Special Relativity and Hyperbolic Numbers

A brief introduction to Hyperbolic Numbers and their application to SR.

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Happy - LoFi Ocean

[cosmicvoidtree]

I believe these also go by the name split complex numbers. I’m not sure which is more common, but something I think is worth mentioning

[rudyyee]

Thank you, great video. It is not so easy to find a good explanation regarding the fact that spacetime interval is time minus space coordinate.

[ChaoticNeutralMatt]

Your channel has an interesting transition, but anyway. This was a cool find. Appreciate the time spent and the upload.

[erawanpencil]

It seems like these Hyperbolic Numbers are more fundamental than the complex numbers, especially considering that seemingly arbitrary boundary conditions of 0 and 2 pi radians the latter have. (How do we know physically if we’ve gone “all the way around” a perfect center point?). But with hyperbolic numbers, you can go one-way to infinity, which seems more natural (look off into the distance, and there is a vanishing point at infinity). Why then do complex numbers and analysis have so much more attention?

[hyperduality]

Sine is dual to cosine or dual sine -- the word co means mutual and implies duality.
Sinh is dual to Cosh -- hyperbolic functions.
Space/time symmetries are dual to Mobius maps -- stereographic projection.
Space is dual to time -- Einstein.
"Always two there are" -- Yoda.

[mustafaercumen]

Why instead of adding we multiply? I mean I can make sense c^2t^2-x^2 from Einstein light mirror experiment but I can't visualize it on hyperbola like Phytagoras on Circle