What is randomness?

Randomness is pretty important. Science would fall apart without it. Not just because randomised control trials wouldn’t be randomised, but because almost any experiment would produce junk. Say Galileo dropped his spheres of different weights, but their falls were affected by other (external) things non-randomly. The results would be biased or inconsistent, and we might never have evidence that all things fall at the same rate.1Like most nice simple historical stories, it’s possible Galileo never performed this experiment, though others certainly have since.

Fortunately, randomness is abundant, and we have ready access to it with things like coin flips, which is almost the poster child for randomness. Except there’s a problem: Persi Diaconis had a machine built that can flip coins with the same outcome every time.2Diaconis also found humans might be slightly biased (by which side is up) in their coin flips, too, although this might not be the case. So maybe coin flips aren’t all that random?

Let’s break things down. A coin moves through the air the same way regardless of who or what flipped it. Only the initial toss and final catch are different. This includes which side is up, where the coin’s launched from, how fast it’s launched into the air, how fast it rotates (and how) and where it lands. Let’s call these the “conditions” of the coin flip.3These might also be called parameters, initial conditions, exogenous factors and several other terms besides. The key difference is this: in the case of the machine, the conditions are set and known; in the case of humans, the conditions vary and are not known.4More accurately, we should say “known (or not known) precisely enough”, but we will omit “precisely enough” for clarity.

But there’s something particularly special about coin flips. So long as the coin rotates fast enough, the heads or tail outcome is extremely sensitive to these conditions. Tiny changes in these conditions will lead to a potentially different outcome. So to predict the outcome of the coin flip, you either hope the conditions repeat or you’ll need to know the exact conditions — both of which are true for the machine coin flip.

So here are 3 things that make a coin flip random: 1) the sensitivity to conditions, 2) the conditions don’t repeat and 3) the lack of knowledge of the conditions. The last one means that randomness is at least partly subjective. If you know the conditions (e.g., the machine coin flip) and I don’t, the outcome will look random to me, and not you.

Are human coin flips truly random? If you think randomness has to be completely objective — let’s call that physical randomness — then no, it’s not truly random. If you think it can be subjective, then yes, it’s truly random. Specifically, it’s true subjective randomness.5Random number generators in a computer are sometimes called pseudo random number generators, because if you know the current seed and the algorithm, you can predict the sequence exactly. But in most cases, we don’t know the current seed — and in those cases, they are truly subjectively random.

Do we need physical randomness in order to do valid science? No, we only need subjective randomness. In fact, it may be surprising, but under the right conditions, subjective randomness can do everything we need — including cutting out other influences so that we can properly test what happens when we make a choice (e.g., by walking to work rather than taking the bus). With any luck, we’ll see how this works in the next post.

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