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:

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.

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…

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

https://en.wikipedia.org/wiki/Normal_distribution

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 -1. 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.