Eric Holloway at Mind Matters summarizes very well:
In 1966, an unusual symposium was hosted at the Wistar Institute of Anatomy and Biology at the University of Pennsylvania. The topic of the symposium was “Mathematical Challenges to the Neo-Darwinian Theory of Evolution” where mathematicians and engineers presented what they saw as fundamental problems with the theory of evolution. One of the mathematicians, Marcel-Paul Schützenberger (1920–1996, pictured) worked closely with Noam Chomsky (1928–) on the intersection between linguistics and computer science.
Schützenberger’s fundamental objection to many claims about evolution is that DNA, as modified by mutations, produces a very simple kind of language. On the other hand, the organisms and the environment they live within is a very complex domain with very far-ranging interactions. It seemed implausible to Schützenberger that such a simple structure could match the complexities of the real world to the extent that evolution based on natural selection acting on purely random mutation could produce highly complex new organisms.
Think of the word ladder game, where we transform one word into another by changing only one letter at a time. The rule is, each time we change a letter, the new sequence must itself be a valid word. As an example, here is a word ladder that takes us from the word CAT to the word DOG.
Changing a three-letter word to another three-letter word is easy. But transforming longer words rapidly becomes more difficult until it becomes impossible. For example, there is no such transformation possible from the word TRANSMUTATION to the word PERAMBULATION.
And that was Schutzenberger’s point with respect to evolution. There is no ladder that randomness can reach. Yet evolution, as described in approved textbooks, is more like turning TRANSMUTATION into PERAMBULATION than it is like turning CAT into DOG.
So, to justify the theory of evolution, biologists must explain the pathway from the simplest organism to the highly complex organisms of today.
It is not a scientific argument to merely assume that such a transformation is possible, especially when we can see with our example from the word ladder game how quickly a transition becomes impossible merely by changing one word into another. That is many orders of magnitude (a great understatement!) simpler than transforming one DNA sequence into another.
Schützenberger offered the example of computer programs, which are extremely brittle and even more difficult than transforming English words. A single character out of place will render an entire computer program invalid and inoperable. His question is simple: What is it about DNA and evolution that makes the process so much more productive and robust than mutating computer programs or human languages? It is even more mysterious if this process makes the modifications “randomly,” in other words without any information regarding the environment nor what would benefit the organism. As we know, the debate rages today as to whether the way evolution is supposed to have happened is even possible.
Schützenberger is remembered for many reasons, one being that he was a teacher and inspiration to mathematician David Berlinski. In his book Human Nature, Berlinski offers a beautiful detail about his mentor. Berlinski lives in the shadow of the Notre-Dame in Paris and poignantly remembers the cathedral before it burned. He would habitually enter “and light a candle for M.-P. Schützenberger. He had wished to return as one of the gargoyles, and, perhaps, he had.”