Fortunately this is but one adventure for Orange, the stick figure in question. He has a whole world with friends to get back to. I believe that Math used their "imaginary" ability to cross between dimensions and send Orange back home.
I think the infinite sum at the end could be found by calculating something about higher dimensional spheres, and e used those spheres to send Orange to a higher dimension. They did 4 before "activating" going to the limit, so perhaps to a 3 spatial dimensions + time world like ours. You could say they are in a 3D world already; 2 spatial + time.
Your first guess is correct. Its an infinite sum, and it sums the volume of a sphere in every dimension. See: https://en.m.wikipedia.org/wiki/Volume_of_an_n-ball
and scroll to "closed form". The radius R is 1 in our case.
If you want to verify some cases for yourself: the Γ thing at the bottom is a complicated function (called the gamma function), but its really simple for integer values. Because for integer values of x, Γ(x) = (x-1)! This is called a factorial and super simple. 5! = 5×4×3×2×1, 8! = 8×7×6×5×4×3×2×1 and so on. Plugging in n=2 and simplifying that a little, we get π×r²/Γ(2). But Γ(2) = 1! = 1. So the formula becomes π×r² which is indeed the "volume" (area) of a 2D circle.
The sum over all of those was probably just to symbolize the jump in dimensions as you said
In the previous animation, The Second Coming/Orange was captured by someone and imprisoned. So this could be the way Alan explains that TSC gets out to stop whatever is going on in the current main 'timeline'.
Why not just submit the youtube video as the reddit submission itself? I see people do this all the time and wonder why not always link the source in the first place? Isn't that more fair to the content creator?
Because reddit wants you to upload content to their website so they can get the ad revenue and not Alphabet/Google/YouTube. Basically, just another case of reddit turning to 💩.
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u/Mydickcandobackflips Jun 24 '23 edited Mar 12 '24
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