Can Newtonian dynamics really be derived from relativistic dynamics? What would such a derivation look like? Imagine a set of statements, E1, E2... En, which together embody the laws of relativity theory. These statements contain variables and parameters representing spatial position, time, rest mass, etc. From them, together with the apparatus of logic and mathematics, is deducible a whole set of further statements including some that can be checked by observation. To prove the adequacy of Newtonian dynamics as a special case, we must add to the Ei's additional statements, like (v/c)2 << 1, restricting the range of the parameters and variables. This enlarged set of statements is then manipulated to yield a new set, N1, N2... Nm, which is identical in form with Newton's laws of motions, the law of gravity, and so on. Apparently Newtonian dynamics has been derived from Einsteinian, subject to a few limiting conditions.
Yet the derivation is spurious, at least to this point. Though the Ni's are a special case of the laws of relativistic mechanics, they are not Newton's Laws. Or at least they are not unless those laws are reinterpreted in a way that would have been impossible until after Einstein's work. The variables and parameters that in the Einsteinian Ei's represented spatial position, time, mass, etc., still occur in the Ni's; and they there still represent Einsteinian space, time, and mass. But the physical referents of these Einsteinian concepts are by no means identical with those of the Newtonian concepts that bear the same name. (Newtonian mass is conserved; Einsteinian is convertible with energy. Only at low relative velocities may the two be measured in the same way, and even then they must not be conceived to be the same.) Unless we change the definitions of the variables in the Ni's, the statements we have derived are not Newtonian. If we do change them, we cannot properly be said to have derived Newton's laws, at least not in any sense of "derive" now generally recognized. Our argument has, of course, explained why Newton's Laws ever seemed to work. In doing so it has justified, say, an automobile driver in acting as though he lived in a Newtonian universe. An argument of the same type is used to justify teaching earth-centered astronomy to surveyors. But the argument has still not done what it purported to do. It has not, that is, shown Newton's Laws to be a limiting case of Einstein's. For in the passage to the limit it is not only the forms of the laws that have changed. Simultaneously we have had to alter the fundamental structural elements of which the universe to which they apply is composed.
*The quantum example in "What Are Scientific Revolutions?" somewhat obscures its revolutionary character by not alluding to the many changes wrought by the quantum but instead focusing on the vocabulary shift from "resonator" to "oscillator" that accompanied the recognition that the resonator's energy levels were discontinuous rather than continuous.
**My analogy on the Kuhn 20 thread was to say that our continued use of Newtonian mechanics was like our continued use of the words "sunrise" and "sunset," which have a real and irreplaceable function (at least not replaceable in any way that I can see) but whose existence hardly makes the Copernican Revolution less revolutionary or means that Ptolemaic/Aristotelian cosmology are still partially in effect.
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Date: 2009-07-16 09:12 pm (UTC)no subject
Date: 2009-07-16 09:32 pm (UTC)no subject
Date: 2009-07-16 10:06 pm (UTC)"The two leading popist critics are both American, both men - Sasha Frere-Jones, a staff writer for The New Yorker, and Frank Kogan, whose 2006 book Real Punks Don't Wear Black devotes as much energy to Mariah Carey as it does to the Contortions"
"How else to explain Frank Kogan's briefly notorious assertion in 2007 that critical divide over Paris Hilton's debut album was analogous to the rift in American Society caused by the Vietnam War? As several other critics and bloggers were quick to point out, America was (and still is) actually embroiled in a war that bears some resemblance to the conflict in Vietnam in terms of its social effects -one does not need to look to celebrities for proof that America is in conflict, both inside and outside of its own borders. It is also worth pointing out that Ms Hilton's musical recording vanished, even from the truncated attention span of pop cultural discourse, with chastening rapidity -the 'debate' about her album was over before it could properly begin, because her music was so boring that it was not worth arguing over. That Kogan could mistake such a trite artefact, not even vulgar enough to rise to the level of kitsch, for something of merit, signals, I think, the wilful abandonment of the critic's first duty: discernment.
Discernment, however, or judgement; deciding between what is good and bad music, is something which the popist critic is very unwilling to do. (...) This statement needs further qualification: critics such as Kogan are unwilling to give the impression of being critical in any context which might underline the difference in position -and in authority- between themselves and their idealised listener, the teenage girl".
"The point can be examinde further by looking at another piece that Kogan penned in 2007, entitled 'What's Wrong With Pretty Girls?'(...) For Kogan, beauty does indeed appear as a virtue: 'Is beatuy bad for us? Does it oppres us?' he asks. Frankly, Kogan, yes and yes".
If you want it, I can type the entire article and post it here (later you can delete the comment). The strange thing is the article can't be that old (there is a mention about "All the Singles Ladies")and it's kind of sad expending all that time with that thing inside.
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Date: 2009-07-17 03:14 am (UTC)In any event, here are the two pieces she mentions, which I'm proud of. But if you want to discuss them we'll do so on another thread, 'cause really, comments here ought to be at least tangentially related to Kuhn.
Paris Is Our Vietnam
What's wrong with pretty girls?]
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Date: 2009-07-17 04:21 am (UTC)So I’m sorry for bringing here all this stupidity again. More than anything, I felt it was kind of unfair not to advise you about the article, not because it’s great or good or anything, just for future reference. So, sorry again. : )
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Date: 2009-07-17 04:57 am (UTC)Yes, rock criticism has been a disappointment, overall, but the story is not over.
The odd thing is that on at least a few of these issues I might be inclined to be some of these people's natural allies (Reynolds', anyway), except they're so busy projecting stupid ideas onto me that I don't actually have that they don't notice the smart ones that I do have.
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Date: 2009-08-23 06:31 am (UTC)no subject
Date: 2009-07-17 07:32 pm (UTC)Thing is, the "several other critics and bloggers" were basically, in their entirety, Simon Reynolds on my comment thread. And when I explained what the column, which he seemed not to have read, was really about, he agreed with me.
And she also stopped reading your "Pretty Girls" essay after her convenient quote; otherwise she would have seen more words that, shock, actually provided context for the quote:
"The thing is, to say robustly, “Nothing’s wrong with it” doesn’t seem completely right—Nathan felt a justified discontent with the high-school social system—but no other answer seems any good, either. “Reinforces social inequalities and sexism” is just hand-waving, and no one’s ever shown how this reinforcement takes place or how society would benefit from pretty girls being denied their dance.
Yet I don’t think Nathan’s gut feeling is 100 percent wrong, either. Maybe it’s aimed somewhere wrong, but where should it be aimed? As Dave Moore points out, only pretty girls get to make music, or so it often seems, but whose choice is that—seems to be the consumers’—and how does lying to ourselves and claiming that the music is bad bring the world to rights?"
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Date: 2009-07-17 08:06 pm (UTC)Well, not quite. I was sympathizing with the people who were getting the rocks thrown at them. But the crucial point is that I was feeling the beginning of an impetus to change my ideas from pro-war to anti-war not on the merits of the positions (which basically I was too young and ignorant to understand) but so that I could stop aligning myself with one set of people (stone throwers) and start aligning myself with another (those getting the stones thrown at them). The stuff where I then point out that I've thrown stones too and so it turned out did antiwar people was just to show that the story them becomes complicated. But the crucial point was that my impetus here to rethink my ideas had nothing to do with the ideas themselves.
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Date: 2009-07-17 08:07 pm (UTC)and the sentence was too complicated, too, but "them" should be "then."
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Date: 2009-07-18 01:56 am (UTC)no subject
Date: 2009-07-17 08:19 pm (UTC)no subject
Date: 2009-07-18 02:14 am (UTC)no subject
Date: 2009-07-17 08:51 pm (UTC)But even without Crawford and K-Punk and the Noise Board creeps and people like that, there's a basic brokenness in rock and pop criticism that has been there all along, and has frustrated the hell out of me; the brokenness is that music critics don't know how to sustain an intellectual conversation, and the problem that I perceived early on back in my fanzine days hasn't lessened: it's that there's a fundamental inability to communicate and an unwillingness to do what's necessary to understand. I don't expect this to change, and I certainly don't think music criticism can or should become like a science, but by Kuhn's account, scientists working within a paradigm have a basic advantage over us: words hold still for them, so that the scientists who share a paradigm are not running circles of miscommunication around each other.
My insight here isn't that we should try to make words hold still, but rather that we should notice the motion, and in that way come to understand each other - those of us who want to - rather than hitting each other or withdrawing. (Not that we can't hit each other or withdraw while also understanding each other. But if the motive to hit is there, people usually can't be bothered with the understanding. And withdrawal usually comes from simply giving up all hope of being understood, or anyway feeling too tired to keep on.)
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Date: 2009-07-18 07:00 pm (UTC)Don't listen to the words; the words are turds. (or "terse"?)
It's Kuhn's birthday today, and that of Screamin' Jay Hawkins and Martha Reeves as well.
Happy Birthday!
AK
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Date: 2009-07-19 06:26 am (UTC)"I can't hear the words
I can't hear the words"
"You don't wanna hear the words
The words are turds"
(I fear that my self-evaluation in this instance might not have been so far off.)