My guess would be that - depending on the number of digits you are looking for in the sequence - you could calculate the probability of finding any given group of those digits.
For example, there is a 100% probability of finding any group of two, three or four digits, but that probability decreases as you approach one hundred thousand digits.
Of course, the difficulty in proving this hypothesis rests on the computing power needed to prove it empirically and the number of digits of Pi available. That is, a million digits of Pi is a small number if you are looking for a ten thousand digit sequence
But surely given infinity, there is no problem finding a number of ANY length. It’s there, somewhere, eventually, given that nothing repeats, the number is NORMAL, as people have said, and infinite.
The probability is 100% for any number, no matter how large, isn’t it?
Disclaimer: haven’t done this type of math in years.
The problem is math is strick about absolutes, so we have to be able to prove things to say 100%. The tricky part of that with this question is that “no pattern” random doesn’t mean “equally likely” random.
When I flip a coin it’s equally likely that its heads or tails, so we as humans consider it random.
We know how coin flips work, and can mathematically tell you things like “to get 100 heads in a row you need to flip about a million times on average” (idk actual odds).
Then we call things we don’t see a pattern in random, 16364758858271716165536618183636471771 is a random number I types out, but since I didn’t include 9 no matter how many times I hit 1-8 we will never find 191.
Pi is more like the second type of random, we can’t find any pattern in it, although a quick Google search says every digit seems to be used equally.
Infinity is weird, and pi hitting every number equally is a good sign, but without being able to figure out its pattern I can’t prove that after 100 billion it doesn’t start being all 1s or only od numbers, or only 1-8 etc. so while I believe it’s 100% for every number, math nerds will hesitate to say it’s 100% since it can’t be proved.
My guess would be that - depending on the number of digits you are looking for in the sequence - you could calculate the probability of finding any given group of those digits.
For example, there is a 100% probability of finding any group of two, three or four digits, but that probability decreases as you approach one hundred thousand digits.
Of course, the difficulty in proving this hypothesis rests on the computing power needed to prove it empirically and the number of digits of Pi available. That is, a million digits of Pi is a small number if you are looking for a ten thousand digit sequence
But surely given infinity, there is no problem finding a number of ANY length. It’s there, somewhere, eventually, given that nothing repeats, the number is NORMAL, as people have said, and infinite.
The probability is 100% for any number, no matter how large, isn’t it?
Smart people?
In theory, sure. In practice, are we really going to find a series of ten thousand ones? I would also like to hear more opinions from smart people
Disclaimer: haven’t done this type of math in years.
The problem is math is strick about absolutes, so we have to be able to prove things to say 100%. The tricky part of that with this question is that “no pattern” random doesn’t mean “equally likely” random.
When I flip a coin it’s equally likely that its heads or tails, so we as humans consider it random.
We know how coin flips work, and can mathematically tell you things like “to get 100 heads in a row you need to flip about a million times on average” (idk actual odds).
Then we call things we don’t see a pattern in random, 16364758858271716165536618183636471771 is a random number I types out, but since I didn’t include 9 no matter how many times I hit 1-8 we will never find 191.
Pi is more like the second type of random, we can’t find any pattern in it, although a quick Google search says every digit seems to be used equally.
Infinity is weird, and pi hitting every number equally is a good sign, but without being able to figure out its pattern I can’t prove that after 100 billion it doesn’t start being all 1s or only od numbers, or only 1-8 etc. so while I believe it’s 100% for every number, math nerds will hesitate to say it’s 100% since it can’t be proved.