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willis77 | 5 years ago

The digits of pi contain every pdf that ever could and ever will exist.

discuss

order

vcxy|5 years ago

"Find the earliest valid pdf in consecutive digits of pi"

paulmd|5 years ago

I mean, the answer is trivially zero, there exists a PDF-like structure somewhere in Pi, and the offset of that doesn't have to be zero, it can start or end anywhere. So the range [0, N] is a valid PDF.

drevil-v2|5 years ago

Please don't give them any ideas.. the whiteboard interview coding tests are hard enough as it is

btown|5 years ago

Imagine if it was a PDF that simply rendered the number 42.

mtzet|5 years ago

Well maybe. We don't know if pi is a normal number.

poizan42|5 years ago

Actually it only needs to be a disjunctive (or rich) number which is a weaker condition.

We don't know whether pi is that either for any integer base.

SteveGoob|5 years ago

> We don't know if pi is a normal number.

Sure we do. There are plenty of proofs out there that pi is an irrational number.

gorgoiler|5 years ago

Is this correct, mathematically?

I understand the point that PI contains every possible piece of information, theoretically.

However, the chance of finding a given string in PI depends on the string’s length. The longer the string, the more the probability tends to 0.

The paradox therefore is that PI contains every PDF, but you will never find them, so in what sense does it really contain them at all?

lsiebert|5 years ago

No, all strings theoretically exist in 𝛑 given enough digits, so longer strings don't reduce probability of existence, they just mean that it will take more digits to find them.

rezeroed|5 years ago

If a tree falls in the forest and no one is around to hear it fall. Or a modern take, if a disease has no symptoms is it really a disease.

nroets|5 years ago

<citation needed>

Including a PDF that generates the digits of pi

adtac|5 years ago

actually, if you find the citation, let me know, you might be in for an award

egocodedinsol|5 years ago

I'm not sure that's necessarily true. It is true (at least with a non-constructive proof) that if you pick a 'random' real number then it contains all possible PDFs with probability one ( or that the set of numbers for which this is not true has lebesgue measure zero). But I'm not sure it's known that pi has this property.

dheera|5 years ago

Pi is thought to be normal but it hasn't been proven yet, so we can't say that for sure, but it's likely true.

ducktective|5 years ago

I don't think that is a proven fact.

rbonvall|5 years ago

Since a PDF can begin with non-PDF content, then pi itself is a valid PDF file.