Pi – the ratio of the circumference of a circle to its diameter – is an irrational number, meaning its decimal expansion never ends or repeats. As such, it could never be written out in full. If Pi is also a normal number, roughly meaning that the value of an arbitrary digit is random, an interesting property arises. Specifically, that every possible string of digits will be located in it somewhere. Given that any text can be perfectly converted into a number and any image or sound can be very well approximated by a number, this means that every possible written document, painting, photograph, symphony, and lecture can conceivably be located somewhere within that endless string of digits.
Quite a while ago, I had the idea that you could refer to any information in terms of a ‘Pi address’ – where to look within Pi to find the desired data. It would work for anything from the newest Tori Amos album to the first edition of the Oxford English Dictionary. The biggest problem is that the address would, in most cases, require more storage space than the actual data.
This website proves the point by letting you search the first 200 million digits of Pi for any string you want. My birthday begins at digit 196,469,286; my office phone number begins at digit 124,573,291. Because it is mathematically possible to calculate Pi from any arbitrary decimal place, it isn’t necessary to find all the prior digits to convert those back into the numbers they represent. That said, for large pieces of data (like the book and album mentioned), the Pi address would almost certainly be a lot longer than a data file containing the entire work. Pi addresses may not be a good way to refer to information, though they do provide a relatively dramatic perspective on the nature of infinity.