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Azathoth123 comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion

28 Post author: Punoxysm 16 October 2014 05:58PM

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Comment author: Azathoth123 18 October 2014 06:08:17PM *  3 points [-]

I'm curious whether I could have gotten the physics to work out if all rotation was independent, and what else would be different about that world.

Well, for one thing it would be mathematically incoherent.

Actually, rigid rotation is more complicated than you seem to think. While instantaneous rotational velocity (at least in 3 dimensions) is always representable by an axis and an angular velocity, the angular velocity can change even in the absence of torques.

Edit: Also how are you representing orientation as (ox, oy, oz)?

Comment author: jkaufman 18 October 2014 11:42:18PM 1 point [-]

it would be mathematically incoherent.

I'm not sure what you mean. You're saying it's not possible to make a coherent mathematical description of a physics system where something rotates around multiple axes? It wouldn't correspond to our world very well, but why are the mathematics impossible?

the angular velocity can change even in the absence of torques.

Yikes! Yes, even the model I ended up with sounds like it didn't represent rotations properly.

Also how are you representing orientation as (ox, oy, oz)?

This was about a decade ago, so I'm not confident I remember what I did properly. But I think you can represent orientation as a one-time rotation from an initial position. So (ox, oy, oz) are a vector representing an axis with the magnitude indicating how far around that axis it rotates. Does that not work? (It's also possible that I kept orientation as a matrix.)

Comment author: Douglas_Knight 19 October 2014 06:50:54AM 3 points [-]

Rotation is a mathematical concept, not a physical one.

In 4d, an object can rotate about two axes at once. Say the 4 coordinates are w x y z. The w and x coordinates can do the usual rotation, while the y and z coordinates rotate together, perhaps at a different rate. Or instead of 4 real coordinates, take 2 complex coordinates a and b, and have them evolve by (a,b) → (exp(i.r.t).a, exp(i.s.t).b), where t is the time and r and s are speeds.

Comment author: Azathoth123 20 October 2014 04:29:17AM 0 points [-]

I'm not sure what you mean. You're saying it's not possible to make a coherent mathematical description of a physics system where something rotates around multiple axes?

Not in 3 dimensions.

So (ox, oy, oz) are a vector representing an axis with the magnitude indicating how far around that axis it rotates. Does that not work?

Come to think about it, yes it can.

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