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.

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6 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.

      • Eric,

        I’m curious how the field of Computational Biology or Computational Genetics defines random. A quick Google search didn’t turn up anything different than what I normally see elsewhere. Google Scholar gives me, for example this paper:

        The author begins by talking about noise in the context of engineering, which is exactly what I, Noble, Shapiro and anyone in mathematics or physics means by this term. The article is relevant because stochastic resonance is when you harness noise for some particular purpose, which happens often in biological systems.

        But this is not to be confused with the idea that a transposition or horizontal gene transfer event is random because it’s not. It’s not random with respect to coding sequences and it’s also not random with respect to fitness either.

        So when Swamidass criticizes Shapiro for saying that evolutionary mutations are random, we have to note that what Swamidass hears is different than what Shapiro is trying to say. I have not encountered anyone else whose definition of randomness is similar to Joshua’s. But again I’m not sure what his definition is.

        I am unable to follow these threads closely so if Joshua offers a definition please let me know.

        P.S.: In my work I try to conform to standard definitions and conventions as much as possible. This is why I conform to the Claude Shannon model of information theory. I use randomness the same way Claude Shannon does in his seminal 1948 paper. He uses the term over a dozen times. Swamidass uses it differently.

        • Eric and Mark,

          A year ago I wrote this blog post “My New Years Resolution for 2018”: I said: I will only engage with people who FIRST read my books or other similar books, because I have earned the right to be taken seriously in this business. Evolution 2.0 has endorsements from some of the most respected scientists in the world. And the largest origin of life prize in history. Not to mention well over 100 glowing Amazon reviews.

          I engaged with Dr. Swamidass and several people on his forum as you see here.

          It is clear that Dr. Swamidass, while he may have read parts of Evolution 2.0, did not understand it, and likewise for some reason also refuses to understand the people whose works I cite at the end of that blog post, like Noble, Shapiro, Margulis etc. So far as I can tell he does not understand what they are actually trying to say.

          Swamidass misrepresents my views as well as their views. He condemns their work by imposing onto their work his own (unconventional) definition of randomness, instead of the standard definition they themselves use. He says, for example, that Perry Marshall does not use a mathematical definition of randomness, even though I do and I stated it in my very first blog post about this,

          In his modeling work, he seems to want to define everything as a random variable, even if it’s deterministic. (He models deterministic things as random variables with entropy = 0.) He insists on labeling non-random things as random.

          In my Appendix “All About Randomness” and throughout my work I point out that it is impossible to prove anything is random. (There is a proof in mathematics for this.) That being the case, Swamidass’ starting point in his mathematical models is to begin with something you cannot prove and make everything you should be able to prove a subset of that.

          If this isn’t exhibit “A” of obfuscation I don’t know what is.

          And even then his language is still inconsistent because he still makes valid statements like “mutations are not random with respect to fitness” in which case his use of the word random reverts back to conventional.

          I find that when I discuss these issues with him and the other people on his forum, they generally refuse to read or understand what I have actually written. Then they misquote me and misrepresent my views.

          This has dragged on for five months. Nothing has been accomplished. Other than me writing four blog posts which I think state my case quite succinctly – like the one above.

          I do not know what his intentions are but I consider engagement with Joshua Swamidass to be poor use of my time.

  3. Paul Adams says:

    Development of life is not the selection-biased random process that is the basis for natural selection. Indeed, as Perry Marshall in his book, Evolution 2.0, explains, the world-class mathematician Gregory Chaitin has shown that it is impossible to prove that any event is random. In other words, there are unavoidable natural environmental and exogenous conditions that affect heredity. If there is direction, purpose, then selection is redundant. The phenotype is by definition a survivalist.
    Is that a fair conclusion from the the lack of randomness in the natural selection theory.

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