avevale_intelligencer (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
avevale_intelligencer) wrote2004-11-14 10:13 am
avevale_intelligencer) wrote2004-11-14 10:13 am
For entertainment only
I've been reading Asimov again...
THE WISE OLD PHYSICIST: We can best understand the Einsteinian interpretation of gravity if we picture the universe as a flat, thin, superflexible sheet of untearable rubber. If we picture mass as being associated with weight, as it is on the surface of the earth, then we would expect a mass, resting on the rubber sheet, to make an indentation. The greater the mass, the deeper the indentation. In the--
ME: Excuse me. Why?
THE W.O.P.: Why what?
ME: Why would it make an indentation?
THE W.O.P.: Well, because the weight would pull the mass--
ME: Why would it pull the mass?
THE W.O.P.: Because we're picturing mass as being associated with weight. Do try to listen.
ME: Aha. So somewhere under this rubber sheet there is a large mass to which these other masses are attracted.
THE W.O.P.: Yes.
ME: By gravity.
THE W.O.P.: Yes.
ME: Which is what this analogy is supposed to be explaining.
THE W.O.P.: Yes. Um--
ME: We're going to need another rubber sheet.
THE W.O.P.: Look, it's just an analogy.
ME: Not a very good one, is it? Gravity exists because masses in the universe exert a force upon it, which is gravity. A bit circular, don't you think?
THE W.O.P.: We don't know why gravity exists--
ME: A-ha!!!
THE W.O.P.: But this image accounts for the way gravity operates better than the old model of a force operating between masses.
ME: That's because it's got the old model of a force operating between masses built into it. It's turtles all the way down. If you take out the little man pedalling the car won't run. If you take the force of gravity out of your analogy the masses just sit on the rubber sheet and it stays flat.
THE W.O.P.: Look, just shut up, will you.
ME: Thank you, Professor, I understand so much better now.
THE WISE OLD PHYSICIST: We can best understand the Einsteinian interpretation of gravity if we picture the universe as a flat, thin, superflexible sheet of untearable rubber. If we picture mass as being associated with weight, as it is on the surface of the earth, then we would expect a mass, resting on the rubber sheet, to make an indentation. The greater the mass, the deeper the indentation. In the--
ME: Excuse me. Why?
THE W.O.P.: Why what?
ME: Why would it make an indentation?
THE W.O.P.: Well, because the weight would pull the mass--
ME: Why would it pull the mass?
THE W.O.P.: Because we're picturing mass as being associated with weight. Do try to listen.
ME: Aha. So somewhere under this rubber sheet there is a large mass to which these other masses are attracted.
THE W.O.P.: Yes.
ME: By gravity.
THE W.O.P.: Yes.
ME: Which is what this analogy is supposed to be explaining.
THE W.O.P.: Yes. Um--
ME: We're going to need another rubber sheet.
THE W.O.P.: Look, it's just an analogy.
ME: Not a very good one, is it? Gravity exists because masses in the universe exert a force upon it, which is gravity. A bit circular, don't you think?
THE W.O.P.: We don't know why gravity exists--
ME: A-ha!!!
THE W.O.P.: But this image accounts for the way gravity operates better than the old model of a force operating between masses.
ME: That's because it's got the old model of a force operating between masses built into it. It's turtles all the way down. If you take out the little man pedalling the car won't run. If you take the force of gravity out of your analogy the masses just sit on the rubber sheet and it stays flat.
THE W.O.P.: Look, just shut up, will you.
ME: Thank you, Professor, I understand so much better now.
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This is what happens when analogies get glibly repeated by a second or third generation of people who didn't invent them, who accepted them when they first heard them, and haven't really thought them through in a long time, if ever. They just assume their readers will find them as easy to swallow as they did (or that any who don't are congenital idiots), and don't bother exploring the analogy's assumptions, limits and pitfalls.
I'm curious, though: Do you see your current beef as being with Asimov, or with Einstein, or with both? You've made clear your displeasure with "scientific dogmatists", but I'm still not clear on whether you actually disbelieve the "orthodoxy" wholesale or just reserve the right (as any proper scientist should) to question it.
Y'see, I don't really see any point in continuing to argue with Asimov at this point. He's dead now; he was always a bit of an arrogant bastard; and he was writing quite some time ago - a lot of data has flowed under the bridge since then. Einstein's model is already known to be "incompletely true", and Einstein himself would have no problem with that: It was a big step forward in our conceptualisation of the universe; there are plenty more steps to go. *He* liked the rubber sheet analogy not because it really *explained* the phenomenon of gravity, but because it gave him a life-raft in coping with all that horribly complicated 4- and 5-dimensional geometry that he never was very good at. (He cribbed most of the equations from a textbook borrowed from a colleague, you know. Up 'til then they'd just been an abstract branch of mathematics of no practical use to anyone.)
The accurate statement of the rubber sheet analogy is that 'the mathematics of what we observe happening in the universe corresponds more closely with the idea of a 3 dimensional "rubber sheet" with a constant* source of gravity somewhere "below" it in a 4th dimension, than with the newtonian 3 dimensional model. This picture also gives us a convenient way to visualise what a gravity well is, and specifically what a black hole is, which is consistent with what the equations predict about their behaviour. This helps us to keep clear in our heads what it is we're looking for when we're designing experiments to test the theory. And it turns out that (so far) our observations are more consistent with the new model than with the old.'
*(Yes, constant. This is where your slit above breaks down: The rubber-sheet model assumes that the "pseudo-gravity" force is acting uniformly in a single direction, not that it's caused by an object somewhere. The purpose of the model is to *describe* the interaction between the rubber sheet and the objects sitting on it, not to explain *why* the situation occurs or what is causing the attraction. Explaining why is a later step.)
But it's also generally accepted that the "rubber sheet universe" is not the be-all-and-end-all. So... I'm still not quite sure who you're arguing against, or why.
I thoroughly recommend the supplement issued with a recent (9th October) issue of New Scientist, "State of the Universe", which looks at currently popular (and some not so popular, but disturbingly plausible) theories in cosmology. It shows a refreshing view of many enthusiastic teams of researchers, all slightly daunted by the questions being raised by the latest observations, all keen to put forward their own ideas as to how to solve those problems, and many of them with the humility to admit that there's a lot they don't know and that even what they do know could be wrong. (Maybe the next time you run into a scientific dogmatist, you just need to hand him/her/it a copy, and say "No need to take my word for it: Look, even the bleeding edge scientists are having a tough time believing what you've just said!")
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I mean, how in touch with reality is a system which includes something that you multiply by itself to get minus one? :)
Again, for entertainment only.
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Heh. If you really want maths to start hurting your head like that, read John Conway's Winning Ways. He constructs and equivalence between numbers and "simple games" (the betting return sort rather than Monopoly), then uses that to construct some deeply weird numbers. Things like the number which is less than zero but bigger than all negative numbers. I don't even pretend to understand this stuff, and I have a Maths degree.