Posted on 01/07/2002 8:19:37 AM PST by dead
There's an interplay between math and physics, so it's like what came first, the chicken or the egg.
In the case of general relativity, Einstein was floundering around for how to mathematize it until he happened upon tensor analysis. Same thing for quantum mechanics; the Hilbert space was there first, and turned out to be an excellent fit.
Sometimes it goes the other way, e.g., physics first, as with Newton and Fourier.
With boundary?
Albert Einstein said that "World War IV will be fought with sticks and stones".
There is a lot of wisdom contained in that statement, I think (and fear). The fallacy that Einstein is refuting and that the author of this article instead embraces is that progress, technology and civilization proceeds in an ever upwards direction. In some ways, this is the same fallacy that propelled the stock market to stratospheric heights a scant 2 years ago. The reality is that this is not true, as demonstrated recently by the stock market collapse, and historically by the rise and fall of many great civilizations. An ancient Roman or Greek could probably not fathom that things would get so bad during the Dark Ages. But they in fact got very bad indeed. And there are evidence of advanced civilizations such as Crete and Minoa that predated Greece and Rome.
The facts are, recent history aside, that things don't continuously get better and better, just like stocks don't always go up and up and up. All this talk about a "singularity" in the article sort of proves the point. Singularities are theroretical maximums or minimums of infinite height (or depth) that are either never achieved or achieved only under quantum or relativistic conditions e.g. black holes. Far more likely, it seems to me than our technology reaching a "singularity" is that something will derail the train, and history will resume the up and down cycle that it has followed since the beginning of time.
To think otherwise is to believe in the promises of tulip bulb mania, or in utopia, or world peace or in all these other absolutes or infinites that people always seem to talk about, but never seem to really occur in real life.
Lacking even a simple thing such as a single center. You can start with any two assertions and derive the rest. Although it is easier with four.
Furthermore, you could argue against the point of Riemannian geometry also by pointing out that Gauss was fond of measuring distances on the surface of the Earth. He too, thus, was compelled by rather practical considerations.
On the other hand, these are relatively basic mathematical constructs to begin with. I suspect that the area under, or the slope of, a curve is not exactly tensor calculus
Not to argue here --- this is after all a question of taste --- but this remark is rather curious. I never thought that tensors, to the extent that Einstein needed them, were any less "basic" than integration. Should we no judge how "basic" these notions were at the time of their invention?
I'm not sure about any point with B-T. It was an example, (in your favor) of a well-established mathematical fact which you would never expect to describe a physical phenomenon.. Thanks for the clarification on this. Interestingly, this is exactly what people said about the work of Lobachevsky, Gauss, and Riemann in mid 1800s: what can this geometry possibly do with the real world?
Can't say it isn't. I think we are opening a new view of the cosmos. It might not pan out, most times these things don't work out.
Nice counter to the religion of quantum uncertainty. I read an article once where the author claimed that God DOES play dice and MUST play dice because even He cannot get around the uncertainty principle.
Observer determined quantum reality is a widely believed crock.
Well this thread has touched on just about every non-trivial thing I've been privy to in the last few days, including Collective Electrodynamics
So there. My secret's out. I hope you feel proud of yourself.
As far as I know, tensor analysis before general relativity was a rather specialized field of pure math being pursued by people like Ricci and Levi-Civita in Italy. There was some good work done in what could be called Riemannian tensor analysis by the German Christoffel around the time of the Franco-Prussian war. He came up with the celebrated Christoffel symbols which give the Riemannian case of Levi-Civita's parallel translation.
Minkowski was the real deal in relativity. Tragically his life was cut short. Physics might be a different place if he had another 20 years.
Any sufficiently advanced semantics is indistinguishable from the truth.
:-) Sorry, couldn't resist. It was a joke, BTW
The truest things are spoken in jest... (or however that saying goes)
Ok, got it.
......and gee, like, um, if the Rebel guys had, like, you know, nukes 'n' s**t, they coulda won the Civil War against the Yankee dudes 'n' all...........and......and if the Romans had, like, machine guns, they'd'a conquered like everybody and we'd all be, you know, like eating spaghetti 'n' s**t every night!!
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