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The difference between a theory and a mathematical kludge. - The year was 2081 [entries|archive|friends|userinfo]
matt

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The difference between a theory and a mathematical kludge. [Oct. 29th, 2003|02:28 pm]
matt
[Current Mood |annoyedannoyed]

Yes, I watched the program "Elegant Universe" last night. Not surprisingly, I had problems with it.

First, the program is voiced not from a scientific point of view, but from a position of authority. There's no distinction made between what is a personal philosophical interpretation of a scientific observation, and actual observation. If you shrunk yourself down to the quantum level, and observed what was going on, you wouldn't "see" chaos. You wouldn't "see" anything at all, because the photons of light you see with would probably be bigger than the events you were observing. It's too easy to get wrapped up in the presentation of "parallel universes" and just assume that parallel universes are some sort of theoretically-discovered "fact". This is not true. Just because there's a probability that a thing is black and white at the same time does not mean that there is a universe where it's black in one and white in the other. That's just a convenient way of describing what is hard to visualize. When you speak from a position of authority, and not as a scientist, it is sometimes difficult to see when someone is describing an actual theory or observation and what is an analogy.

What they should have done is spoken in the language of science: start me off with a premise, and then show me through narrative how various theories and discoveries add or subtract from that premise. Telling me that there are versions of the theory that say the strings are little loops or segments or string cheese or twizzlers doesn't add to my understanding of what they're talking about: moreover, we become wrapped up in this idea of little twizzlers zooming around inside our atoms and think we understand what we've seen, but we've been fooled, deceived.

I recall that as a young child (third grade), I did a book report on Bohr's theory of the atom, and the way it was explained to me is that an atom is like a little solar system, with electrons in fixed orbits or "orbitals". I even remember the little construction paper model of an atom that I made for the cover, annotated with the "A+" of a teacher so clueless in the face of a precocious little boy, with little rings for all the electrons. However, that's an excellent example of how the truth gets swept away in the analogy: even Bohr knew that electrons weren't orbiting the atom like a planet, at a fixed distance. He discovered that there were little probability clouds, where the electron was at all places at once with different probabilities. The fact that the electron orbits say, 2.5 atomic distances away from the nucleus is not a planetary sort of orbit but the place where it is most probably that the electron might be found: but in reality, if you asked the question whether the electron is at exactly that position you would find the probability is very tiny, indeed- it's just better odds than anywhere else in the universe. The idea of "shells" and "orbits" became so entrenched in my psyche that years later, in college, I found myself having to unlearn everything I thought I knew about the atom to try to come to grips with what Bohr actually learned many decades ago. You'll still see periodic charts with dots around the atoms in little orbits, and you'll wonder why if say, oxygen and sulfur both have similar orbits of electrons, how is it that sulfur and oxygen behave so differently? If quantum mechanics is telling me that these atoms have similar orbits, and at the same time is telling me the chemistry differences are mostly originating in the behavior of these outermost, similar orbitals, why are the orbits so similar and the chemistry so different? Why is it then so unusual that this becomes a difficult subject to understand? It's the analogies, stupid. Don't buy an analogy- demand the real thing. Two orbits that are drawn the same may have differences not apparent to the eye- you get fooled by the analogy, like your picture of the orbit *means* something, no matter how carefully drawn.

Second, he did his presentations in a sort of way that showed some sort of whiz-bang graphic, and said "if you could see these, we think they would look something like this". Why? What were your tools? Why do you think this string looks like a twizzler? Why would the waitress at the quantum cafe not be able to bring you an orange juice, even if you asked nicely? Even in quantum mechanics, we know that in real world experiments, at the end of things even the most elegant wavefunctions collapse, and schrodinger is either buying a new cat or not. It's very clear to me if the universe where the cat lives has influence and affects the outcome of the world where the experiment came out and the cat died, but there's no explanation why I can't just steal happy schrodinger's cat over into dead schrodinger's cat universe. It's related to the concept of orthogonality: parallel universes aren't actually parallel but at "right angles", and orthogonal clearly seems to say the universes are perpendicular, not parallel. But the problem lies in the description: if these universes are perpendicular, there must be additional dimensions for every probable outcome, and the universe therefore has infinite dimensions. And yet, string theory is saying that the universe has eleven-or-so dimensions- a number less than infinite. So, which is it? The problem lies in the analogies, not the underlying mathematics. You can come up with brilliant analogies, but in the end, if your analogy leaves an idea or mindset in the viewer that is different than the actual thing you're trying to explain, you've used a bad analogy. And, a bad analogy with a nice pretty picture does more harm than not telling me anything in the first place.

Third, there's just never any good way that people sit down and talk about waves. When a string vibrates with a "c" note, it's not just vibrating like a simple sine wave. There's a degree of irregularity to it- it is composed of "harmonics" which makes a cow bell and a piano and an oboe and a cello sound different playing the same note of "c". However, there's also a nice mathematical tool called Fourier expansion which says that this note of "c" can be broken down into more and more additions of multiples, "harmonics" of "c" starting with the big sinusoidal wave of 261.63 hz or a wave 132 cm long and adding (and subtracting!) waves of shorter length, higher frequency until when you add them all together you get the nice little middle C of a cello, rich and nothing like a pure sinusoidal tone. We can marvel at this amazing discovery- that the string is vibrating with many different notes of "C", all at the same time. We might even deny that such a thing really exists- after all, how absurd! How could you have such a thing as a "negative" sound? If I played this cacophony of tones, why does it sound nothing like that cello? And yet- I can do an experiment: hold my finger delicately and carefully at 1/4 and 3/4 on the string, and I wind up getting the same note, more or less, from the instrument. Why is this true, if I'm not touching carefully that point on the string which never moves in all of the many simultaneous sinusoidal waves of the Fourier expansion? There's a real observation going on here, but to anyone who hasn't carefully looked, we only get the idea that whether cello or oboe or cowbell, it's all the same 132 cm long wave. We get fooled by the analogy- of this sinusoidal wave, to simplify and understand the physics, and ignore all the detail and meaning that evokes such passion when we listen to the soloist. Critics call this "reductionism", and decry the scientist for their insensitive generalization, and turn a poweful tool of mathematics into a demon not to be trusted. But it's not the science that should be branded as the whore of babylon, but the analogy- such a pretty thing, we forget ourselves. We remember mother nature as a beautiful woman, and then criticize when she's painted with large breasts.

Science programs, if they're ever going to be a good thing, should start talking like science if they're ever going to get anywhere. Otherwise, when we get our first picture of a string and it doesn't look anything like a twizzler, you're just going to be left hungry. Sagan was a great guy, but he was a really ass scientist. He's an ad-man: you ultimately remember his jingle "we are starstuff", but you have no idea why that matters. Even Einstein got seduced by the beauty of his own theories, playing with a rhinestone here, a bauble there, but you can't let yourself be seduced by a bad theory in a sparkly set of clothes. We had a great movement in quantum theory because it gave us a powerful new capability: atomic power. We've had great advances in general relativity because they're able to explain things like why starlight looks like it does and why we can make particles seem to live longer by accelerating them. Listen carefully to this program: he's telling you- there's no experiment we can do to test this theory. Experiments are what makes science matter- you actually fire a beam of tachyons, and then we'll be impressed. We want to be amazed by the wonderful new species we're going to find on other planets, we want to be comforted that they're really are aliens and we're not madmen. We want to live in that parallel universe, where we won the lottery and married Angelina Jolie. But the reality is not star trek, but more along the lines of what I remember from L Ron Hubbard's "Return to Tomorrow", where our space traveller grows increasingly out of touch with a world racing by through thousands of years in the four light-year trip to the nearest star. Science is not the hope of Sagan's breathy alien worlds but a darkness forged like the increasing depression of Einstein's collapse into irrelevance. Are we so naive, to fill our days with Santa Claus hopes waiting for the fat man to bring us a sack of strings?

It's not all depressing. Nonetheless, we need to face the reality that quantum mechanics and general relativity might put the food on the table for scientists, but most people are missing out how it will ever put food on the tables of everyone else. Popularizing science can be entertaining and educational without being as unrelentingly depressing as my own view of the subject may be. But if you're ill equipped to watch him make such a poor analogy and know the difference, how can you ever hope to integrate what you've seen into your psyche?
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Comments:
[User Picture]From: cogshiftingman
2003-10-29 12:53 pm (UTC)
I agree with a lot of what you say.

But fundamentally I found it a very enjoyable show. Entertainment.

I especially enjoyed seeing chaps in the program that I come across from time to time. Witten and Schwartz, for example.

My view of strings is that, until we can devise an experiment to test their existence or a direct consequence of their existence, they will remain a philosophy, as Glashow said.

In the coffee shop this morning I chanced upon the head of physics here. He enjoyed the show too, in fact he was gushing about the animations more than about the science.

Perhaps if you're in the field, as I am (albeit somewhat less actively than in the past) you simply welcome a refreshing, simple expose of the topic? I dunno ....
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[User Picture]From: hbergeronx
2003-10-29 01:22 pm (UTC)

oh, it was an *enjoyable* two hours

As someone who has studied computational physical organic chemistry at the graduate level, it's nice to see someone speak clearly about a field which is perfectly clear to me, but unintelligible to everyone around me. But, it's frustrating to then go and ask co-workers what they learned about the program, and get a blank stare or have them go on about wiggly strings or parallel universes. It may make for good tv, but it's nutritionally hollow.

It was simple, and mostly, it was sound. But, the errors and omissions in these things stand out like an unused pistol on the mantel in a mystery novel. Why put it there, if no-one's going to use it?

And maybe I'm a bit bitter, having been away from a library for as long as I have been.
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