pozorvlak ([info]pozorvlak) wrote,
@ 2008-05-07 23:30:00
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Entry tags:maths, science

In case you were wondering how I got this way...
The tail-end of a conversation with my Dad last night:

[A discussion of scary-sounding nonlinear dynamical techniques my Dad has been studying, with Poincaré's name attached for extra scariness]
Me: Sounds interesting. Have you come across the idea of considering the Poisson bracket as a symplectic form on the cotangent bundle of phase space?*
Dad: No, I don't think so...
Me: Something like that, anyway. I went to enough lectures on this stuff to pick up the jargon, but not enough to really get my head around it.
Dad: Yes, I know that feeling.
Me: But it's interesting how quickly physics becomes geometrical, isn't it?
Dad: Yes, certainly. You know, one of these days you and I should put our heads together and try to properly understand General Relativity.
Me: Actually, that was my plan for after I hand in my thesis. That, and learning to ride a unicycle.
Dad: [laughs] ...and learn a foreign language and a musical instrument.
Me: thinks: I wasn't going to tell him about that bit...

* My office-mate, who does The Physics, tells met that I meant "configuration space" - phase space is the cotangent bundle of configuration space!



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[info]mauitian
2008-05-07 10:55 pm UTC (link)
You forgot to bring in Poincaré by mentioning the canonical 1-form, and its relation to the symplectic 2-form. And don't put off GR, it's too important.

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[info]pozorvlak
2008-05-08 11:54 am UTC (link)
You forgot to bring in Poincaré by mentioning the canonical 1-form, and its relation to the symplectic 2-form.

How remiss of me :-)

*googles*

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[info]necaris
2008-05-08 09:01 am UTC (link)
That sounds awesome... unicycling is apparently Huge Amounts Of Fun.

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[info]pozorvlak
2008-05-08 11:52 am UTC (link)
It's the season to learn - sunny Sundays in the park are a Good Thing.

I learned to juggle clubs in February, which was a bad idea - my flat's ceiling was too low for me to juggle clubs indoors, so I needed to be outside in the cold, with no gloves on (to get a decent grip on the handles). When you're learning, you catch the clubs wrong a lot of the time, and this hurts - particularly if your hands are cold. I'd practice in five-minute bursts, then dash back in to warm my hands up, then back out again, and so on until I couldn't stand it any more.

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[info]shuripentu
2008-05-08 10:26 am UTC (link)
May I recommend Finnish and the flute. :)

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[info]pozorvlak
2008-05-08 11:53 am UTC (link)
I was thinking Mandarin and the guitar, but I'll take that under advisement. I'm likely to have a Finnish speaker to practice on, which would help a lot.

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[info]michiexile
2008-05-08 01:19 pm UTC (link)
The butler, in the attic, speaking German and playing the clarinet!

Oh, sorry - I thought we started playing Cluedo...

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[info]pozorvlak
2008-05-08 02:11 pm UTC (link)
:-)

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[info]michiexile
2008-05-08 01:19 pm UTC (link)
As for "realer" suggestions: The Theremin.

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[info]pozorvlak
2008-05-08 02:11 pm UTC (link)
Good idea!

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[info]michiexile
2008-05-08 01:20 pm UTC (link)
Oh - so THAT's why one should care about symplectic geometry? It generates Poisson algebras?

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[info]pozorvlak
2008-05-08 02:13 pm UTC (link)
That's one of the reasons, yes. I think there are others, though - I've heard algebraic geometers talk about symplectic geometry, so there are probably connections there.

I'm not sure how much of an equivalence there is - it may be the case that any symplectic form on configuration space defines a Poisson bracket (and thus Physics) on the system. You can certainly go the other way - every Poisson bracket defines a symplectic form. It may be that symplectic geometry is a generalisation of the kinds of things physicists want to do, though.

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