It’s Time to Tighten the Definition of “Random”

S. Joshua Swamidass is an associate professor in the Laboratory and Genomic Medicine Division at Washington University in St Louis. His research uses computational methods solve problems at the intersection of medicine, chemistry and biology.

Joshua and I have met at several conferences and had long discussions. He, like myself, is very interested in ending the war between science and religion.

His blog “A Peaceful Science” has many discussions about evolution. Joshua invited me to respond to numerous conversations where my name has come up.

On a page about the Extended Evolutionary Synthesis (which is the common term for the viewpoints I espouse in my book Evolution 2.0) Joshua says the following:

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.

As far as I can tell from Google searches, Joshua has never defined the word random on his blog, or explained his own working definition.

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.

Here is what I mean by the word random (excerpted from Appendix 1 of my book Evolution 2.0):

The Oxford English Dictionary (2nd ed.) defines random in this way: “Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard.”

More importantly, in statistics, randomness is defined as “governed by or involving equal chances for each of the actual or hypothetical members of a population; produced or obtained by such a process, and therefore unpredictable in detail.”*

Likewise, statistics formally defines a random process as a repetitive one whose outcomes follow no describable deterministic pattern, but rather exhibit a probability distribution, so the relative probability of each outcome can be calculated.

For example, when you roll a fair six-sided die in neutral conditions, you say it’s random because before the die is rolled, you don’t know what number will show up. However, the probability of rolling any one of the six numbers can be calculated if each is equally likely.

In information systems, randomness is non-order or non-coherence in a sequence of symbols, such that there is no intelligible pattern or combination. Formally, a string of numbers or letters is random if and only if it cannot be generated by a formula that’s shorter than the string itself ** 

This is the most rigorous definition of randomness. According to this definition, nothing that has a pattern is random.

As soon as you announce a pattern is random, you have accepted that no further parsing or analysis of that pattern is possible.

Joshua, will you please define what you mean by “random”?

It was good to see you in Boston last month. Thank you.

Perry Marshall

* Philosophy of Statistics offers a number of definitions of randomness on page 35 including this one.

**Chaitin, G. J. (1990). Information Randomness & Incompleteness: Papers on Algorithmic Information Theory. Teaneck, NJ: World Scientific Publishing Company Incorporated. Reprinted from Chaitin, G. J. (1975). “Randomness and Mathematical Proof.” Scientific American, 232(5), 47–52.

3 Responses

  1. Mark Chenoweth says:


    Whenever I check up on your blog, all I ever see at the top is “bacteria cells are really smart” or whatever it says, so it looks like you haven’t posted anything new in months.
    And then I run across a review you post of D. Alexander’s new book on amazon or see a post you made on J. Swamidass’s forum. But these posts are still several posts below the smart bacteria post, so it looks like you haven’t posted anything new for months. Perhaps it’s just my phone/computer being weird, but I have left your site dozens of times because I thought there wasn’t any new content. And that’s not correct. But for whatever reason, your new content is always a bit burried.

    Perhaps there’s a way to remedy this, and maybe it would increase your traffic.

    In other news, I’m anxious to see where you and Swamidass take this.


  2. Mark,

    I have a half dozen blog posts that are pinned to the top because for new people they emphasize what I see as the most interesting items.

    I’ll switch off “sticky posts” and see if that’s helpful for others.

    Yes, I’m quite interested to see how Joshua replies.

    • Eric Holloway says:

      According to Dr. Swamidass, even a deterministic function is “random” because it can be modeled with a random variable…his point of contention is purely semantic. He wants to call everything “random”.

      A boundary case in random variables is a variable that can take on only one value. I.e. they are fully determined. We would still call this a “random” variable, one with a particular sort of distribution, one without any entropy. Yes, the term “random” is that flexible.

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