Ownership

It's late, so maybe that's why I'm having strange thoughts. I don't understand how anyone can claim ownership of any piece of intellectual property that exists in digital form. Once something (say, a song) is stored digitally, it is represented by a long series of 1s and 0s -- the song is essentially translated into a really big number. Depending on the format used for storing the song (MP3, WAV, &c.), the number that represents the song will be different. So does the owner of that song also own the number that represents that song? And if so, the number generated by what storage scheme? All of them?

That's a big problem because any number can be changed to any other number using the appropriate math. For instance, I could easily write a program that takes in the number that represents a particular song and then adds 1 to that number. Does the owner of the song own that number too? I could write a music program that takes this new number, subtracts 1, and then plays the song... so in a sense I simply created a new storage format for music. Adding and subtracting 1 is simple, but there are literally an infinite number of possible storage formats that haven't been invented yet, and they span every single number. Any number, when combined with the right algorithm, can be used to generate any song. So where is the copyright infringement? Is the song stored in the long binary number, or in the algorithm that decodes it? I could write another piece of software that no matter what file you put into it always plays the same song. Is every single file in existance now in violation of that song's copyright?

Similarly, since every song file is just a really long number, what happens if I'm working on some complex mathematics and my answer turns out to be the exact number that represents some song in MP3 format? Does the owner of the song now own my mathematical formulas that just happened to generate their song? If they don't, then I can write a piece of software that takes my formulas as input and plays their song as output. Basically, the song would be stored in the math, and I would have invented a new storage format. It would be trivial to generate formulas that output the number for any song you want.

In the end, it's impossible to own numbers. Since numbers are used to represent everything stored digitally, it seems impossible to me that copyright as we now know it can continue to exist. Add to this other thorny issues such as digital child pornography ("that's not a picture, officer, that's just a really long number I got from my math equations") and decryption warrants and I think we're just on the tip of dealing with the changes that the digital revolution will force upon our civilization.