When I went to the WWDC a few years ago the Australian delegates and I were sitting around eating lunch and as nerds do we started discussing Pi. The number pi that is. We theorised that since Pi does not repeat then presumably every combination of numbers would appear in it atleast once. If you converted Pi to binary then we would have every combination of numbers possible.
So taking this one step further, since all movies are just a stream of ones and zeros then every movie ever made appears inside Pi. And every movie that will ever be made will also appear in Pi. Every book ever written and every piece of music would also appear somewhere in Pi.
Imagine the possibilities. Instead of distributing 2Gb movie files I could simply give you the start and end position of where the movie is in in Pi. Say Mission Impossible 4 (where Tom Cruise finally dies!) could be 345566777999 to 3445678388292929. Say.
Having said that. If I patent (or say it's my IP) Pi then I have just patented every movie, song and book ever. I'm rich!
Comments
For brevity, I'll refer to the segments within Pi as the "Pi-space".
If a movie exists within "Pi-space", does that mean that movie studios (such as the MPAA) can no longer claim copyright infringement? Since the work already existed within Pi, they no longer have claim over the copyright.
The main problem with your idea is that every consequent digit of Pi takes (basically) exponentially longer to figure out. CPUs would need to get a hell of a lot faster before this could become a reality. With Intel CPUs have essentially being capped at 3.8Ghz for the last few years, it doesn't look like this will happen anytime soon...
All we need to do is create a specialised computer that can compute Pi to trillions and trillions of digits with ease. Those DES crackers can work much faster than conventional computers because they are built to only deal with that specialised function. This Pi computer will revolutionise the industry! I like the idea of Pi-space. Good name!
Bellard's Formula allows you to calculate an arbitrary binary bit of Pi.
GPUs (i.e., the chips on video cards) nowadays are basically massive parallel computing engines. You can write 'shaders' for them, just like you can write programs for an operating system. The only difference is they operate on pixels and vertices. To give you some perspective, ATI's X1900 has 48 pixel shader processors and 8 vertex shader processors, running at 650Mhz.
So, calculating the bits from a segment of Pi would be quite easy, and probably quite fast.
The hard part is finding the segment of Pi you want in the first place (i.e. "compression"). You'd need to search a really really big chunk of Pi-space to find your offsets. Considering it took 1.2 million CPU hours to calculate the quadrillionth digit of Pi, this could take a reeeally long time.
The worst part about this is that if we take this to it's logical conclusion all of human knowledge, conversation and written works is in Pi. This means that the entirety of human knowledge can be summed up as the number Pi. Quite depressing really.
I know I'm a bit late, but as the resident math nerd I need to point out that just because a number is irrational doesn't mean it contains every possible combination of digits. Eg 0.121122111222... etc.
But if a number goes on forever then it must have every combination of numbers since it can never repeat. But then I suppose if your number only had 1's and 2's then it would never repeat, so you are right in that regard. However if we convert the number to binary then every combination of 1's and 0's should appear.
Not true. Let me give you a counter example in binary:
0.010011000111... etc This obviously does not contain the sequence 010101. However there a an infinite number of sequences which do contain every finite sequence. Let me give you an example: 0.0 1 00 01 10 11 000 001 010 100 011 ... etc,
where basically, you methodically list every sequence of 1 digit, then every sequence of 2 digits etc. It is important to note that NO infinite decimal can contain EVERY possible binary sequence (including the infinite ones). To see this note that if a sequence is of the sort that contains every finite sequence, then it is obviously infinite. So for a counterexample consider the example given above (call it X) and another number of this type, Y=0.1 0 00 01 11 ..., that is it differs from X only in the first two places. It is easy to see now that X does not contain Y and Y does not contain X.
Thus it does not follow that pi contains every sequence of numbers just because it is irrational.
Ah hah -- here's the problem: Toffee is referring to a sequence as in a mathematical sequence. Joel is referring to a sequence as "a collection of bits", where that collection is of a finite length.
Clearly Toffee's interpretation of "sequence" doesn't hold. I still think Joel's idea of locating a section of Pi where the binary bits equals the data you're talking about is plausible.