I don't fully understand it myself, but this answers your question:
Q10. If two files are compressed with the Recursive Compression Technology, even if only one bit is compressed after each pass, eventually they could both be reduced to a single 0, or, or that matter, a single 1. How could this same bit be decoded back to two different files?
This will never happen, because after a file has gone through a large number of passes, it will first get into a phase of diminishing returns, and eventually reaches the optimum, when the effects of further passes would become negligible. Furthermore, even in the event two files become exactly the same at their optimum by sheer coincidence, the decompressed files will surely be different, because the two files would have gone through different numbers of passes to reach the same optimum.
As for the doubting Thomas' spurious critique about Shannon's theorem, entropy and all that jazz, and in particular the smart Alec argument that, if two different files can both be compressed recursively to a single 0, how one can decode a single 0 back to two different files. This simply doesn't even hold water and I have already refuted it in our website in a simplistic example: our technology can compress a number of 0s to half the number at each pass, therefore in decoding, a single 0 will be decoded back to two 0s at the first pass of decoding, then four 0s at the next pass and so on. Therefore, if one file has gone through four passes to become a single 0 and another file has gone through five passes to become the same , by decoding the single 0 four times, it will be restored to the original file of 16 0s and the other five times to its original file of 32 0s, respectively, thus you have two completely different files decoded from the same single 0! Of course this is a very simplistic example. I can give you a slightly more complex example. As our technology compresses by replacing bit strings with a shorter signal, and the shortest replaceable string is, say, 9 bits. Then if many files can be compressed recursively to become a 8 bit file, there will be 256 different compressed files, and each can be decoded through different number of passes, resulting in an infinite number of different files. Furthermore, not all string over 8 bits can be replaced by a signal, therefore files can reach eventually a string of 9, 10, 11, 12 bits, etc, which cannot be replaced by a signal; if we apply the same principle to them as with the 8-bit irreplaceable strings, the number of files that can be restored from these last-pass strings would be astronomical! That is what I mean by an optimal point, when a compressed file cannot be compressed any further, as it can no longer be replaced by a signal.
From the FAQ:
http://www.recursivedigital.com/faq.html
