Ok, let's say you're instantaneously flying through the center of a transparent globe, looking outward and seeing the painted surface. Each frame of this animation is a different instantaneous speed, leading to a different set of angles entering your eyeball. 5/ - ThreadSky

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duetosymmetry.com • 27 days ago

Ok, let's say you're instantaneously flying through the center of a transparent globe, looking outward and seeing the painted surface. Each frame of this animation is a different instantaneous speed, leading to a different set of angles entering your eyeball. 5/

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astrodunham.bsky.social•27 days ago

Thanks! I was imagining sonic running right at me and being translucent so I could see light from his front and back, to avoid involving angles 😅

duetosymmetry.com•27 days ago

Now, if Sonic is in his ball form, he's approximately a circle when viewed from every direction. Since a Möbius transformation maps a circle to another circle, that means that no matter how fast Sonic is traveling, he would still look like a circle! No pancaking!! 6/

duetosymmetry.com•27 days ago

It's obviously more complicated for other shapes... but it's definitely not "pancaking"! 7/7

astrodunham.bsky.social•27 days ago

This is neat stuff. Complex Riemann spheres are outside of my comfort zone, but now I think they may be worth investigating :)

duetosymmetry.com•27 days ago

Don't sell yourself short, they're not so complicated! And they are extremely beautiful

astrodunham.bsky.social•27 days ago

Thanks, I believe you and I’m looking forward to seeing it for myself :)

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