> and the size of the position would be much larger than 50-billion in, but the idea is the same.
The crucial part is that the size of the position will be larger than the file you are seeking. This is unintuitive, but necessarily true for most possible files because of the pigeonhole principle. If you don't believe me, just try it out. Decide on random 4-digit sequences in pi and find their indexes. The mean of their indexes will be >4 digits. Same is true of any sequences of any length.
> I don't get this at all. You're talking about multiple files, which has nothing at all to do with my proposal.
No, I'm talking about multiple possible files, of which you must be able to compress and decompress any single one for your proposal to work in general.
General compression is mathematically proven to be impossible. If you have a compression algorithm f() which can take any input, in order for it to be able to compress some input of length x into a form that is shorter than x, it must also compress some other input of length x into a form that is longer than x.
Or, to put in another way, the sum of len(f(y)) for all possible y where len(y) = x is always greater than or equal to sum of len(y).
The crucial part is that the size of the position will be larger than the file you are seeking. This is unintuitive, but necessarily true for most possible files because of the pigeonhole principle. If you don't believe me, just try it out. Decide on random 4-digit sequences in pi and find their indexes. The mean of their indexes will be >4 digits. Same is true of any sequences of any length.
> I don't get this at all. You're talking about multiple files, which has nothing at all to do with my proposal.
No, I'm talking about multiple possible files, of which you must be able to compress and decompress any single one for your proposal to work in general.
General compression is mathematically proven to be impossible. If you have a compression algorithm f() which can take any input, in order for it to be able to compress some input of length x into a form that is shorter than x, it must also compress some other input of length x into a form that is longer than x.
Or, to put in another way, the sum of len(f(y)) for all possible y where len(y) = x is always greater than or equal to sum of len(y).