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Not exactly the same but 2-dimensional beings on a curved surface can discover the 3rd dimension using math, we did this proof in a differential geometry class
by lazyant 7y ago
Not exactly the same but 2-dimensional beings on a curved surface can discover the 3rd dimension using math, we did this proof in a differential geometry class.
- lavp 7y agoI would love to see a proof of it if you happen to have it!
- lazyant 7y agohttps://fsw01.bcc.cuny.edu/luis.fernandez01/web/texts/dgcs.pdf https://fsw01.bcc.cuny.edu/luis.fernandez01/web/texts/dgcs.p... Ctrl-F for "2D" (2-dimensional creatures), although I can't find the "discovery", maybe I remember it wrong. Btw, this was one of the mindfucks I learned studying physics. Other ones are: - dimensional analysis: checking if formulas can be wrong, and more importantly, finding formulas (eg, period of a pendulum) just by analyzing units that can be involved (no constants obv) - similarly, rate of growths in dimensions: why giants can't exist (bone resistance is proportional to section area and load (weight) is proportional to volume - Conservation laws derive easily from symmetries (energy from invariance in time, momentum from invariance in direction etc)
- lavp 7y agoThis is brilliant, thank you!
- Koshkin 7y agoI think you may be talking about the curvature of the surface (the Riemann tensor). It is intrinsic, i.e. does not depend on the notion of the surface being embedded into a higher-dimensional space.