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FQXi BLOGS
CATEGORY: Blog
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TOPIC: Deferential Geometry
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We've had a series of late season storms sweep through Tahoe this past week. Flurries of snow swirl around briefly, then settle and melt in the spring sun. During a break in the clouds today C and I hiked up the fire road behind our house to watch the storm clouds chase each other around the lake.
This world of ours is a remarkably beautiful place. Perhaps it only seems beautiful to us because we've evolved to live here, but the rich complexity of it all is inarguable, whatever the perspective. On the largest scale possible for us to see, the universe looks like nothing but geometry -- the curving spacetime of general relativity, punctuated by matter. Closer in, the matter has formed into galaxies, composed of mysterious dark matter and stars, with planets and other chunks of burnt-up star stuff circling about and between them. On our personal scale, the physical world is dominated by the chaos of our environment and biology, with complex interactions between an infinite variety of living things. But a closer look shows this biology to follow many of the same patterns, with intricate dances of biochemistry repeated within each cellular building block. And this chemistry is made up of molecules composed from only a hundred or so different kinds of atom. And each of these atoms is built from a handful of particles, which, as far as we can tell, are each exactly the same. But what are they?
As we look deeper, the world appears to be built from fewer and simpler building blocks, with its every motion orchestrated by mathematics. We clearly live in a mathematical universe. But our home is not composed of random mathematics -- if it was, things wouldn't look any more elementary at smaller scales. The mathematics has to defer to what is real, to what we see with our experiments, and not just be stuff someone thought would be fun to make up. The universe should be described by a fairly uncomplicated bit of math that we just haven't figured out yet.
By this measure the most successful bit of mathematics staring us in the face is Einstein's geometric description of the universe on the largest scale. If the whole universe, down to the smallest scale, is going to be described by a unified, simple bit of mathematics, it's going to have to be geometry all the way down. The smallest subatomic particles are themselves going to have to have a geometric description, as a bit of deferential geometry.
So when I look out at the clouds over the lake, under a patch of beautiful blue sky, the snow falling in the distance, with wind rustling the pine needles nearby, and Blue Jays hopping between branches, that's what I see at play underneath it all -- whirls of geometry. And when I return home, to play with equations, that's what I look for.
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Garrett,
Thanks for this inspiring post! However, as part of the FQXi administration, I am a bit concerned about your FQXi grant . My reading of the report from the review committee was that the money was specifically for thinking deep thoughts about physics while sitting on beach in Hawaii, whereas here you seem to be thinking physics while sitting and viewing Lake Tahoe. I will have to ask the ad-hoc committee to look into this...
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Hi Anthony,
I was getting a lot of deep thinking done in Maui, but the mountains here in Tahoe -- where I'm spending a lot of time in the lab -- provide an ideal environment for working on gravity. I hope the committee will consider this when deciding whether I'm spending the funds properly.
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