George Szpiro

If you do a lot of numbers with a random number generator, you get approximately as many sequences 3, 4, 8, 9 as you will get 1, 1, 1, 1.

But so how do you know when you see a sequence whether it's random?

Well, if you can recognize it as a random sequence, then it can't be random because randomness means you can't recognize it.

There's no pattern.

There's no rhyme or reason to the sequence.

So you can never actually recognize or decide whether a sequence of numbers is random or not.

The only thing you can do is investigate how the sequence was produced.

If it was produced by a random process, let's say by throwing dice or flipping coins, then it's random.

But actually to see a sequence and say this is random, that you cannot do.

No, because you'd never come up, if I'd ask you to produce random numbers, you'd never come up with 1, 1, 1, 1, 1, 1, 1.

You'd never say that.

And actually, in a really true random number generator, this sequence 1, 1, 1, 1, 1 should actually appear every once in a while.

But a human being, we just wouldn't come up with such a number.

Or 1, 2, 3, 4, 5, 6, 7.

That sounds totally unrandom.

But in a random number generator, this sequence should actually appear every once in a while.

Yes.

Okay.

So we talked about veridical and falsidical paradoxes.

There's a third kind of paradox, which is called an antinomy.