. Kant’s conclusion was that we can’t know that the world looks the way we see it, but at least we can know that it’s there. If there are multiple worlds, or if everything we see is a three-dimensional analog of some two-dimensional world without gravity, or if all of the possibilities contained in every probability wave are really being played out simultaneously, it might never matter to us on a day-to-day basis, since our real equipment (our senses) is built to see the world the way we see it (granted, their might be technological and scientific applications of this knowledge, but our perceptions will stay the same).

There’s another philosophical overlap regarding mathematics and the structure of the universe. Descartes thought that the idea of a circle was built in to the human brain. David Hume thought that mathematics was essentially a game, where we all agreed on the rules. This caused problems (how do we keep “discovering” new rules?). Kant thought that our concepts of mathematics were necessary for cognition — our ability to live depends on our ability to distinguish between different points or intervals in space and time. I always liked this idea, because, for me, it implied some sort of Cartesian correspondence between the true nature of physical reality and the mathematics that exists only within our minds (Descartes thought that we were born with certain notions ingrained in our minds that we could not have obtained through empirical experience, such as the concept of infinity). But one of the arguments in TFOTC seems to be that the same physical phenomena can be expressed mathematically through several different, yet equivalent, frameworks. Such a multiplicity, in my mind, implies that mathematics might be only another metaphor for “real reality,” not a reflection of the true nature of things. Granted, it would be a very apt metaphor, at least from our present point of view, but my comforting perspective of mathematics as presenting access to the external world is weakened.

Enough. Think about the nature of the nature of things too long and you’ll forget why you care about the world in the first place.

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