Randomness of PI and other musings

I just stumbled across a Slashdot thread discussing the randomness of PI. It was a pretty typical discussion as far as Slashdot threads go; lots of noise, dozens of assertions and refutations, and a few interesting points. It got me thinking about randomness. Taking the value of PI for example, some say it's random because no patterns emerge when you apply statistical analysis to a string of PI digits. Others are uncertain because nobody has ever actually calculated all of PI and been able to show that no overall pattern exists. Some say PI is obviously not random because it can be calculated by an algorithm, giving the same results each time.

But really (and I love pretending that I have the last word) the only difference between these viewpoints is the conditions they take into account. By definition, randomness describes an event whose cause is unknowable (as opposed to unknown), or a series of events with no knowable (as opposed to known) correlation other than being part of the same series. There are different conditions you can use to determine the knowability of something. The ones who say that PI is random are saying that according to statistical analyzer X, which ran against a given series of PI digits, PI is unpredictable and therefore random. Statistical analyzer X is the condition. The ones who are uncertain take into account the broader condition that there may be other sets of PI digits that might give different results when run through statistical analyzer X. It's just that nobody has gotten around to testing them yet. The ones who say PI is obviously not random are using the common sense condition that PI digits are generated by an algorithm, or another way of looking at it: all of the digits of PI can be compressed into a simple expression. Definitely not random. So randomness depends on what conditions you allow yourself to consider.

Anyways, I guess that was pedantic enough. Shifting gears, I think it's interesting when debates swirl around unspoken considerations like this. Two people arguing back and forth about something like the randomness of PI, but not able to agree because they doggedly follow their own unspoken definitions and hope that the other will eventually submit to it. It's more of a verbal arm-wrestling match than an intellectual discussion. (Slashdot gets me all riled up.)