3 ms·
Similar ideas have floated around for a while. I’ve always enjoyed the elegance of compressing things down to a start and end index of digits of Pi. It’s utter
by everforward 2y ago
Similar ideas have floated around for a while. I’ve always enjoyed the elegance of compressing things down to a start and end index of digits of Pi.
It’s utterly impractical, but fun to muse about how neat it would be if it weren’t.
- LtWorf 2y agoAFAIK it's not been proved that every combination does exist in π. By comparison, you could easily define a number that goes 0,123456789101112131415… and use indexes to that number. However the index would probably be larger than what you're trying to encode.
- everforward 2y agoHuh, I presumed that any non-repeating irrational number would include all number sequences but I think you’re right. Even a sequence of 1 and 0 could be non-repetitive. I am curious what the compression ratios would be. I suspect the opposite, but the numbers are at a scale where my mind falters so I wouldn’t say that with any confidence. Just 64 bits can get you roughly 10^20 digits into the number, and the “reach” grows exponentially with bits. I would expect that the smaller the file, the more common its sequence is.
- LtWorf 2y agoWell with my number you can at least calculate the digits at any position without needing to calculate all the digits before. Let's do it for a similar number but in binary format… a 1mb file has 2²⁰ digits. If we optimize the indexing to point to the "number" instead of the "digit"… so that the index is smaller. Magically the index is as long as the file!