3 ms·
English literature vs. the digits of pi (π), which has more entropy?
- inphovore 4y agoDigits of pi are a conceptual illusion. These digits represent points of precision on the circumference of a circle, nothing more. As precision increases infinitely, so too there are more imaginary numbers to append. There are a finite product of English literature, no matter how vast. It would be different to ask “sensible arrangement of English words vs. the digits of pi.” Of which, words describing the digits of pi are as infinite as the digits themselves. Also, I wish modern information theory would redefine entropy as “the distribution of potential over negative potential.” Which I believe a more concise and sensible definition.
- PaulHoule 4y agoThis is an example of why kolgomorov complexity theory is an intellectual tarpit right up there with the EPR experiment. Digits of pi are straightforward to compute with a simple formula but if you are presented with something like that it is by no means obvious which formula to use. Barring an algorithm which is that smart I’d say pi has more entropy in that it it has log2 10 worth of bits per character whereas English text is maybe 1 bit per character although that is better than any current compressor.
- h2odragon 4y agoKind of like asking "which is heavier, Love or Guilt?" append the phrase "in this particular encoded form" to "which has more entropy" and the question can be answered; but the answer is determined by your choice of code. Pi can certainly be encoded in such a way as to take more space than all of english literature to date (and probably in the future). Or you could encode it in a numerical system based on Pi and represent it with a single symbol. Then your "entropy" in Pi is an artifact of how finely you're quantifying, which is still potentially infinite.