Perry Marshall: What is Random?


I have replied to the discussion about “random mutations” on my blog:


This is mostly going to be a reply to your blog post. And any quotes below will be quotes from that blog post.

I’m not Joshua. I probably cannot satisfactorily explain what I mean by “random”, and Joshua probably cannot explain what he means.

For me, as a mathematician, “random” is a term in the mathematical theory of probability. But the theory does not explicitly define “random”. Rather, “random” is implicitly defined by its role in the theory.

When we leave mathematics and get to the word “random” in ordinary speech, it is even more murky. Some people are determinists. They believe that everything that will happen in reality is already determined. And, for determinists, the word “random” could not strictly apply to anything in the real world. But even determinists find it useful to talk of random events, though they may insist that they are not strictly random. Or, to say that differently, many people use “random” quite loosely without needing a tight definition.

I should note that some Christians are deteriminists, though they prefer to use the term “predestination” rather than “determinism.”

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

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.

That’s fairly close to how biologists are using “random” when they talk of random mutations. But I’ll note that I am a mathematician, not a biologist.

I’ll have to disagree with that one. In particular, I disagree with the “equal chances”. You would have equal chances with a uniform probability distribution, but not with other important probability distributions.

In biology, I would not expect “equal chances” to apply. Some genes mutate at a higher rate than other genes.

I suspect that your miscommunication with Joshua has more to do with “pattern” than with “random”. You are thinking of a sequence of random events, and not expecting a pattern in the particular sequence of events. And I think Joshua was looking at the overall distributing, and that was where he was suggesting there could be a pattern to the randomness.


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:

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).

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.


By the way @Perry_Marshall , I was promoted to tenure and am now an Associate Professor. Do you mind fixing that in your article?

My ideas about randomness are included in almost every paper I published that got me to tenure. Actually the are not “my” ideas. They are just the basics of probability theory and probabilistic modeling.


4 posts were split to a new topic: Mark’s Thoughts on the Forum

I got my description of you on your website:

I fixed it on my blog post.

Please define precisely what you mean by random when you say evolutionary mutations are random.

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What’s an evolutionary mutation? Did Joshua really use that term?


No harm done. Thanks for finding the error on my website too. July 1 is when the promotion happened.

I think there are some typos in the quote you pulled. Can we fixed those and remove the capital case? I did not know it would attract your attention.

Do you concede now that there are patterns in randomness? In fact, even intelligent choices are modeled as random variables. If you wrote incredulously:

@nwrickert and I presented several examples where EE’s actually do describe randomness has patterns. I showed you also how even a gaussian random variable has a pattern, a gaussian distribution. I even pointed to an excellent article on how randomness has patterns. Did you catch this quote?

Although real systems look noisy there’s usually an underlying structure
Noise Functions and Map Generation

Randomness always has a pattern we can predict (the order, the structure, the constraints, the explained details) and part we cannot (the entropy, or unexplained details). There is not a single type of randomness I know of that does not have structure of some sort. Even MAXENT must be defined across a domain. In probability, statistics, and information theory I cannot think of a single example of randomness with zero structure or order.

Let’s start with hashing that out first before moving on. It seems that you may be unfamilar with how those of us in statistics use the term “random”, though you seem to have even missed the examples of ordered randomness in EE. It is certainly not an oxymoron, it is more like a ying-yang.

Once we settle that charge, we get to your next question. However, I do not know what you mean by:

What are evolutionary mutations?


My reply:

@Perry_Marshall my friend, that was an interesting blog post. I’m not planning to respond to it till you ask your questions here and engage. I just wrote a post to you. Please answer it here, or at least quote the key portions of your blog post here

Let’s sort it out here before make another post. What do you think? Look, if you really must do it this way, please at least explain why?

I looked at your interesting blog post. And I agree with parts of it. But, as Joshua said, it would be better if you bring that argument here.

I agree with what you describe Shapiro as saying, with one exception. I do not agree with “No sir. They’re not random at all.” Shapiro may have said that, but he is mistaken. His reasoning shows that the mutations do not follow a uniform distribution. But it does not show that they are not random.

You say “Everything I had ever seen was the result of some intentional process.” I agree with that. Biologists try hard to avoid mentioning “intention”. I understand why they do that, but I think it is a mistake. In any case, they fail. When they say that mutations are copying errors, they are implicitly asserting an intention to copy.

The theory of evolution, as understood by biologists, is a pretty good theory. It works well to guide the research. But it is a failure at marketing.

If you can bring some of your arguments here, I’ll try to engage with you in discussion of them.



You make frequent public statements about the Extended Synthesis (and on occasion, my work as well). Our discussions will likewise be in public - in full view of everyone. I need you to define “randomness” so I can understand exactly what you mean by a statement such as: “The mutations do appear to be ENTIRELY spontaneous. The fact they take place in a largely constant rate does not make them less random.” Please explain precisely what you mean by this.

@nwrickert :

You need to provide rigorous support for your assertion that said mutations are random. Shapiro provides abundant empirical support for all his assertions. I ask that you read Shapiro’s book before you continue to critique it.


I do make those statements. I’ve also found that @sygarte and I are largely on the same page about this. Though we do cross the same circles enough it would be great to sort this out. I’ve tried in person on this exact point, but it did not seem to make sense to you. Doing this on the forum could make progress.

This forum is public. I’m inviting you quote the key parts of your article here, and hash it out with me.

@nwrickert, I’d request also that you let me hash this one out with @Perry_Marshall alone first, before you jump in. It has to be a bit challenging to get critique from multiple angles, but the two of us need to clarify some points first. When we are done, certainly jump in at that point. Sound good?

I am happy to explain this, but you need to answer my last post here first, perhaps by quoting relevant sections of your blog response (or the whole thing if you like) here on this forum. We can hash it out here, then post on your blog what we came to.

Note, you still have not answered:

I really feel like this conversation could do loads of good lots of laypeople. I personally only feel like metaphysically naturalistic evolution is the only type of evolution that would truly be random in a sense that is problematic for Christianity. If neo-darwinism is true and mutations take place regardless of their benefit to the organism, this seems to cause no real problems for the Christian because God could still orchestrate the process to achieve His desired ends through either front loading at the big bang and/or origin of life or by periodically supernaturally directing the process (perhaps even through quantum events).

Yet I find this response just doesn’t do it for most Christians. Stephen Meyer will just go back to his “how can God direct a directionless process” line. Many Christians would follow. I think they’re dead wrong and Meyer’s repeated line strikes me as pretty silly. But most Christians hate the “random” word.

Yet if mutations aren’t even random in a scientific sense, then not only would evolution be metaphysically compatible with Christian theism, it would have science to back up the idea that mutations aren’t random! Christians could have something more tangible to grab onto than metaphysical jargon.

Nevertheless, even if Swamidass is correct, this understanding of randomness is far more at-home in Christian theology than is Dawkins’ “happy accident” theology (and it is theology).

So please keep at it you two. Other than the Adam question, and the death before the fall question, I feel like this one is the third biggest issue for Christians.

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Neo-Darwinism is not true: see The Neutral Theory of Evolution. Nonetheless the point bears repeating there is no claim of metaphysical, ontological, or epicurean randomness in science. Period. To say otherwise is to miss just the basic facts about the limits of science and statistics.

Yes I agree!

I’m hoping @Perry_Marshall will return. I’m still not sure why he started the conversation then left. Do you know why?

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I suspect he’s a busy guy! Evo2.0 is only one thing out of many that he does. :slight_smile:

Oh my, it appears that discourse decided @Perry_Marshall was spam for some reason, and silenced him. That might be why he did not respond. I just fixed that and unhid his posts. It appears that posting too many links to his own site triggered a spam flag?

I’m sorry about not catching that sooner @Perry_Marshall. We should be able to move forward now. Looking forward to your response.


I delayed responding to this, as requested by @swamidass

It is unclear what you are expecting when you ask for “rigorous support”. I am just using “random” in the ordinary way.

Think of a Las Vegas casino. They have roulette wheels that they spin for a random outcome. If they were to spin those roulette wheels twice as often, they would still produce random outcomes. What you quoted from Shapiro was about the rate of mutation. Changing the rate of mutation is like spinning the roulette wheel twice as often. The rate of producing random outcomes will increase, but they are still random outcomes.

I did not question any of his empirical assertions. I only questioned his characterization of them.

I have read Shapiro’s book, though it was a while ago. My main disagreement was that he tended to overstate his conclusions. I agree with Shapiro view, that there is intelligence in the cell.

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43 posts were split to a new topic: What are “Mutations”?