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 Posted: Sun Nov 30, 2008 9:00 am
glad you're ok! Looks like that blaze could have easily spread.
That sort of thing always leaves me with a sick feeling...
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Posted: Wed Dec 31, 2008 11:08 am
More and more I'm starting to think that math grad school isn't right for me. (And that's not just 'cos I don't wanna do the applications.) Anyone have suggestions for how I can start breaking into environmental engineering? Getting a master's or something in that - even if it's mostly through an applied math department - would be awesome, but I don't have much coursework in the subject.
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Posted: Tue Jan 06, 2009 1:56 am
I want to create an intro to general relativity thread, but I'm not sure I have the patience to write up an explanation of what the Christoffel symbols actually mean or how to get geodesics out of metrics.
Also, the current amount of work on the intro to quantum thread demonstrates quite well how good I am at finishing things.
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Posted: Tue Jan 06, 2009 8:09 pm
Layra-chan I want to create an intro to general relativity thread, but I'm not sure I have the patience to write up an explanation of what the Christoffel symbols actually mean or how to get geodesics out of metrics. Also, the current amount of work on the intro to quantum thread demonstrates quite well how good I am at finishing things. Heh... I was actually browsing through the old 'intro to QM' thread when I decided to post up the QM lecture series. I, too, seem to be only motivated by deadlines (hence me being up this late). And a general rel intro would probably be an even bigger task than a QM intro, as I can't think of any way you might talk about field equations without spending considerable time on discussing the language of tensors. Maybe a good strategy would be to make the Penrose chapters more digestible for Gaians. Swordmaster Dragon, I unfortunately can't help much, as I'm still not even sure what grad school really is. But I wouldn't let a lack of coursework discourage you. If you can demonstrate a capacity to learn then that's all you'll need for a conversion course.
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Posted: Wed Jan 07, 2009 12:28 am
I started writing up a derivation of all the machinery, but it's just the machinery, no explanations or illustrations or anything of the sort. I've just gotten too used to Einstein notation to remember to explain tensors and covariance/contravariance. Also, I'm having a bit of trouble describing what the Ricci tensor is supposed to mean. It's not helping that I'm trying to avoid the language of forms. Someone check this. It's late and I don't know how to explain things well.
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Posted: Wed Jan 07, 2009 8:04 am
Layra-chan I started writing up a derivation of all the machinery, but it's just the machinery, no explanations or illustrations or anything of the sort. I've just gotten too used to Einstein notation to remember to explain tensors and covariance/contravariance. Also, I'm having a bit of trouble describing what the Ricci tensor is supposed to mean. It's not helping that I'm trying to avoid the language of forms. Someone check this. It's late and I don't know how to explain things well. Well definitely a good start. Just be sure to mention that the Christoffel symbols are not tensors. And perhaps it would be a good idea to expand on the Einstein field equations by, say, comparing the Einstein vacuum field equation to the Newtonian and Maxwellian(?) equivalents. It might give a better idea of what the equation means.
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Posted: Wed Jan 07, 2009 4:25 pm
Layra-chan I started writing up a derivation of all the machinery, but it's just the machinery, no explanations or illustrations or anything of the sort. I've just gotten too used to Einstein notation to remember to explain tensors and covariance/contravariance. Also, I'm having a bit of trouble describing what the Ricci tensor is supposed to mean. It's not helping that I'm trying to avoid the language of forms. Someone check this. It's late and I don't know how to explain things well. I'm still going through it... but I need to leave my office... here's a few syntactic thoughts on page 1 and top of page 2: 1. (pg 1) Do you really want to say "derivative of the manifold at x"? 2. (p1 definition of directional derivative) You may have done this on purpose, but the procedure that you outlined doesn't take into account different parameterizations for the pointset comprising gamma(-epsilon,epsilon).... and the ambiguity extends to the difference between finding the derivative in direction v and 2v. 3. (top of pg 2) "we an object" should be "we have an object" 4. (top of pg 2) you may want to define l_gamma before using it. I'll finish the rest tomorrow night. I've enjoyed what i've read so far though.
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Posted: Thu Jan 08, 2009 6:15 pm
Have you read Wald's GR book? He explains a lot about the meaning of connections, parallel transport, and in particular how curvature corresponds to local path-dependence of the derivative. I feel like it really helped a lot, not so much on defining the different objects, but later when you connect it to physical things.
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Posted: Thu Jan 08, 2009 6:57 pm
Thanks for the comments! I wrote that in like fifteen minutes at about 5 in the morning, so I'm glad to see that I wasn't completely crazy while doing so.
I haven't read Wald, but if you'd like to point out some interesting tidbits and techniques, Dragon, I'd be happy to incorporate them.
Or else someone else could take a stab at this; I won't have the free time to really go through this until at least the 13th.
On a completely separate note, although I know that it's a work of speculative fiction and that Neal Stephenson is not a mathematician or physicist, and that I should be glad that he included appendices to begin with, I'm a little bit miffed that in his appendix about configuration spaces he conflated the six-dimensional position-velocity phase space for a non-rotating rigid body and the six-dimensional position-orientation configuration space for a stationary rigid body.
Nonetheless, the fact that he has an appendix explaining configuration space is highly amusing. There's another appendix about cutting a square into eight equal pieces, and at least one more that I haven't read.
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Posted: Fri Jan 09, 2009 9:39 pm
More thoughts on Anathem: there are a lot of interesting metaphysical ideas in the book, none of which I trust Earth philosophers to be able to tackle in any meaningful fashion.
Perhaps my favorite is the expansion of Plato's world of Forms, in particular the expansion from a single path from Forms to Shadows to a general directed acyclic graph of which we (and our art) are not the lowest level of purity.
Also the idea of causal domain shear is hilarious.
There's also a bunch of stuff on the quantum-consciousness hypothesis linked with Everett's Many Universes interpretation, and the implications this might have for the graph of Form-Shadow relations and causal-domain shear where the causal domains are taken to be alternate universes. I didn't like this so much.
Perhaps my favorite question raised by the book was: supposing we eventually managed to recreate a Big Bang event, temporarily reunifying the forces and the fermions and such. Do we have any expectation that the subsequent freezing out and symmetry-breaking would be the same as the one that generated the universe we currently live in?
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Posted: Sun Feb 01, 2009 2:30 pm
I've started writing my thesis. Whoo.
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Posted: Mon Feb 02, 2009 5:55 pm
Layra-chan I've started writing my thesis. Whoo. What area of mathematics? I can't say I'm surprised, but there's been a spectacular lack of interest in my CUDA guild. crying
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Posted: Wed Feb 04, 2009 11:07 pm
Symplectic geometry, specifically as applied to a simple Hamiltonian system
In other words, I'm over-analyzing the hell out of the Lagrange top (axi-symmetric top, tip fixed, in a constant gravitational field).
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Posted: Fri Feb 06, 2009 1:31 pm
Morberticus I can't say I'm surprised, but there's been a spectacular lack of interest in my CUDA guild. crying I wish I could be more interested in CUDA. I have seen some pretty and shiny things I like from it. The two problems I face are CUDA is still quite new, and I have no actual use for it. Then again, it is not as though practicality should ever be a real concern.
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Posted: Mon Feb 09, 2009 8:16 pm
Morberticus Layra-chan I've started writing my thesis. Whoo. What area of mathematics? I can't say I'm surprised, but there's been a spectacular lack of interest in my CUDA guild. crying I didn't even now about it. CUDA is on my list of things to do within the next year. (right now I'm finishing up with ASN.1 and regular expressions)
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