since this is the comment thread where we can get technical about it, we can kinda say π definitely doesn’t have “all the answers” because that would mean it’d need to have stuff like 1/3 or √2, which we know it doesn’t have
best we might be able to assert is that it has any sequence of integers of finite length, but that’s covered by the “normal” comment here
We know it’s irrational since like 1800s, but we don’t know if it’s “normal.” Compare 0.110100100010000… which can be demonstrated to be irrational but is clearly not normal - it only contains the digits 1 and 0 so all other digits aren’t evenly distributed
Most numbers are uncomputable too lol can’t even tell you the first digit of 'em. There’s functions that we can’t represent at all like the irrational indicator function, no idea what it looks like and its not possible to know. Lots of functions like that in function space
Even in that case, the answer can be encoded in pi, such as in your example, which could be an encoding for the answer in binary. You just need to decypher it, then you’d have all the answers (that can be expressed as a finite string).
It’s a funny joke, but if you want to get into it we don’t actually know if that’s true or not it’s an open question
since this is the comment thread where we can get technical about it, we can kinda say π definitely doesn’t have “all the answers” because that would mean it’d need to have stuff like 1/3 or √2, which we know it doesn’t have
best we might be able to assert is that it has any sequence of integers of finite length, but that’s covered by the “normal” comment here
https://en.m.wikipedia.org/wiki/Proof_that_π_is_irrational
We know it’s irrational since like 1800s, but we don’t know if it’s “normal.” Compare 0.110100100010000… which can be demonstrated to be irrational but is clearly not normal - it only contains the digits 1 and 0 so all other digits aren’t evenly distributed
Okay, I knew pi isn’t normal, but I assumed there were some other numbers that were (like e or something).
But apparently all the known normal numbers are dumb bullshit people constructed just to demonstrate that there are normal numbers?
And yet most of the reals are normal??
And yet we still can’t find any of them???
Math sure gets weird sometimes.
Most numbers are uncomputable too lol can’t even tell you the first digit of 'em. There’s functions that we can’t represent at all like the irrational indicator function, no idea what it looks like and its not possible to know. Lots of functions like that in function space
That one is less weird to me honestly. Not such a surprise that we can’t find the numbers whose whole thing is not being findable.
Yes, this state of affairs is called “finding hay in a haystack” and we’re pretty bad at it.
“if it weren’t for all of this damn hay I might actually be able to find the fucking hay!”
Even in that case, the answer can be encoded in pi, such as in your example, which could be an encoding for the answer in binary. You just need to decypher it, then you’d have all the answers (that can be expressed as a finite string).
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