Randomness and unpredictability

Thursday, December 1, 2011 1:39 pm PDT

I’ve been reflecting recently on the concept of “randomness” and how it differs from “unpredictability”.  We apply these terms rather loosely to a lot of things, from lotteries to stock markets to ballgame scores.  All these are unpredictable, meaning we cannot know the outcome in advance, but are they truly random?

A lottery appears for all practical purposes to be truly random–at least, as random as human ingenuity can contrive.  Stock markets may appear to behave at random, yet we know that this is an illusion: in reality the prices are determined by the actions of many competing participants.  This is also true of a ball game, yet we do not consider its final score to be random: we know it’s the result of human inputs, and can see the processes leading to it in action.

When we consider a process (something that develops over time, like a sequence of numbers, or a series of coin tosses) we naturally look for patterns.  We cannot help doing this, it’s the way our brains are designed to work (as well as being a very useful survival skill).  If we spot a pattern, then we can use it to predict the process.  But what if we can’t spot one?  Is it because no pattern exists, or just that we haven’t found it?  Consider the sequence of digits 2, 6, 4, 5, 7, 5, 1, 3, 1, 1, 0, 6, 4, 5, 9, … .  It may look random, but once we recognize it as the square root of 7 then we know how to predict it–and, of course, we know that it is not random.

This highlights the difference between randomness and unpredictability: unpredictable events follow no discernible pattern, but truly random ones follow no pattern at all.

Can a process ever be truly random? The people that run the lottery hope that no-one will ever discover if there is a pattern underlying the numbers they draw.  (Or at least that if one is ever discovered, it will be too complicated to permit predictions.  Otherwise, they would very rapidly be out of business.)

Likewise, the theory of Quantum Mechanics is based on the assumption that subatomic processes are truly random.  But what if there is an underlying pattern, but it’s just too complicated to calculate in practice?  That wouldn’t invalidate the theory, it would just change our interpretation of it.  And that is what PQR Theory asserts: nothing that happens in our Universe is truly random, even though for all practical purposes we may assume it to be.  We may discover the formula that guides our destiny, but we will never be able to predict it.

In the words of the old song: “Que sera, sera: whatever will be, will be.”  But the future’s not ours to see.