Chance and certainty

In a comment to the Spanish version of a previous post of mine, JL advised me to read the book entitled Chance and Certainty, by Georges Salet, who wrote it to prove that the origin of life and its subsequent evolution are impossible, if we apply the calculus of probabilities. In addition, he challenged me to refute at least one of the arguments proposed by the book, in the following words:

The work contains hundreds of arguments and demonstrations; if you, or anyone else whose help you ask, are able to refute a single argument or demonstration, I will readily admit that life can indeed arise spontaneously.

Salet's book is out of print and very hard to come by. I am grateful to another comment contributor, who provided me with the opportunity to read this book. I can therefore accept JL's challenge.

In its Spanish edition, the book has over 500 pages. The first six chapters are an introduction, explaining some of the procedures on which the rest of the book will be based. The first argument proper appears in Chapter 7, on page 158. It pretends to calculate the probability that a mutation occurs, and I needed not go any further to find a wrong proof, so I have adequately answered the challenge. Also, the probability of a mutation occurring is the starting point for what comes next in the book, so if that calculation is wrong, the book fails. Let's see why it is wrong:

The book calls P_ij the probability that, during reproduction, a mutation occurs that changes the genome of a living being from genetic state i to genetic state j. Salet states that the probability of this happening in n generations is the following:

P_ijn = P_ijⁿ

From this he deduces that, if the mutation probability P_ij is small and n is large, the probability that the mutation occurs in n generations tends to zero.

This calculation is grossly wrong. Applying the elementary calculus of probabilities, it can be seen that the correct value of the probability P_ijn that the change between the two states will take place with a single mutation during n generations, is the following:

where P_ii and P_jj are the probabilities that there is no mutation, so that in that generation the living being will go from state i to state i, or from state j to state j). If all the probabilities of mutation P_ij are small, the probabilities that there is no mutation, P_ii and P_jj, would be close to 1. If we assume that they are equal to 1, we can approximate P_ijn as follows:

P_ijn = n.P_ij

Now, what happens with this value when P_ij is small and n is large? As n grows, P_ijn also grows, so for very large n, even if P_ij is small, its value tends to 1. In other words, the conclusion is just the opposite of that drawn by Salet in his book. As the number of generations increases, the probability that a particular mutation will occur becomes almost certain, rather than getting lower and close to 0.

This can also be seen by thinking a bit about the matter. The probability that a mutation occurs during n generations is equal to the sum of the probabilities that the mutation takes place in the first generation, plus the probability that it does not happen in the first, but it does occur in the second, plus the probability that it does not occur in the first two, but it does happen in the third, and so on, plus the probability that it does not takes place in the first n-1 generations, but it does occur in the last (in generation n). It cannot be, therefore, much lower than P_ij, as Salet says, but on the contrary much greater, if n is large.

In fact, the probability must be even higher, since in this calculation we have ignored those cases where we go from state i to state j through other intermediate states, i.e. through more than one mutation. But what I have said is enough to see that Salet's calculations are worthless.

In Annex 2 (page 385 of the Spanish edition) Salet tries to give a proof of the formula that he gave on page 158. This proof is incorrect, because first he builds the matrix of probabilities of mutations between different states, and then he argues that the probability that mutations occur once in n generations is obtained by multiplying the matrix by itself n times. That is, he makes the same mistake in the proof that he made in the summary formula, and he doesn't realize it.

My conclusion is that the book has no scientific value, because it contains flagrant errors. The probability of mutations taking place is much higher than Salet claims, and consequently, it is not true that evolution is outside the scope of chance. It is a mistake similar (but not the same) to that made by Lecomte de Noüy some forty years before Salet. Incidentally, Salet quotes Lecomte favorably, showing that he has been influenced by him.

Consequently, I reaffirm what I said in this other blog post:

Intelligent design or random evolution. In my opinion, this is not a scientific problem. The dilemma on whether God exists or not, on the creation of the universe by an intelligent being or its spontaneous appearance (starting from what?) is a metaphysical question that science will never solve.

And I say this, despite the fact that I believe in God and his Providence, as I have made clear in other posts. But I reject the use of spurious, supposedly scientific arguments to prove it, in the same way as I’m also against atheists doing the same.

The same post in Spanish

Thematic Thread on Evolution: Previous Next

Manuel Alfonseca