In case you were wondering how I got this way...

[pozorvlak]

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

Comments

[mauitian]

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.

[pozorvlak]

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*

[necaris]

That sounds awesome... unicycling is apparently Huge Amounts Of Fun.

[pozorvlak]

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.

[shuripentu]

May I recommend Finnish and the flute. :)

[pozorvlak]

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.

[michiexile]

The butler, in the attic, speaking German and playing the clarinet!

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

[pozorvlak]

:-)

[michiexile]

Oh - so THAT's why one should care about symplectic geometry? It generates Poisson algebras?

[pozorvlak]

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.