The Quest for Random

Think of a sequence of five random numbers.
Got them?

Good.

Actually, hate to break it to you, but the numbers you just picked aren't truly random. In fact, I can probably tell you a good bit about all of the numbers you just thought of.. They're all most likely:

* Between 0 and 1000. And thus, positive.
* Whole integers, that is, none of them are fractional or have trailing decimals.
* Non-repeating.

To say all of those are probably true about your "random" numbers is pretty bold. But think about the numbers you generated. Are all three assumptions true?

In some respects, humans are poor random number generators. But don't feel bad because I have another surprise; sometimes computers are much worse!

Computers follow precise instructions. It's the nature of a computer. In fact, if it doesn't follow instructions perfectly, it's considered broken. There are formulas that a computer can execute in order to get a sequence of numbers that seem random. And for most purposes these pseudo-random numbers are close enough to random to use in gambling and simulations and such. But true random is hard and maybe even impossible to come by.

It really boils down to how we believe the universe behaves. Some people believe the universe, ever since its inception, is set upon a predetermined course. Others believe that the universe, at some level, perhaps at the quantum/sub-atomic level, is the way it is without cause.

If the universe is deterministic, and we are able to collect information about everything, then randomness becomes impossible to achieve. Even the things "True Random Number Generators" are based on, such as quantum physics, weather patterns, and atmospheric noise, become calculable, predictable, and thus non-random.

What's perhaps even more interesting, even if we were to have a perfectly random number generator, we could not formally prove its randomness! We would need a list of infinitely long numbers from it as well as an infinite amount of time to conduct statistical analysis on it.

Having said all this, I'd like to claim back the word 'random'. To be able to use it colloquially, we distinguish it from 'true randomness' by defining regular old randomness as simply being "unpredictable".