Criticism of Darwinism in Mathematics

Darwin's theory of evolution is essentially based on a mathematically describable algorithm which uses a random trial and error process to produce complex organisms. Some prominent mathematicians have argued that the observed complexity of life cannot have been achieved by chance.

What does generating new forms of life mean? Most biologists agree that it would entail generating a new protein. Genes are segments of DNA that spell out the links of a protein chain. DNA has the shape of a spiral staircase.

A section of DNA
A section of DNA

Mutations occur when DNA splits in half down the center of the staircase. Each half-staircase attracts a matching set of molecules (nucleotides) from the surrounding chemical soup and two complete new DNA molecules emerge. A random mistake in this replication process yields a mutation, and if it occurs in a so-called germ cell, it can be passed on to the next generation.

In 1967 Victor Weisskopf, the former Group Leader of the Theoretical Division of the Manhattan Project, organized a picnic lunch at his house in Geneva. "A rather weird discussion" took place between mathematicians Weisskopf, Schützenberger, Ulam and Eden, and the biologists Kaplan and Koprowski. The subject was evolution by natural selection. The mathematicians were highly skeptical of the optimism of the evolutionists about what could be achieved by chance.

After heated debates it was proposed that a symposium be arranged to consider the points of dispute more systematically. The symposium was held in 1966 at the Wistar Institute in Philadelphia. It was called Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution and its proceedings were published under the same title in 1967 (Wistar Institute Press, 1967, No. 5).

The general consensus among mathematicians at the symposium was that Darwinism was simply not mathematically tenable. "It seems to require many thousands, perhaps millions, of successive mutations to produce even the easiest complexity we see in life now. It appears... that no matter how large the probability of a single mutation is, should it be even as great as one-half, you would get this probability raised to a millionth power, which is so very close to zero that the chances of such a chain seem to be practically non-existent." (S. Ulam, "How to Formulate Mathematically Problems of Rate of Evolution").

The author of this quote, Stanislaw Ulam participated in the Manhattan Project and is known as the inventor of the Teller-Ulam design of thermonuclear weapons. Ulam also originated the Monte Carlo method of computation, and suggested nuclear pulse propulsion.

The first test of the Teller–Ulam design (a staged fusion bomb)
The first test of the Teller–Ulam design (a staged fusion bomb)

A protein molecule is a chain of around 150 links. Each link consists of one of 20 amino acids. There are thus 20150 (~ 10195) possible amino acid sequences of length 150, but less than 1012 actual proteins are believed to exist. Amino acids cannot be grouped at random, only certain combinations will form themselves into stable proteins.

The chance of assembling a single stable protein from amino acids at random is estimated at 1 in 1074. The total number of organisms that have ever lived on Earth is estimated only at 1040, and this number is dominated by bacteria. Most bacteria pass on their genetic information unmutated, but even if we assume each one of them yielded one mutation, the chance of randomly achieving the complexity of any single existing protein is 1 in 1034, which is infinitely smaller, than, for instance, the chance of winning the jackpot in a nationwide lottery (1 in 108).

Similar numbers arise in the analysis of natural language. Murray Eden of MIT, another participant of the Wistar Symposium, was also concerned with the element of randomness, which supposedly provides the mutational variation upon which evolution depends: "No currently existing formal language can tolerate random changes in the symbol sequences which express its sentences. Meaning is almost invariably destroyed".

For instance, there are 27150 (~ 10214) possible sequences of English letters (with spaces) of length 150. It can be shown that of these only around 10125 entirely consist of valid English words. Thus the chance of generating a valid sequence is 1 in 1089.

Genes that are obviously variable within natural populations seem to affect only minor aspects of form and function, while those genes that govern major changes, apparently do not vary or vary only to the detriment of the organism.

The German geneticists Christiane Nüsslein-Volhard and Eric Wieschaus won the Nobel Prize in 1995 for the "Heidelberg screen," an exhaustive investigation of mutations of Drosophila. "We think we've hit all the genes required to specify the body plan of Drosophila," said Wieschaus in answering a question after a talk. "Not one promising as raw materials for macroevolution", because mutations in them all killed off the fly long before it could mate.

A large number of mutations occurring at once is guaranteed to be deadly, because, as has been shown, the chances of accidentally producing a viable result in such case are infinitely small.

Starting from a valid sequence and introducing only a few minor changes during a lifetime would not kill an organism, but then the number of lifetimes needed to progress from the simplest to the most complex organisms would be infinitely larger than the total time life has existed on Earth. The total number of organisms required (given that most mutations do not produce useful results) would by far exceed the estimated total number of organisms that have ever lived.

Common examples of observable "evolution" in humans—the ability to digest lactose (useful when milk becomes available) and easy accumulation of body fat (to better handle periods without food, but leading to obesity when food is always available) are based on (complexes of) genes already present in a population, rather than appearing as a result of mutations. The number of individuals with such genes can indeed grow or shrink depending on how useful or harmful they are in a particular situation (simply because this affects the probability of reaching adulthood and having offspring).