Probabilities, Monkeys, and Natural Selection

(Originally published in Creation Matters, Vol. 5, No. 1, January/February, 2000, and updated since then.)

One of the biggest challenges for creationists has been to clearly illustrate the absurdity that passes off as probability  arguments in the naturalistic/evolutionary model of origins. The old adage keeps popping up anew: “Given so much time the ‘impossible’ becomes possible, the possible probable, and the probable virtually certain. One has only to wait: time itself performs miracles.”1 The reality is that the impossible is still impossible, even with the magic elixir of huge spans of time.

On June 30, 1860, at the Oxford Union in England, Anglican Archbishop of Oxford University, Samuel Wilberforce, and evolutionist and agnostic Thomas Huxley were engaged in the “Great Debate.” Bishop Wilberforce, a Professor of Theology and Mathematics at Oxford University, argued that the design we see in nature required a Designer. Therefore, the information found in living systems (an evidence for design) could not arise by random chance. Huxley, on the other hand, declared that given enough time all the possible combinations of matter, including those necessary to produce a man, will eventually occur by chance molecular movement.

Typing monkeys

To prove his point, Huxley asked Wilberforce to allow him the service of six monkeys that would live forever, six typewriters that would never wear out, and an unlimited supply of paper and ink.

“It was, I think, Huxley, who said that six monkeys, set to strum unintelligently on typewriters for millions of millions of years, would be bound in time to write all the books in the British Museum.  If we examined the last page which a particular monkey had typed, and found that it had chanced, in its blind strumming, to type a Shakespeare sonnet, we should rightly regard the occurrence as a remarkable accident, but if we looked through all the millions of pages the monkeys had turned off in untold millions of years, we might be sure of finding a Shakespeare sonnet somewhere amongst them, the product of the blind play of chance.”2

Since then, creationists have often employed this classic monkey myth to illustrate the probability problems inherent to the naturalistic/evolutionary scenarios. A good example of the evolutionists’ response is given by Hawking. After citing the monkey illustration he comments, “very occasionally by pure chance they will type out one of Shakespeare’s sonnets.”This is absurd. The assertion that the monkeys will not in fact perform this feat is as close as we can get to a scientific fact. ReMine drives this point home:

“The monkeys could not randomly type merely the first 100 characters of Hamlet. If we count only lowercase letters and spaces (27 characters in all), then the probability of typing the 100 characters is one chance in 27 100 (one chance in 1.4×10 143). If each proton in the observable universe were a typing monkey (roughly 10 80 in all), and they typed 500 characters per minute (faster than the fastest secretary), around the clock for 20 billion years, then all the monkeys together could make 5×1096 attempts at the 100 characters. It would require an additional 3×1046 such universes to have an even chance at success. We scientifically conclude that the monkey scenario cannot succeed. For the scientist it would be perverse to insist otherwise.”4

Creationists generally employ illustrations like this to three of the most unlikely naturalistic/evolutionary scenarios: a fine-tuned universeabiogenesis, and biological complexity arising by random mutations. Their opponents may grumblingly take the first two scenarios sitting down. However, the evolutionists will rise to their feet to cry foul in the third instance. Here the mechanism of natural selection is proposed to save the day, supposedly extricating naturalism from the probability mire.

Hence an important modification to the monkey and Shakespeare story is suggested by Ruse. “Suppose, however, that every time the monkey strikes the ‘right’ letter, it records; but, suppose also that ‘wrong’ letters get rubbed out (literally or metaphorically!) And suppose the elimination of the wrong letter is the full consequence of a ‘mistake’: one does not lose what has already been typed.”5 The idea is that natural selection acts as an invisible cosmic teacher, allowing successes, while rubbing out failures.

A bottle of white-out

There are at least three problems with Ruse’s scenario. First, Ruse takes a very naïve view of natural selection. If one follows the analogy, the poetic sensibility and grammatical complexity become “fitness.” On the bottom of the proverbial hill is a random jumble of the various marks capable of being produced by a typewriter. On the relative top of the incline is the sublime prose of Shakespeare. Ruse’s suggestion of a cosmic teacher with Shakespeare’s text and a bottle of white-out implies that natural selection inexorably, step by step marches only in the direction of the optimal design. But the more realistic picture is that of a “fitness terrain,” where words are mounds, sentences are hills and prose is a mountaintop. In between are valleys of misspelled words, canyons of improperly punctuated sentences, and ridges of nonsense sentences. The cosmic teacher only whites out the worst efforts of the monkeys, letting some get “stuck” with a word or two, even though it does not yet even make a sentence.

No guarantees

Secondly, there is no guarantee that “one does not lose what has already been typed.” While the monkeys are busy typing away, there are multiple forces working against them, like a bad accident (mutation) jamming a typewriter or random natural destruction extinguishing the whole project. Thirdly, Ruse ignores the challenge of polygeny. “Selection simply cannot see genes and pick among them directly. It must use bodies as an intermediary…Hundreds of genes contribute to the building of most body parts and their action is channeled through a kaleidoscopic series of environmental influences…Parts are not translated genes, and selection doesn’t even work directly on parts. It accepts or rejects entire organisms because suites of parts, interacting in complex ways, confer advantages.”6

A generous selection mechanism

I would propose another variation on the monkey story in order to more realistically take into account the play of natural selection. Suppose that the monkeys were randomly typing at computer workstations equipped with advanced word processing instead of typewriters. The word processing application is not only capable of spell-checking and punctuation-checking, it automatically eliminates the mistakes in spelling and punctuation! Thus the primates would slowly produce words and, if they were lucky enough to type a sentence, the punctuation would be perfect. This modification (a generous selection mechanism) would improve their odds tremendously. However, they are still left with the “fitness hill” problem. That is, they might produce words that satisfied the system yet did not make sentences (no grammar check). Moreover, computer crashes and viruses could wipe out promising attempts or even the entire system!

Some have countered that this scenario is unrealistic since prose poorly models genetic encoding. For example, one can change a single letter in a word and you usually destroy its meaning, whereas a change in an amino acid usually does not prevent the protein from performing its function. Also the gene order, it is argued, is unimportant in the genome.

Three problems

There are three probability problems that should be modeled here: First, the whopping unlikelihood of a truly beneficial mutation that adds new information which becomes the basis for an evolutionary novelty. Secondly, assuming that sufficient of these mutations can be observed over the course of time so that we can accurately determine the odds, we move on to Haldane’s Dilemma and the cost of mutation problem. That is, since by anyone’s calculation the great majority of mutations are deleterious, can the population reasonably bear the cost of removing these through differential survival? And what is the impact of harmful mutations on the reproductive capacity along the way? To simultaneously substitute numerous genes in a generation, evolution requires a very fortuitous set of reproductive circumstances. Thirdly, assuming the positive mutation keep occurring and the population can continually produce the enormous host of specimens that must march off to genetic death, then we can finally get to Gould’s polygeny and Behe’s “Irreducible Complexity.”7 What then are the odds that a whole system can simultaneously be put in place so that it can actually be selected (an immune system, metamorphosis, sexual reproduction, altruism, etc.)?

Say the odds of getting a “word” models the mutation problem. Then successfully dealing with the cost-of-mutation issue could be analogous to producing an intelligent sentence; and obtaining a reasoned paragraph could then model the evolution of an irreducibly complex system. The “poetic sensibility and grammatical complexity” that I mentioned earlier would finally be analogous to the beautifully complex, highly adapted creatures we observe, in which many of these systems ultimately work together in exquisite symmetry.

Does this scenario solve the monkeys’ probability challenge with the sonnet? Let’s rework the calculation using ReMine’s assumption that we have as many monkeys as protons in the observable universe. Furthermore, let’s upgrade the monkeys skills to typing a miraculous 500 random words per minute (while generously having the “nonwords” removed and mercifully being spared system crashes) around the clock for 20 billion years. There are 114 words in Shakespeare’s famous sonnet When in Disgrace with Fortune and Men’s Eyes. There are over 75,000 words just in my dated Webster’s Collegiate Dictionary, so let’s grant that many in the “spellchecker.”  The probability of typing, in order, all the sonnet’s words is just one chance in 75,000114 or 5.77×10555. This would require 4.1×10412 universes more than the ReMine illustration above to have an even chance at such an enterprise succeeding!

1. Wald, G., 1955. “The Origin of Life,” The Physics and Chemistry of Life, p.12.
2. Jeans, Sir James, 1930. The  Mysterious Universe, p. 4.
3. Hawking, S.W., 1988. A Brief History of Time: From the Big Bang to Black Holes, p. 123.
4. ReMine, W.J., 1993. The Biotic Message: Evolution Versus Message Theory, p.80.
5. Ruse, M., 1982. Darwinism Defended: A Guide to the Evolution Controversies, p. 308.
6. Gould, S.J., 1980. The Panda’s Thumb, pp. 89-90.
7. See Behe, M., 1996. Darwin’s Black Box, pp. 39-45.