3 ms·

But some numbers will get larger when compressed. And some here means most of them.

• colanderman 12y ago
  You're not compressing just any number... you're compressing a number representing a bitmap that's mostly white. That that can be done is not just theoretical... it's done all time time. (Computer files are, after all, just large numbers.)
  • danbruc 12y ago
    You are of course correct, somehow I tricked myself into believing this would require compressing the number for every image into its image. But on a second thought there might still be a tough problem - altering the number will alter the image which will in turn require altering the number again. So the (possibly) hard problem is finding a fixed point which may actually not even exist (for a given formula).
    • colanderman 12y ago
      Ah, but there is a science behind writing such things. They're called quines. Here's one I wrote: http://chris.pacejo.net/postscript/quine.ps http://chris.pacejo.net/postscript/quine.ps The trick is that the part of the number (program) that encodes the image of the number doesn't need to encode the image of itself -- that can merely be created directly from that part of the number. See e.g. the source of (or output of!) the quine I linked. The first half of the program is the "image"; the second half basically just prints the "image" once as it is represented in the source, and again after interpreting it a bit. (In fact this way you don't even need to compress the "image"... the compression comes from the fact that your "program" is roughly just two copies of the same thing.)