Comments by "EebstertheGreat" (@EebstertheGreat) on "Hunt for the Elusive 4th Klein Bottle - Numberphile" video.

  1. Azivegu You said you could find the volume of "any n-dimensional object," but so far it looks like you can only calculate the volume of an n-sphere. You cannot define volume in infinitely many dimensions, but that doesn't mean the limit of the volumes of a sequence of objects of increasing dimension is zero. Consider the sequence of n-orthoplexes with edges of unit length. The 1-volume (length) of a unit line segment is 1, the 2-volume (area) of a unit square is 1, the 3-volume of a unit cube is 1, the 4-volume of a unit tesseract is 1, and in general the n-volume of a unit n-orthoplex is still 1. For a sequence of orthoplexes all with edges of the same length L < 1, the limit as n approaches infinity is 0, and for L > 1, the limit is infinity. Don't make the mistake of thinking everything is like a ball.
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  2. Azivegu "I can now calculate the volume of any n-dimensional object." That's very impressive. Name one you can calculate that Wolfram Alpha can't.
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  3. ***** Nobody expects or wants your input on the value of what we do in our free time. Why are you wasting your time posting here?
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  4. Azivegu Seriously, what are you talking about?
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  5. Not to mention in large systems analysis you can easily have thousands of dimensions in phase space.
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  6. ***** Exactly my point.
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  7. Harrison Smith It's not just sets either, but "objects." What is the volume of '+'? That's a two-dimensional operator. Operators are mathematical objects.
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