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Cake day: July 2nd, 2023

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  • you could think about it this way: one sphere and two spheres have the same “number” of points. (in the same way that there are just as many real numbers as there are real numbers in the interval (0,1).)

    so, it becomes “”plausible”” that you could use one sphere to construct two spheres (because in some sense, you aren’t “adding any new points”).

    but in the real world, “spheres” only have a finite number of atoms. so if we regard atoms as “points”, then it’s no longer true that one sphere and two spheres have the same number of “points”. and in some sense, this is why the sphere duplication trick doesn’t work in the real world.

    it’s also worth mentioning that you have to do some pretty fucked up and unusual things in order to actually duplicate the sphere, and if you don’t allow such weird things to be done to the sphere, then it’s no longer possible to duplicate it, even with the axiom of choice.


  • yeah this is true. i should have clarified a bit better that a well ordering wouldn’t give you a “least gay” person in that sense of the word. it would be more correct to say there is a well ordering ⊰, and so there is a “⊰”-least gay person. but of course a “⊰”-least gay person could be in the middle of that spectrum.

    but the number of people on earth is finite, so in fact the usual ordering is a well-ordering in this case. so i guess those two mistakes i made cancel each other out, and the axiom of choice isn’t even needed here.





  • from a topological perspective, wraps and tacos are two different beasts.

    in a wrap, the bread completely surrounds (and encloses) the other ingredients, so theres a 2-dimensional hole involved (which basically means the inside is hollow).

    in a taco, no such wholes are present.

    you can also distinguish sandwiches from tacos and wraps (since sandwiches involve two pieces of bread, like you said). but unfortunately, you can’t topologically distinguish a burger from a sandwich


  • it is possible to rigorously say that 1/0 = ∞. this is commonly occurs in complex analysis when you look at things as being defined on the Riemann sphere instead of the complex plane. thinking of things as taking place on a sphere also helps to avoid the “positive”/“negative” problem: as |x| shrinks, 1 / |x| increases, so you eventually reach the top of the sphere, which is the point at infinity.