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Far falls the peaceful sun Autumn's red-gold cloak enwraps the sky Where lately summer's blue did brightly burn That soon will sleep beneath Soft winter cloud Yet still the fire burns Refracted glory lights the earth Reminding birds that flock on southern courses Spring longs to return Unveiled in green |
| date | 2000-10-24:11:07 |
| Physics | This is the creative aspect of the argument from invariance. It works like this: suppose we know that the universe is invariant under some transformation. Then our descriptions of the universe had better be invariant under that transformation as well. In my previous entry, I talked about how people use this to infer the existence of entities that will make the results of our descriptions invariant. The more demanding use of the argument is to make the descriptions themselves invariant -- to treat invariance under a particular transformation as a constraint, and to see if we can find a particular way of describing the world that naturally fulfills that constraint, without adding any extra entities to it. This is a really hard game to play. Einstein did it with general relativity -- he argued that the world was invariant under any smooth second order transformation, and showed that there is a particular form that the equations of motion that describe any particle must have if that constraint must be satisfied. This is an amazing act of pure creative force -- having a constraint is not constructive; it doesn't tell you anything about what you have to do to satisfy it. There isn't any mechanical procedure you can use to go from knowing the constraints to the object that satisfies them. There are an infinite number of ways the equations of motion could be written. Einstein found the one that satisfied the constraints he believed the universe imposed upon them. It took him many years to do this, and some of the ongoing work in general relativity indicates the difficulty of what he did. 85 years later people are still fiddling around with small variations on Einstein's theme, because while the equations he came up with are the simplest, there are others that are a bit more complex and still satisfy the world's contraints. Einstein's equations have some internal symmetries that people like Moffat argue we could do without, and only experiment will tell who's right. And then there's the value of the famous Cosmological Constant, which Einstein, based on the observational data of his day, set to zero, but which we now think might be something else. It's worth remembering that there's nothing special about zero -- it's just another number, and we know the cosmological constant has a value. Naive theoretical predictions suggest a huge value for it, and any value that's thirty-odd orders of magnitude smaller than that requires some explanation, no matter what it turns out to be. This is typical of the results of arguments from invariance -- they tend to be a bit under-determined. Jaynes makes an argument for the nature of probability based on the invariance of the conclusions of arguments under different (valid) ways of reaching them. In that case, there are two forms of the probability calculus the satisfy his constraints: the ordinary one, where probabilities run from zero to one, and an inverse form, where they run from one to infinity. Both have the same empirical content, but convention dictates we choose the former. This kind of science is a good deal like engineering, which is the art of making arbitrary choices that satisfy constraints that under-determine the solution. And as in engineering, you only find out long after the fact if your choices were really adequate, or if some revision of your theory is needed. I think next I need to talk about knowability, and the importance of the invariance of knowability in the axiomatic foundations of quantum mechanics. |
| SelfConciousness | Communication is weird. I recently read John Searle's Mind, Language and Society: Philosophy in the Real World in which he talks about the nature of speech acts and the way communication works. My very simple take on his argument is this: speech works by inducing in the hearer a state of mind that is the sort of state of mind that would cause a person to say something like what has been said. This is a sort of "understanding via simulacrum" in which my speech is understood because you have the ability to emulate the processes that would induce such an utterance. Hearing -- listening, reading -- on this view is a fundamentally creative act, which makes sense of a lot of stuff, from biblical scholarship to Marxism to the way objectivists read just about everyone. There's a lot more creativity out there than you might think. So what I'm trying to do here, the goal of my writing, is to induce in your mind a little simulacrum of me. If I thought memetics was more than a party game or inappropriate metaphor I'd go off on that tangent now, and say you should wear a condom over your head while reading if you don't want to get infected and/or impregnated. R.A. Lafferty once wrote a story based on the speculative premise that ordinary language is inadequate for communication, and all humans are in fact imperfectly telepathic, which is the only reason we can communicate at all. A scientist in the story finds a way to suppress the telepathic ability in test subjects, and communciation becomes impossible. I can't remember what happened next, but it struck a definite chord in my mind -- this is indeed what communication is like. It only works if there is an element of telepathy involved, and that's what Searle is saying as well, although in his case the telepathy is produced by the intelligence of the listener rather than mysterious waves emanating from the speaker's brain. But often communication breaks down. Some key assumption is not shared, and in its absence the metaphorical telepathy no longer operates, leaving us squawking incomprehensibly, like a chicken who's just laid an egg and wants the whole world to know about it. To our listeners, it's clear that something is going on we care deeply about, but they have no idea what, nor why they should care. When casting forth at random, as this journal does, there's little hope that most people reading it will share enough of my assumptions to understand even a tiny portion of what I'm saying, although that shouldn't stop them from being entertained and even edified by it. I'm fortunate to have in Caro one reader who will understand most of what I say, the way I want it to be understood, and who insists on greater clarity when she doesn't. That's all a writer can ask of his Muse, and more. One of the wonderful things about the 'Net is that people all over the world can try to communicate with each other, and what we call "culture" seems to me to play less of a role than one might think. I'm pretty sure I'm less able to communicate with my next-door neighbors than with Wafa Hakim, for instance, who lives in India and whose remarks on Margret Atwood convinced me to at long last read that most Canadian of Canadian authors. Sometimes communication happens when you least expect it. |