this post was submitted on 26 Dec 2024
222 points (98.7% liked)
Asklemmy
44229 readers
283 users here now
A loosely moderated place to ask open-ended questions
Search asklemmy ๐
If your post meets the following criteria, it's welcome here!
- Open-ended question
- Not offensive: at this point, we do not have the bandwidth to moderate overtly political discussions. Assume best intent and be excellent to each other.
- Not regarding using or support for Lemmy: context, see the list of support communities and tools for finding communities below
- Not ad nauseam inducing: please make sure it is a question that would be new to most members
- An actual topic of discussion
Looking for support?
Looking for a community?
- Lemmyverse: community search
- sub.rehab: maps old subreddits to fediverse options, marks official as such
- [email protected]: a community for finding communities
~Icon~ ~by~ ~@Double_[email protected]~
founded 5 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
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?
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.