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Since Pi is infinite and non-repeating, would that mean any finite sequence of non-repeating numbers should appear somewhere in Pi? (lemmy.dbzer0.com)

submitted 4 days ago* (last edited 4 days ago) by [email protected] to c/[email protected]

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How about ANY FINITE SEQUENCE AT ALL?

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[–] [email protected] 1 points 3 days ago* (last edited 3 days ago) (1 children)

I can't tell if this is a joke or real code... like for this sentence below.

The cat is back.

Will that repo seriously run until it finds where that is in pi? However long it might take, hours, days, years, decades, and then tell you, so you can look it up quickly?

[–] [email protected] 9 points 3 days ago* (last edited 3 days ago)

I can’t tell if this is a joke or real code

Yes.

Will that repo seriously run until it finds where that is in pi?

Sure. It'll take a very long while though. We can estimate roughly how long - encoded as ASCII and translated to hex your sentence looks like 54686520636174206973206261636b. That's 30 hexadecimal digits. So very roughly, one of each 16^30 30-digit sequences will match this one. So on average, you'd need to look about 16^30 * 30 ≈ 4e37 digits into π to find a sequence matching this one. For comparison, something on the order of 1e15 digits of pi were ever calculated.

so you can look it up quickly?

Not very quickly, it's still n log n time. More importantly, information theory is ruthless: there exist no compression algorithms that have on average a >1 compression coefficient for arbitrary data. So if you tried to use π as compression, the offsets you get would on average be larger than the data you are compressing. For example, your data here can be written written as 30 hexadecimal digits, but the offset into pi would be on the order of 4e37, which takes ~90 hexadecimal digits to write down.