On the probability of evolution

 In the following post, I won’t try to calculate specific values but rather to explicate my own Knowledge-dependent frequentist probabilities by using particular examples.


I strongly encourage every reader new to this topic to first read my groundwork (Click here).

The great evolutionary biologist Stephen Jay Gould was famous for his view that Evolution follows utterly unpredictable paths so that the emergence of any species can be viewed as a “cosmic accident”.



Stephen Jay Gould

He wrote:

We are glorious accidents of an unpredictable process with no drive to complexity, not the expected results of evolutionary principles that yearn to produce a creature capable of understanding the mode of its own necessary construction.
“We are here because one odd group of fishes had a peculiar fin anatomy that could transform into legs for terrestrial creatures; because the earth never froze entirely during an ice age; because a small and tenuous species, arising in Africa a quarter of a million years ago, has managed, so far, to survive by hook and by crook. We may yearn for a ‘higher answer’– but none exists”

“Homo sapiens [are] a tiny twig on an improbable branch of a contingent limb on a fortunate tree.”


Dr. Stephen Jay Gould, the late Harvard paleontologist, crystallized the question in his book ”Wonderful Life.” What would happen, he asked, if the tape of the history of life were rewound and replayed? For many, including Dr. Gould, the answer was clear. He wrote that ”any replay of the tape would lead evolution down a pathway radically different from the road actually taken.”


You’re welcome to complement my list by adding other quotations. 🙂


Evolution of man


So, according to Stephen Jay Gould, the probability that human life would have evolved on our planet was extremely low, because countless other outcomes would have been possible as well.

Here, I’m interested to know what this probability p(Homo) means ontologically.

Bayesian interpretation

Image Of Thomas Bayes



For a Bayesian, p(Homo) means the degree of belief we should have that a young planet having exactly the same features as ours back then would harbor a complex evolution leading to our species.

Many Bayesians like to model their degrees of belief in terms of betting amount, but in that situation this seems rather awkward since none of them would still be alive when the outcome of the wager will be known.


Traditional frequentism


Let us consider (for the sake of the argument) an infinite space which also necessarily contain an infinite number of planets perfectly identical to our earth (according to the law of the large numbers.)

According to traditional frequentism, the probability p(Homo) that a planet identical to our world would produce mankind is given as the ratio of primitive earths having brought about humans divided by the total number of planets identical to ours for a large enough (actually endless) number of samples:

p(Homo)   ≈           f(Homo) = N(Homo) / N(Primitive_Earths).


Knowledge-dependent frequentism


According to my own version of frequentism, the planets considered in the definition of probability do not have to be identical to our earth but to ALL PAST characteristics of our earth we’re aware of.

Let PrimiEarths  be the name of such a planet back then.

The probability of the evolution of human life would be defined as the limit  p'(Homo) of

f'(Homo) = N'(Homo) / N(PrimiEarths‘)

whereby N(PrimiEarths‘)  are all primitive planets in our hypothetical endless universe encompassing all features we are aware of on our own planet back then and N'(Homo) is the number of such planets where human beings evolved.

It is my contention that if this quantity exists (that is the ratio converges to a fixed value whereas the size of the sample is enlarged), all Bayesians would adopt p'(Homo)  as their own degree of belief.


But what if there were no such convergence?  In other words, while one would consider more and more  N(PrimiEarths‘) f'(Homo) would keep fluctuating between 0 and 1 without zooming in to a fixed value.

If that is the case, this means that the phenomenon  “Human life evolving on a planet gathering the features we know” is completely unpredictable and cannot therefore be associated to a Bayesian degree of belief either, which would mean nothing more than a purely subjective psychological state.


Evolution of bird

I want to further illustrate the viability of my probabilistic ontology by considering another evolutionary event, namely the appearance of the first birds.

Let us define D as : “Dinosaurs were the forefathers of all modern birds”, a view which has apparently become mainstream over the last decades.

For a Bayesian, p(D) is the degree of belief about this event every rational agent ought to have.

Since this is an unique event of the past, many Bayesians keep arguing that it can’t be grasped by frequentism and can only be studied if one adopts a Bayesian epistemology.


It is my contention this can be avoided by resorting to my Knowledge-Dependent Frequentism (KDF).

Let us define N(Earths’) the number of planets encompassing all features we are aware of on our modern earth (including, of course, the countless birds crowding out the sky, and the numerous fossils found under the ground).

Let us define N(Dino’) as the number of these planets where all birds originated from dinosaurs.

According to my frequentism, f(D) = N(Dino’) / N(Earths’), and p(D) is the limit of f(D) as the sample is increasingly enlarged.

If p(D) is strong, this means that on most earth-like planets containing birds, the ancestors of birds were gruesome reptilians.

But if p(D) is weak (such as 0.05), it means than among the birds of 100 planets having exactly the known features of our earth, only 5 would descend from the grand dragons of Jurassic Park.


Again, what would occur if p(D) didn’t exist because f(d) doesn’t converge as the sample is increased?

This would mean that given our current knowledge,  bird evolution is an entirely unpredictable phenomenon for which there can be no objective degree of belief every rational agent ought to satisfy.



A physical probability dependent on one’s knowledge


In my whole post, my goal was to argue for an alternative view of probability which can combine both strengths  of traditional Frequentism and Bayesianism.

Like Frequentism, it is a physical or objective view of probability which isn’t defined in terms of the psychological or neurological state of the agent.

But like Bayesianism, it takes into account the fact that the knowledge of a real agent is always limited and include it into the definition of the probability.


To my mind, Knowledge-Dependent Frequentism (KDF) seems promising in that it allows one to handle the probabilities of single events while upholding a solid connection to the objectivity of the real world.


In future posts I’ll start out applying this concept to the probabilistic investigations of historical problems, as Dr. Richard Carrier is currently doing.



Thematic list of ALL posts on this blog (regularly updated)

My other blog on Unidentified Aerial Phenomena (UAP)





8 thoughts on “On the probability of evolution

  1. Hello, Marc! Mike Morrell asked me to contact you because he really appreciates your blog and thinks you’d be an excellent candidate for his Speakeasy Blogger Network. Do you like to review off-the-beaten path faith, spirituality, and culture books? Speakeasy puts interesting books in your hands at no charge to you. You only get books when you request them, and it’s free to join. Sign up here, if you’d like: http://thespeakeasy.info

  2. Considering that similar species of animals were able to develop completely separate from one another, chances are that the general path of evolution wouldn’t be all that different under similar conditions. There certainly would be differences, but it’s not a mechanism of randomness, it’s a mechanism of balance.

  3. Hiya Lotharson,

    To some extent you lose me on the mathematical terms used here, but I still think there are currently insuperable issues about the observability of evolutionary processes related to the time-scales involved.

    My own view as a completely untrained and unqualified person, is that the percentage of speculation involved in evolutionary theorising is still too high in comparison to other “scientific” investigations to come to any concrete conclusions. Although, to my mind, there is more than enough evidence to think of a very old Earth and a developing/evolving flora and fauna, trying to come up with dogmatic statements about principal causes and specific paths really ought to be kept in the theoretical camps and kept well away from ideas of “certainty”.

    If both religious and non-religious persons could say that we actually know very little about origins, but have a number of speculative theories, then I think a whole load of pointless argufying could be solved. My Pessimistic Scottish side realises that of course this will not happen for the most vocal of the World’s f***wits, but is probably the position of the “silent majority”.

    Did God create the Universe? well, those of us who believe in revelation will probably say we believe so or yes because, someone powerful enough to do so is probably able to tell us about it. Was it all a cosmic accident, without a directed effort? Well it may well have been so, if there is no prime mover how the hell can we really know. Without the prime mover, then we just have to guess and hope our abilities to investigate are up to getting a fairly accurate answer.

    No-one knows for sure.

    Saying there is definitely no God is unreasonable, because ultimately, absence of evidence is not actually evidence of absence. But statements of God’s existence have to rely on faith, not certainty (though I’m sure that could be argued about for many millennia).

    Ultimately, what has this to do with the price of fish? I believe in God but cannot prove he exists to someone who doesn’t. Those who say there is no God cannot disprove him to me. That is really a bit of an impasse. Getting back to the price of fish, I think it is all a bit of a Red Herring and I don’t know how much they cost anyway. There may actually be more important things to think about and talk about. We may or may not have “evolved”, but whether I am happy or unhappy is actually a lot more important. Whether someone down the road needs help or wants to celebrate the birth of their child is more important.

    Speculating about origins is not bad, wicked or pointless, but really it needs to be seen in perspective. For most people it really isn’t much of an issue and never has been. If it is an issue, then why is it an issue? I’d suggest that looking at the why it is important, is more important than where we came from.

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