Had an idea - looking for a math buff to tell me if it's possible with today's technology.

Fri May 20 18:46:45 UTC 2011

To do this, you only need 2 numbers: the nth digit of pi and the number of 
digits.

Simply convert your message into a single extremely long integer. Somewhere, 
in the digits of pi, you will find a matching series of digits the same as 
your integer!

Decompressing the number is relatively easy after some sort-of recent 
advances in our understanding of pi.

Finding out what those 2 numbers are--- well, we still have a ways to go 
on that.

Despite the ridiculousness of this example, it does illustrate to the 
author that there are extremes of compression. The "single mathematical 
formula" compression method is possible, even trivial. However, the 
computation time for compression may be unreasonably large.

Here is another ridiculous way to compress data: Convert your data 
into a series 

of coordinates to a mandelbrot fractal set. The final picture is a 
fixed size, regardless of the size of your starting data set. From that 
final picture, you should be able to retrieve your original starting 
data set.

Good luck!