A thing I saw on Facebook the other day captured my imagination. Now, this may be hokum - and having the idea play around in my kind in a dream last night won't have helped (so we major religions are founded on equally unstable ground). However, I'll give you the gist of what the Facebook thing said, and then my thoughts.

This gist of this from memory (and the thing was a graphic anyway, so cutting and lasting won't help if I did find it):
"PI is an infinite number - and if you use the digits to represent values of bytes in a computer file, you will get everything - the image you first saw when you were born, to the image you'll see when you die."

I think the notion here is that in an infinite series of numbers derived from the dimensions of a circle, you can effectively get anything if you know how to extract it.

So, thoughts:

1 - If the above is correct (and I'm not a pure mathematician who has intimate knowledge of PI), then the scope for locating, say, Word files containing transcripts of the conversations between Blair and Bush is pretty good. If you know the markers for such a data set, and scan PI's infinite length, you'll find it. You may also find the data needed to cure cancer, build a warp engine, and rebuild all those bits of the Bible that They do 'to want you to see. So, if this is true, then we need to start data mining PI.

2 - Another font of fancy. Given that the number sequence of PI is infinite, and that a data file is, effectively, a string of numbers, it should be possible to locate that string of numbers in PI. If that can be done, then the sudden contraction of a file from gigabytes to a small data string is compelling. So, you ZIP your file (remembering that some files are really bundles), run it through the PIZIP algorithm and bingo - you get two numbers. The first being the position in PI of the start of the data, and the second being the length. A 2 GB file could be compressed to a few hundred bytes in length. To get your data back, the PIZIP algorithm would just go to the location in PI, grab the n bits of data and reconstitute from there. PI would need to be calculated for as long as possible to cover all possible data sets, I expect a massive server farm would be needed to keep this going.

Yes, both are pie (or PI) in the sky - amateur random nonsense, but it's been running around my head the mast couple of days. I like the idea of data mining for stuff we don't already know, but could find out if we know what and how to loom for it coming not from real research, but from calculating a number into infinity.

This is technically true. A friend of mine has a similar theory - he's a computer programmer and, in the end, all computer programmes are just numbers. His idea was to generate an infinite - or at least very,very, very long - series of random numbers and essentially scan through it, looking at each point for sub series of numbers which correspond to working code. And then he can retire, because all the code he (and indeed everyone else) will ever write is in that series of numbers somewhere.

The caveat of course is that such a series of numbers would be astronomically big, and would probably take up all the available storage space on the planet, and need all the available commuting resources of the planet to scan through it in anything approaching a human lifespan. The PI theory is the same; yes, somewhere in the derivation of PI is the sequence of numbers that could represent the pixels of any particular image. Or your home address. or an MP3 of Stephen Fry reading Harry Potter. But finding any particular sequence in the infinite length of PI is an essentially impossible job, because it's equally mathematically true that even with the whole earth's computing resources it could in theory take an infinite amount of time to find the particular sequence you're looking for. Essentially, you don't know if the particular sub series you want starts at position 1, or starts at position 10^100,000,000,000 until you look for it. If it's the former, you're laughing. If it's the latter, you're buggered.

And, spoilering a little, the theory is also the payoff from Carl Sagan's novel 'Contact' (later filmed with Jodie Foster in the lead role), although Sagan's use of the theory in his story is rather elegant.

What you have there is the Library of Babel http://en.wikipedia.org/wiki/The_Library_of_Babel

did some more digging on this. It seems that while it’s a nice idea, others have given it more thought. One problem is that the way in which numbers behave in Pi means that there may not be an even distribution of numbers - meaning that if you expect a numerical sequence to represent a byte sequence of a document, you may just never find it. You may never find your telephone number, come to that.

The other issue is that if you were able to find your phone number, or the byte sequence of that mahoosive file you would like to index, the actual number of the index it’ held at may well occupy more space than the file you were working on. The other issue would be the energy used to calculate PI to accommodate your data, and then seek if out as needed. It could be an expensive job.

So, yes, a kind of Library of Babel - it’s a nice idea, but you may need more than the 2x(10^15) digits - http://en.wikipedia.org/wiki/Pi#Modern_ ... ore_digits - to get anything meaningful.

Some years back there was a company that was touting a lossless image compression scheme based around fractal maths which was a very similar idea. Basically the idea seemed to be they would slice the image into reasonable sized chunks then figure out the fractal seed that would regenerate the pixel array of each slice exactly. so you could take a 10,000 * 10,000 4 bytes per pixel image and compress it losslessly down to a few hundred K, which was a simple 2D array of fractal seeds.

They did seem to end up with a finished product as I recall, but it never seemed to actually get anywhere. Wonder what happened to them?

Jon

That rings a bell. I remember reading about that.

What I also remember was some idea presented on Tomorrow’s World where they were postulating TV pictures getting bigger - and the idea they was showing was based on fractals rather than a scanning line (this was in the 1980s). The idea was that you broadcast the fractal seed for the frame, and that would be used to generate the image to the size the TV was. The aim was bigger images with no detail loss. I think, given the computational power needed, this was a loser at the time.