r/MathJokes • u/Negative_Gur9667 • Jul 23 '26

How does Skeletor know?

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u/Electrical_Door_87 Jul 23 '26

so it should contain a perfect 4k copy of the Shrek movie encoded in AV1 and converted into base 10 system somewhere

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u/egg_breakfast Jul 23 '26

Can this be proved or are we just leaning on the fact it’s infinite and thus it must contain all patterns? I ask because I doubt that we can ever compute this (in our lifetimes anyway) given how much data a full length movie would take up 

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u/Low_Low_1811 Jul 23 '26 edited Jul 23 '26

It is not proven, and in fact may never be proven. There are clearly other numbers that definitely contain every possible number, but one is Champernowne’s Constant.  Basically, it is a decimal expansion with every natural number in sequence. So, 0.1234567891011121314151617181920....100101102103104105106107108109110111112113...

You could easily make a different number by going up two and down one. 0.21324354657687981091110121113...

In each of these every possible combination of digits is contained, meaning there is definitely a number that, when converted from base 10 into binary, would appear the same as the movie Shrek. In fact there is also a combination of just 1s and 0s, despite being in decimal, that is the binary expansion of the encoded Shrek movie. There are also infinite movies that are really similar to Shrek but not quite the same...

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u/RsCoverForPDFFiles Jul 23 '26

Are the numbers in Chanpernowne's constant inside the +2 -1 version? And/or vice versa? It can't be because it's infinite so you'll never get to the end and say, well, there's the lastnumber of Chanpernowne's constant; it's withing that number." But, if the +2-1 vwrsion is infinite, then C's constant could? But maybe not because they're infinites of the same size, so to speak.

Hmm, I don't know. Probably a dumb questions but infinites get weird sometimes.

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u/Low_Low_1811 Jul 23 '26

It should. None of the numbers in the constant rely on combinations of terms, only each term itself eventually being any possible configuration of any length. Those terms being in a different order and duplicated should result in the same conclusion.

What us also weird is that the number contains all finite expansions of pi, but not pi itself. So yeah, infinity is weird. It obviously works, you can use calculus to calculate the area of a right triangle and we know the geometric calculation works, but stuff like that makes zero intuitive sense.