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).
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).