Comments by "kazedcat" (@kazedcat) on "Numberphile2" channel.

  1. In set theory if they are isomorphic they are the same. For example {🎉,🎉} is the same as {🎉} but clearly they are different objects.
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  2. He is talking about bubble multiverse. The multiverse itself is infinite but the bubbles embedded on it is finite and each bubble have unique physics inside them. So a universe is define as a finite bubble with a unique set of physics. Going outside the bubble the physics changes and you are on either a different universe or the great void between universes.
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  3. nex The conway result is define for a finite game. They want to extend it to an infinite game where the result migth not apply. You can have a program that does not stop. Now can we have a reverse game that will eventually fill the lower half of the board 5 rows below the starting point using only finitely many instructions? The proof shown does not tell us the answer to this question. You may need infinitely many instructions to fill the board or it migth be that there will always be gaps that even with infinite instructions cannot be filled. But if there is a program to do so what will the program look like.
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  4. He was talking about our human ancestor. All modern human can be trace back to one individual and all of us are descendant of this one person. It does not mean she is the only human at that time. It just means the descendants of all other people all died out.
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  5. That is just a physicist that is poor in math. There are infinite points between 0 and 1 non of them is 2.5 . Infinity does not mean everything. What is worst is that an uncountably infinite set can have an uncountable missing pieces.
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  6. Robert Blair 0,1 and 0.5 are just labels in mathematical language. You can define 0.5 however you want by choosing different axioms. Did you know that the integer positive five and natural number five is define differently by our mathematics. +5 and 5 are two entirely different things they are like apples and chickens they are not even the same classes of things.
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  7. Shakal Draconis actually the proof does not show what is possible but only what is not possible. It show you that it is not possible to reach row 5 with finitely many moves but it did not show you that reaching row 5 is possible with infinitely many moves. You know you have just the right amount of fuel to get there but you don't know if the path to get there is blocked. To prove the second you need to show that you can create a program for the reverse game that does not halt.
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  8. The distribution is the probability. On the first method 1/3 of the chord length is less than S on the second 1/4 is less than S and on the third method 1/2 is less than S they are all linearly distributed the only difference is the slope of the distribution.
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  9. Except for classes they are their own category.
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  10. Lucas Balaminut thinking in 4d is impossible. Understanding it can only be done with lower dimensional slices and shadows. Giving up higher dimensional global understanding makes it easier to slice and dice 4d object to analyze parts in lower dimension. It is also easier two follow the numbers than thinking about it geometrically
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