Perry Marshall: What is Random?

[swamidass (S. Joshua Swamidass)]

Great to see you @Perry_Marshall. Happy to explain how we understand random mutations in science. Far from being idiosyncratic, I’m explaining some key things about what mathematical biologists mean when they say something is “random.” The quote in question is, given in response to @Mark:

@swamidass

The mutations do appear to be ENTIRELY spontaneous. The fact they take place in a largely constant rate does not make them less random. That just tells us there is a pattern to their randomness. Remember, random does not imply “without pattern.” Just because there is pattern to random mutations does not mean they are magically not random. It just means they are “random with said pattern.”

This is not a matter of opinion, but one of definitions. Nothing in the definition of “random” precludes that mutations follow patterns. In fact, the statistically definition of “random” itself assumes that mutations follow some patterns.

I think you have a false conflict in your mind between RANDOM and ORDER. That needs to be stamped out if you want to make sense of this.

And @Perry_Marshall asks…

I invite Joshua to explain what he means by the word “random.”

The word “random” in biology is often very poorly defined, if at all. An Electrical Engineer would never make a statement like: “that just tells us there is a pattern to their randomness.”

Why? Because random means “no pattern.” “Pattern to their randomness” is an oxymoron.

@nwrickert beat me to the punch on this. I’ll highlight the part consistent with the point I was making.

@nwrickert

An electrical engineer might well use the expression “white noise”. And that’s a term used to specify a particular pattern of randomness.

Notice also there is blue noise, red noise, pink noise and so on. A great tutorial on this, with great interactive section is this tutorial on procedural map generation:

https://www.redblobgames.com/articles/noise/introduction.html

These are all different types of random noise that are defined by different patterns. Far from being an oxymoron this is exactly how random variables are defined, as randomness with a pattern. As @nwrickert explains…

@nwrickert

We often talk of probability distributions. There are some important ones, such as the Normal distribution, the binomial distribution, the exponential distribution, the Poisson distribution. These probability distributions are patterns of randomness.

Let’s look at the distribution of two random variables, each one with different patterns (i.e. distributions).

Normal distribution - Wikipedia

Notice how the four different distributions are all “random” but they all fit a separate pattern. The Blue, Red, and Yellow all have a mean of 0. The Green has a mean of -2. They all have different variances. Each one has a different set of constraints or “order” as I put it before. The fact that that there is order does not remove the randomness (unless the variance is zero). Rather we see that random variables are actually defined by the constraints that they obey, by the order that they follow.

That is why I was emphasizing that “random” is linked to “order”. There is no such thing as a “totally random” quantity. That has no meaning. In every context where randomness is used in mathematical biology, we are defining variables that have uncertainty, but also follow constraints of one sort or another. There are random and ordered at the same time.