Comments by "angeldude101" (@angeldude101) on "The Most Powerful Diagram in Mathematics" video.

  1. I had the same question. The labels are arbitrary, so they could just as easily been colours, fruits, letters, emoji, or any other set of 24 distinct elements. The elements don't need an intrinsic order, so reordering them changes nothing, so if you're going to use ordered elements, what's stopping you from just writing them in order? The MOG in general, while pleasing to look at (not counting the numbers in the corner), never seemed particularly meaningful other than being a specific instance of a Steiner system.
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  2. Group theory is cool, and the MOG is quite clever, but it also just looks like a compressed look-up table. Steiner systems were also really cool, but at no point did it feel like there was anything special about S(5, 8, 24) in particular other than generating the MOG. The patterns on the MOG were mildly interesting, being ways to split a set of 8 elements into two sets of 4, and the 4x4 squares also had a pleasing pattern, but I couldn't find a consistent connection between the squares and rectangles, and the numbers in the corner were just confusing. (The last part does make some sense since labels are arbitrary and can be permuted as much as you want and it stays isomorphic, though that also means that there shouldn't be a difference from the numbers just being listed in order from 0 to 23, at which point why even bother including them?) I should mention that I have a tendency to treat isomorphism as full equality. The two S(2, 3, 7) systems shown were just the same system with no meaningful difference between them. This also plays into my opinion on the different labels for the permutation group: Math is around 50% giving the same name to different things and 50% giving different names to the same things.
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  3.  @AnotherRoof  "given a 5-set you literally had to look up elements in a list of 759 octads" I'm sure that why you'd need to do this for this specific type of 5-sets and octads will be answered in the next video. Without an application, it's just a special case of something I'd rather be able to more generally solve for an arbitrary Steiner system.
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  4. In colloquial terms, probably the closest relationship they have is that the number of choices is the log of the number of options. What base the logarithm has depends on how the choices are presented. If only yes-no questions, then having n options means having log_2(n) choices.
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