4 ms·
This trick reminds me of that game ten year old children play where one of them shoots the other with a "gun" and the child who was "hit" suddenly declares a ne
by bane 6y ago
This trick reminds me of that game ten year old children play where one of them shoots the other with a "gun" and the child who was "hit" suddenly declares a new rule, "I have a forcefield!".
Meaning, you can't pinch or cut. So sphere eversion is obviously impossible...but the suddenly, "I can pass surfaces through one another!"
So I guess the game here is not in finding interesting solutions within a set of constraints (no pinching or cutting!) but in just making up arbitrary new rules when the problem becomes intractable?
- zodiac 6y agoIf you think the constraints make it trivial, try producing a solution with the same constraints. (intersection allowed but pinching and cutting not)
- bane 6y agoI think the constraints make it impossible. It's obvious that allowing free passage through a surface is the same as cutting.
- aesthesia 6y agoSelf-intersection is not the same as cutting. The disconnect you’re experiencing is between the mathematical description of the problem—-does there exist a smooth homotopy of immersions between two embedding a of the 2-sphere in 3-dimensional space—and the colloquial description. The mathematical phenomenon corresponding to cutting would be discontinuity of that homotopy, which is different from the description of self-intersection, which amounts to the difference between an embedding and an immersion.
- zodiac 6y agoI'm not sure what sense you're using "the same" in. Eg a cylinder can be transformed into a mobius strip (in 3d space) by cutting and gluing, but if we allow only self-intersection, this can't be done. To me this shows that they're not "the same".