Falter: Every Birth is a Statistical Impossibility

Greetings and salutations, Jon -

Hmm, I cannot imagine how a bacterium in a flask maintained under standard conditions would be able to influence which nucleotides in its DNA would be mutated. Can you?

I suspect stochastic factors would have far more influence, if not 100% influence. The factors I have in mind would be the random position of interfering ions, chemical instability of purine and pyrimidine bases, the deamination of cytosine to uracil, and the like. I do not understand how an E.Coli would have agency over such factors. As molecules, atoms, and particles are interacting, the complexity is such that (I would think) predictions of interactions based on momentum and energy of the enormous number of particles would eventually require a resolution finer than Planck units. And once we reach the Planck scale we are in quantum mechanics territory.

Does this make sense?

Most assuredly. However, I am not sure whether this is due to foreknowledge or due to hidden agency. Or both.

Chris, I don’t pretend to know enough about how organisms manage their genomes to say, and I don’t think anyone else does either. The studies that Jim Shapiro referenced in his 2011 book in support of “natural genetic engineering,” however, were mainly about bacteria, so if it occurs it is not restricted to more “advanced” life. It is certainly true, however, that the reason all biological experiments lack the precision of experiments in physics is that organisms always react in more compex ways than do molecules.

On the other hand, since I read R J Russell in 2012 I’ve been keeping an eye on the literature for evidence that quantum events actually can bias mutations to alter the macro world. So far, the consensus appears to be that they cannot, and that quantum indeterminacy, whatever determines that, really does disappear into the larger scale processes of the macro world. The consensus may be wrong, but since it would radically change how quantum mechanics affects the world, it needs to be demonstrated rather than assumed.

If that is the case, then the mutations in Lenski’s bacteria would be due to bog-standard Maxwellian statistical randomness, that is, determined by the usual physical forces, and only random with respect to our ignorance. I’m unaware, outside of quantum events, of any evidence that natural laws vary to create physical indeterminsm. Are you?

That leaves the question of divine foreknowledge or agency exactly as it was before, only (as I’ve often reminded people) Maxwell himself was in no doubt, regarding statistical mechanics, that it did not lessen divine providence:

Would it not be more profound and feasible to determine the general constraints within which the deity must act than to track each event the divine will enacts?

Of course, if one wants to explain why a particular mutation happens, one would have to track the individual events, but it would leave as a matter of worldview choice whether the events were enacted by God, or by some as yet undiscovered force called “chance.”

But always remember that probability distributions are only and always measures of our ignorance (in the form of abstractions), and never causes of anything in the real world.


I think this is entirely correct.


Physical chemists look at the boundary between quantum mechanics and classical mechanics all the time. We’ll often model things classically, quantum mechanical, and usually some hybrid, and then see which matches the real data. I don’t know the details for mutations, but I’d be surprised if there was much for quantum effects coming from indeterminacy.


I’m not so sure about this. What are we ignorant of? Are you just saying that we are ignorant as to why a particular trial gave a particular value? I guess that makes sense, but a probability distribution doesn’t seem like “a measure of ignorance”, in fact, to me they seem quite the opposite. It’s a statement of how much we do know.

My colleague next door, who is our probability and statistics professor, would be out of a job if it was just all ignorance. We can describe and use various probability distributions, and even manipulate them, so in what way are they a measure of ignorance?

Your colleague next door, would be a very wealthy man if he had any knowledge of next roll of the dice besides the probability of each number coming up. Also note that statistics is always about the past and never knowledge about the future.

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There are a lot of wealthy people who use statistics to predict the future. If we couldn’t predict anything about the future based on probability, what’s the point of actuaries or all these health predictors (cancer risks, etc.). Saying we have incomplete knowledge is different than saying we have no knowledge, and that’s what it sounded like what @swamidass and @jongarvey were saying.

We have a very very hard time getting humans to understand probability and statistics, we need to be careful with how we describe things like probability distributions.

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Quite so. The roll of a dice is a nice example, in that in the absence of knowledge about the exact dynamics of a particular roll (though that information is, in theory, available) a probability distribution takes those dynamics as unknowable, but on average unbiased, and then makes a mathematical abstraction on the basis of the stability of the dice in only six states.

In practice, if you look at the websites of high-quality dice producers, even the highest quality dice have a slight bias, and of course the throws are never precisely distributed.

If one could measure precisely everything going on a dice throw, the probability of the result would be 1. The probability of 1 in 6 is nothing but a measure of that uncertainty.

And that is why it is useful, because probability produces a degree of predictability in an otherwise unpredictable situation. But that unpredictability is always an ep[istemic situation, not an ontological one (with the possible exception, in physical terms, of quantum phenomena, which we have excluded from the macroscopic situation anyway.)

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Amen - and that’s why to say something like “events governed by a probability distribution” is entirely misleading. Events produce a probability distribution, and a probability distribution has no causal properties, being a deduction from results.

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I agree. The probability distribution may tell you something about the cause of the event.

Can you expand on that Bill? In itself the probability distribution is just numbers, though I guess deductions made from that might give some clues. For example, if the results from some submicroscopic dice show exactly 6 states, smoething of the nature of the hidden system could be deduced.

A simple example would be observing the point plot of 1000 die rolls that is claimed to be simply shaking and rolling die. We would expect an even distribution around all six numbers given simply shaking the die and throwing it. If we instead we saw instead a bell curve with a peak at the number 3 that would tell us that there was more to the process than simply shaking the die and throwing it.

The shape of the curve can either reject or validate the cause of the distribution we are observing being simply shaking and rolling the die.

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OK - though of course such a bias would require us to investigate whether the problem was in the dice, in the rolling, or both (or in our counting, I suppose).

I agree

Agree that it is one of humans greatest accomplishment to understand probability and statistics. A very good book on how we did it is here:

A better book on what we actually discovered is:

Uncertainty - William Briggs

Hi Jon,

My point is that quantum events are not the only form of indeterminancy. Physicists have identified 3 regimes: classical, chaotic, and quantum. And it is entirely possible that the occurrence of mutations belongs, in part or in whole, to the chaos regime. If so, this would imply that your binary view of the possibilities (biological events are in theory 100.0% predictable with sufficient data and models vs. quantum indeterminancy) is too reductionist.

I read a couple of articles for background on the chaos regime and its relationships to the others that seemed helpful. I share links below.

Being neither a biologist nor a physicist, I have no idea of any work being done at the intersection of biology and physics that would classify the physics regime of DNA transcription. I would love to learn more from anyone who knows the literature.

Links to popular articles on the 3 physics regimes:

EDIT: The impression I have is that it is a faith claim to believe that the chaos regime must eventually reduce to either the classical or the quantum regime in the presence of sufficient data.

I do know that John Polkinghorne is said to have backed off from chaos as an alternative “guidance” mechanism to quatum uncertainty, probably because most physicists believe chaos is classical.

The problem of chaotic uncertainty is that, because miniscule inaccuracies of human observation are magnified, we are radically unable to predict their outcomes. That’s why they tend to be modelled and statistical evaluations made of the aggregate results. Such observational limitations, though, are again epistemic rather than ontological - they would not apply either to God or some demon with powers of exact measurement.

One really interesting facet of that (to me anyway) as regards both divine and human interaction with the world, is how many natural systems are operating on the edge of chaos. In effect, this makes them relatively easy to change, whilst being stable within limits. One classic example of that is the solar system. Another is the weather.

As far as I can tell, Jon, this is a faith statement that physicists might not agree with.

But again, I am neither a physicist nor a biologist. I have studiously followed the Bard’s maxim, “Neither a physicist nor a biologist be.” :wink:

This is a very good point. Thanks for sharing it.

According to a paper I found on DNA polymerase from E. coli, there is a loose fit between the incoming nucleotide and the active site of the enzyme. This is responsible for a large chunk of the substitution mutations:

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