The Meaning of "Random"

I’m noticing that the word “random” seems to often be a hangup in discussions here. So I want to say a little about randomness that I hope might clear the air.

I’m an agnostic

Let’s first clear the air about my agnosticism. I’m going to be talking about God, so you need to know that I am agnostic. It’s not just that I say I don’t know whether there’s a god. It is more that I doubt the possibility of knowing that there’s a god. So when I comment on whether God could use randomness, best to understand that have no commitments to there being a god.


I’ll start with two examples of randomness.

Example 1: the lottery

We mostly know about lotteries. You buy a lottery ticket. And it is a matter of luck as to whether you win.

Would God use a lottery? As an agnostic, I don’t have a say on this. However, it does seem unlikely that the Abrahamic God would use a lottery. And this seems to be one of the objections that some folk have to evolution. They see “random” cropping up in discussions of evolution, and they worry that this implies that their God is depending on a lottery-like use of randomness. Einstein’s famous “God does not play dice” about QM was a similar reaction. As far as I know, Einstein was atheist or agnostic.

Example 2: baking a cake

You want to bake a cake. So you put the ingredients in a bowl. And then you stir them up.

Stirring up that cake batter is a process of randomization.

This is very different from the lottery example. When you play the lottery, you hope for a lucky but unlikely result. When you stir up the cake batter, your aim is that it turn out to be rather even and uniform. You are not looking for a lucky outcome. Stirring (i.e. randomization) is just a good way of getting a pretty uniform batter and a good cake.

If God were baking a cake, would God stir up the batter? Or would God micromanage where every molecule goes? Or would God come up with a special supernatural form of stirring, so that He could just stir up the batter in such a way that He could then micromanage where every molecule goes?

As an agnostic, I don’t know. But I think I prefer the kind of God that would just stir up the batter, and not attempt to micromanage at the molecular level.

Randomness in evolution

So how is randomness used in evolution? Is it more like the lottery idea? Or is it like the cake batter example? Or is it somewhere in between?

People disagree about this. The neutral theory seems to be closer to the lottery example. My own view of evolution is closer to the cake batter example.

I try to look at it from the vantage point of a population (of organisms). The population depends on a particular ecological niche. And the risk for the population is that the environment is always changing. And it could change in a way that eliminates the niche being used by the population.

The “intelligent” thing for the population to do, would be to prepare for the possibility that the environment will change. One way of doing this, is to have some variation within the genetics of the population, so that at least some part of that population might survive the environmental change. We normally think of the variation as arising from mutations. But the population cannot guess the future. So it cannot guess what particular mutation would work. So the best that it can do is “mix it up” and have mutations favoring many possible directions. And then see which work better as the environment changes. So that’s a use of randomness that seems like stirring the cake batter.

We also see meiosis, and crossovers that occur during meiosis. That’s a kind of randomization that results from sexual reproduction. And it is really a mixing up of variation already existing in the population.

Additionally, we see transpositions. A piece of DNA is transposed to a different part of the genome. Perhaps what was previously junk DNA is transposed to where it might become active. And the junk DNA may have originated as a DNA segment that was once useful in the past history of this population. So there’s an apparent stirring up of memories of formerly useful DNA segments.


The critics of evolution see random as bad, something like luck or something like noise. But the use of randomness can also be intelligent, as in when we stir the cake batter.

My hope is that this post, and subsequent discussion, will help people broaden their ideas about how randomness is used in evolution.


Your description fits quite nicely to my own thoughts on the subject.

If mutations were directly tied to systems that created specific mutations in response to specific challenges then a population would be severely limited in how it could respond to a changing environment. Mixing things up allows for surprise discoveries. I think it could be argued that a species using random mutations could outcompete a species with non-random mutations because the randomly changing species could find more solutions to the same problem.

We could even use human ingenuity as an example. When we arrive at a new problem we often come up with new ideas. If we were limited to the solutions given to us in a book written by our ancestors we may not solve all of the problems we face. Flexibility is often preferred over rigid adherence to a set of rules.


It seem some people are trying to claim that ergodic processes are not random processes. I can’t make any sense of this because ergodic processes are just one type of random, and in fact they are the usual type of randomness to which we refer. Every random variable obeys some distribution and said distribution is the pattern of the random variable. This is even true for MaxEnt distributions. What are they getting at that I am missing?

[note: edited to be more precise]


I think they are just confused.

But perhaps the way we (society in general) talk about randomness is what leads to confusion. I guess we need to work harder to help people come to a clearer understanding.


I’m not sure that is it.

Even providentialists (@jongarvey and @rcohlers) and determinists will exclaim at some fortuitous coincidence, “that is so random!” Then interpret this as God’s work because it is random.

In common usage, random means unexplained and unpredictable from a given frame of reference. In modeling, random is the part of the system we cannot or do not fully predict or explain. Both uses are essentially equivalent.

It can apply to the actions of intelligent agents such as other humans, to events that might be entirely deterministic from a different frame of reference, things that might even be feasibly predictable just remain outside out scope of inquiry, or outside our view. Effective modeling is much like effective storytelling. The best of both are economical the details they include so as to reveal the the systematic interrelations between otherwise randomly correlated entities. The entities outside the story are random introducing plot twists and error into our otherwise pristine platonic starting points.

So I am not at all convinced that we use the word random differently. It seems rather as though it is a very selective opposition to the term.

What do you think @mark and @nwrickert?

We see people using “random” where “arbitrary” would be a better term.
We see people using “random” as implying unintelligent.
We see pastors saying that hurricane Florence was an action by God because of some probably bogus purpose.

The public see very mixed messages.


Well said Neil, I think much along the same lines. Whenever someone comes up with a proof for something that ought not to be provable, I’m fairly certain they haven’t actually proven anything. OTOH, I believe faith can have value independently of what I consider to be proof (there is undeniable evidence this is so.).

More Thoughts on Meaning of Randomness
To many people randomness seems to be interchangeable with chaos and unpredictability, but this is not always the case. Most people are familiar with the basic concept of “The Law of Averages”, but are unaware of the implications and just how strongly this law applies. More formally, the Law of Large Numbers describes how the sum of small variations add up to something much more predictable than the original randomness. Random processes often converge to a simplers system, such as the very well known Normal distribution. My entire profession is based on this and similar laws of convergence.

Sometimes I tell people, doing my best imitation of Jedi Master Yoda:

“For my ally is the Law of Large Numbers, and a powerful ally it is. Randomness creates it, makes is converge. It’s presence surrounds us and guides us. Random beings we are, not this crude determinism”.

OK, I don’t really say that, but sometimes I want to. :slight_smile:

Example: Evolution of the eye
The eye is thought to have evolved independently at least 40 times (or is it 70?). This is often given as an argument from incredulity; ie: “How could something so fantastically impossible happen 40 times!”
The thing is, when some event happens more than once, that ought to be taken as evidence the event is somehow MORE common instead of less common. In evolutionary terms the ability to detect and interpret light (act of the detection) is clearly a strong survival advantage. It should not be surprising to find different branches of life “converging” towards developing some form of eye.


Thanks, Dan. We pretty much agree.

On the eye – I actually think of the eye as a rather crude organ. It basically uses a bag of water for focusing. Compare that to the lenses in modern cameras. What makes vision work very well is mostly the visual cortex of the brain, which manages to work around the crudeness of the eye itself.

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The key here is that important phrase “a given frame of reference.” “randomness” is entirely epistemological. It means no more than a causal pattern we have not yet found.


Exactly. Or even a “causal pattern we know about, but for convenience are ignoring for the moment.”.

There is just no sensible reason to object to it. Nor is their reason to selectively challenge its use in science, while using in all these other places. The bigger question for me, given the immense precedence for the term in other domains that does not create conflict, why is it such a stumbling block here in evolution? I can’t give a good account of why people are so tweaked out by it here, and not elsewhere. It almost appears like indoctrination of conflict…?


Now that is an example of a “bad design” argument, and is not very plausible. It is value-laden, subjective, and ungrounded.

Also, bonus points to you for being up front about where you stand @nwrickert. That is really helpful for people.

That is a question I find myself asking. The only answer I can come up with is the importance people assign to different things. For example, the random scattering of light in gas clouds doesn’t concern them that much. However, the natural history of life and humans in particular have much more significance to us humans, so they must think that God is much more involved in these processes than in others. I get the impression that “random” is stuff that God just lets happen without really caring about the outcome. Since God would really care about how life evolved and how humans came about then that process would not be random.

Or I could be reading way too much into what people write. That is entirely possible as well.

Because “Monod”?

You are going to have to educate the poor scientists here. I have no idea what that is. At the moment, I’d rather declare my ignorance than untangle the puzzle on a Google hunt for wild geese.

Tell it not in Gath! What do scientists read?

Jacques Monod (biochemist) Chance and Necessity (1971). Much cited.

His take on "chance?

“The first scientific postulate is the objectivity of nature: nature does not have any intention or goal.”

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It wasn’t an argument. It was an opinion. I don’t do “bad design” arguments. People often joke around about what they see as bad design issues in the human body, but they make for poor arguments.

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I don’t know if we are just using a different language, but for physicists and mathematicians, ergodic and random are indeed distinct.

Ergodic systems satisfy the ergodic theorem, which by itself is a consequence of the postulate that the system evolves by operators that are ergodic transformations. Ergodicity is a property of the dynamical system, which can be either deterministic or random. Even deterministic systems can be classified as ergodic if they evolutions are not ergodic transformations.


I think Neil meant crude as in simple rather than bad. A bag of water is pretty simple and it gets the job done…


Yes, precisely. And it is easily within the range of what could feasibly evolve.

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