The randomness of the digits of π

“If you were to assign letters of the alphabet to combinations of digits, and were to do this for all human alphabets, syllabaries, and ideograms, then you could fit any written character in any language to a combination of digits in pi. According to this system, pi could be turned into literature. Then, if you could look far enough into pi, you would probably find the expression “See the U.S.A. in a Chevrolet!” a billion times in a row. Elsewhere, you would find Christ’s Sermon on the Mount in His native Aramaic tongue, and you would find versions of the Sermon on the Mount that are pure blasphemy.”

Richard Preston “The Mountains of Pi”, New Yorker -March 1992

A few weeks ago I was inspired by the quote above to create a system to translate the digits of Pi into English, and though my main pursuit will likely remain unfulfilled, I hope to share what I have found today, on Pi day. My initial approach was based on the idea that integers, and also series of integers, would not be evenly distributed throughout the digits of Pi. What I quickly found, however, was that as the sample size of the digits of Pi increases, the distribution of different integers ( and also series of integers ) becomes more equal.

I am sure that this observation is trivial to anyone with a stronger understanding of Number Theory or Statistics, but it was surprising enough to me that I wrote a program to visually demonstrate the results I was seeing. The video below demonstrates both the observations I made and also how to use the program.

You can use the program here, view the source of it here, and also, if you’d like, have the first 10 million digits of Pi for yourself to play around with here.

In my endeavors, I’m indebted to the maker of apfloat, a program that can be used to efficiently calculate many digits of Pi, among other things. Keith Peters and Justin Windle are also awesome for creating the Simple GUI components set used in the tool.

Though my initial intentions did not involve making a tool to create pretty pictures, I think that’s what I ended up with. I hope in the future to re-purpose this code to visualize different data sets ( a tool is only as interesting as its possible uses ), and also plan to port it to both JavaScript and Objective-C, but that will have to wait until some of my other projects are a little more complete. Please let me know with any ideas on improving the interface of the tool and how it should function. Since it was developed in a vacuum I would very much appreciate any ideas. Also, if you’re interested in print resolution images from this tool let me know as well.