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| Yes, today's article is from Quanta. Yes, it talks about mathematics. You didn't really expect that to stop when I changed blog themes, did you? Proof Finds That All Change Is a Mix of Order and Randomness  All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker conjecture.” I've accepted the "mix of order and randomness" thing for a long time (my method for selecting articles to feature here uses just such a combination), but it's nice to know there's formal proof—even though I don't understand it. This particular article is from 2019, so something might have superseded it by now. I don't know. Imagine a garden filled with every variety of flower in the world — delicate orchids, towering sunflowers, the waxy blossoms of the saguaro cactus and the corpse flower’s putrid eruptions. Now imagine that all that floral diversity reduced to just two varieties, and that by crossbreeding those two you could produce all the rest. I'm sure there's a better metaphor for this idea. That is the nature of one of the most sweeping results in mathematics in recent years. It’s a proof by Tim Austin , a mathematician at the University of California, Los Angeles. Instead of flowers, Austin’s work has to do with some of the most-studied objects in mathematics: the mathematical descriptions of change.And, again, so far beyond my own knowledge that it might as well be orbiting Betelgeuse. That's why I read stuff like this. Though it's hard to be skeptical when you don't have the necessary background to ask the right questions. These descriptions, known as dynamical systems, apply to everything from the motion of the planets to fluctuations of the stock market. I can understand being skeptical about this sentence, though. Planets are predictable, right? Like, we know when the next transit of Venus will occur, and when Jupiter aligns with Mars. The stock market is the antithesis of predictable; even weather forecasts are more accurate than stock market speculations. And yet, both are chaotic systems (so is weather). It's just that the planets' orbits are indeterminate after a much longer time frame. Wherever dynamical systems occur, mathematicians want to understand basic facts about them. And one of the most basic facts of all is whether dynamical systems, no matter how complex, can be broken up into random and deterministic elements. I'm not entirely sure, but I think this means that true randomness really does exist. I'd been contemplating that question for a long time. Even dice rolls can be seen as deterministic, relying on initial state, the configuration of the hand that rolls them, and the surfaces they roll against and upon. Also, I have to remember, "deterministic" doesn't necessarily mean "predictable." The article, of course, delves into more detail and contains helpful illustrations. There's nothing else in there that I really want to comment on. Again, I can't say I understood it all. But I think the reason I saved this article, lo these many months ago, is because it's not some high-flying proof unrelated to anything in the real world. As the article notes, it can apply to planetary motion and to stock market fluctuations. I added weather up there. But there's another real-world system that people get wrong all the time (though I can't claim that I get it right all the time), and that's evolution. Evolution deniers have been known to look at organisms (such as humans) or organs (such as the eye) and assert "that couldn't have happened at random!" Their alternative, of course, is that some supernatural intelligence designed everything. But I'm not here to argue that, at least not today. In fact, I'd say that assertion, as far as it goes, is correct—ignoring extremely tiny quantum probabilities, anyway. Because it didn't happen at random. I've been saying for years that it's not random, but there are random elements (such as gene modifications) operating against a backdrop of physical constraints. What I'm still unclear about, and this may be more in the realm of philosophy than math or science, is just how much randomness is actually in play in a given system. But, mostly, it gives me another chance to crow that John Calvin was Wrong. Some years ago, and I had to look it up, I wrote: "To me, as an outsider, 'divine will' is indistinguishable from random chance working through the laws of physics." And behold, here we have a supposed mathematical proof that random chance works through the laws of physics. Look, I try to be skeptical about these things, to the extent that I question even those things with which I agree. But right now, at least on this subject, I'll just assume I'm right and there's science backing me up. |
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