On Pi


For some, the infinite sequence of decimal places generated by the ratio of a circle’s area to the square of its radius that we call π is extremely provocative. I’ll confess that the subject has some interest for me.

When you hear that a number doesn’t end, that it cannot be completely represent by any means known to man (or at least this man), then you might start to think that this number is as close to magic as we’re likely to come in this mortal coil.

That said, there are many ways of calculating π.

One popular thought experiment is to imagine what sort of messages are contained in π. People have been encoding messages with numbers and other symbols for many centuries. One could argue that the alphabet itself is just a symbolic encoding of thoughts anyway.

Does π have a message for us?

Well, it might and it might not. You’d have to figure out how the message is encoded. What’s the alphabet of the message? What language do those letters belong to?

In the computer world, there is a popular mapping between numbers and letters called the American Standard Code for Information Interchange (take THAT, XML!), abbreviated ASCII. In ASCII, capital “A” is represented by the decimal number 65, lowercase “a” is 97. These numbers represent the character’s order in the list of 128 characters that compose basic ASCII. The word “dog” is presented by the ASCII sequence of decimal numbers: “100111103”. In the programming language Perl, you could find this out with the following snippet:

printf("%s", join("", map { ord($_) } qw[d o g]))

Is the ASCII sequence for “dog” contained in π? It’s certainly possible.
The sequence is short compared to the decimal places in π.
Since I don’t have the the means to generate π with any accuracy, I can’t tell you the offset in sequence of decimal numbers in π that “dog” appears. However, I’m pretty confident it is there.

Of course, there may be other encodings lurking in the limitless parade of numbers in that magic ratio. One method popular for encrypting messages these days is called Public Key Infrastructure(PKI), which uses a prime number raised to the power of another prime number. The product of such an operation is very hard to factor (having only one correct solution). If you give these numbers to a friend, she will be able to decode your messages fairly easily. However, if your message is intercepted by a ne’er-do-well, he will have a hard time finding the right magic numbers to unlock your missive.
There are other transcendental numbers known to us. Perhaps these are part of a galactic PKI encrytion scheme? Perhaps π really is some universal truth encoded in such a way as to challenge sentient beings.

The decimal numbers in π are thought not to repeat themselves. In emperical tests, this appears to be the case.
However, we can’t know that the number doesn’t repeat until we can either generate the entire number or come up with a fancy, mathematical proof that explains the behavior of these never-end decimals.

One jumping off point for the philosophical meandering about π is to think that if this number generates an infinite sequence of non-repeating numbers, then π might be nature’s random number generator. If that’s the case, then you might be tempted to think that any sequence of arbitrary size can be contained in the π.
If your imagination is wild enough, you might be tempted to be believe that there is a numeric representation of the universe contained somewhere in π.

This sort of thought leads a lot of freshman math majors to soil their bed sheets.

The unsettling conclusion to this idea is that π is either a numeric “backup” of the universe or perhaps it is the blueprint of reality. Both of these notions imply an automaton or purely natural universe. By this, I simply mean that all processes of reality have a non-supernatural cause. This will no doubt make some uncomfortable. If the accepted rational view of the universe’s origins is true, then at some point, something “beyond” nature had to be, since “nature” didn’t exist prior to that. But perhaps math did and these special numbers are a relic of that pre-relational universe. It’s an odd paradox and one that Dr. Hawking suggests is the product of fundamentally flawed thinking.

But that’s gets into the nature of time and that’s a completely different essay.

What is most interesting about π is, perhaps, not the number at all, but how people react to it. It’s a number that promotes cosmological thinking in those that consider it deeply. Perhaps π is like the monolith in Clarke’s 2001 in that the more we attempt to interact with it, the more it tells us about what we are.