What we know is that π is infinite and quite likely it contains every possible finite string of digits (disjunctive sequence).
I've seen recently some prototype of πfs which assume that every file you've created (or anybody else) or you will create, it's already there so it's a matter of extracting it. There is also piFile which can convert your files to pi metadata.
There is already BBP type formula (as part of experimental mathematics) which allows us to compute nth binary digit of pi. So storing position of our start and length of the data, we can theoretically extract the data of our interest. There are some arguments against it that our metadata (e.g. the offset to our data) could be larger than the extracted data. The matrix symbols and π can be encoded in base-256 to make it more efficient (see the joke).
Based on above, my main question is:
- Are there any compression algorithms based on PI?
If not, does it make sense? Or were there any researches in that area?
Or maybe π is not the right one, so what about Euler's constant or Tau (τ)? Would it make any difference?
Image credits: Dinosaur Comics
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