Monkeys and typewriters

Monkeys and Typewriters

Darwin's insights in the earlier Nineteenth Century were combined with other discoveries about the same time, notably the geological evidence that the Earth was much older than the 6,000 years generally taken for granted. Darwin's theory of Evolution by Natural Selection was published without an explanation of how the inheritance of traits was accomplished. How, for example, can we inherit Grandfather's blue eyes when both our parents have brown eyes? These problems had already been solved in the middle Nineteenth Century by the monk Gregor Mendel, but his work did not become widely known until the Twentieth Century. It very neatly answered this question, and greatly strengthened Darwin's theory. It became clear how desirable traits could be passed on from one generation to another, and how undesirable ones could be weeded out. Whether this mechanism was capable, however, of providing an all-encompassing explanation of the origin of present day life from its very beginnings, has always been questioned by evolutionary biologists. Opponents have remarked, 'Natural selection explains the survival of the fittest, but it does not explain the arrival of the fittest.'

Reaction of Christian Denominations

One section of Protestants have held grimly to a literalist interpretation of the Book of Genesis, and simply deny that evolution happens at all, or that the Earth is older than 4004 BC (a figure derived by adding together the ages of the Patriarchs given in the Hebrew Bible). Some Catholics have also adopted this literalist position, but it is not official Catholic teaching.

Liberal Protestants, led by the German Biblical Scholars of the Nineteenth Century, began to question the credibility of Biblical accounts, at the same time that many other legends worldwide were being subjected to a ruthless scrutiny. [Some legends that were dismissed at this time have since been vindicated by archaeological discoveries.] The Biblical scholars adopted what they believed to be a fair and objective approach, but tended to operate from the assumption that miracles cannot happen. This led to a predetermined wholesale rejection of most of the Bible on these grounds alone. They also treated the Gospel accounts, claimed to have been written within living memory of Christ, in exactly the same way that the scholars treated accounts of events placed thousands of years before they were written down. Many were led to reject the Bible entirely and to pass into scepticism or agnosticism. G.K.Chesterton remarked ironically, 'My compatriots, having rejected the Catholic Church on the grounds that it disbelieved the Bible, were excitedly finding out that they did not believe the Bible themselves.'

The Catholic Church has always been cautious about the interpretation of the Bible, especially the earliest accounts. It has been realised from at least the Fourth Century that the Biblical account of Creation in Six days might be in some sense symbolic, and represent rather a schematic way of describing the Creation of the world by God out of nothing. At the end of the Nineteenth Century, in response to (i) the rapid advance of science (much of it due to practising Catholics, as in every century, despite the common misconception), (ii) the development of Biblical study, some of which was self-defeating, and (iii) the rise of an aggressive materialism; the Pope established a Pontifical Biblical Commission to take a fresh and honest look at the status of the Biblical texts. The outcome was a statement of the principles of Catholic Biblical interpretation, and guidelines for differentiating direct statements necessary to the Faith, from legend or literary devices and conventions. Avoiding the extremes of both the Biblical Literalists and of the Radical Sceptics, the operation of evolution in the making of the world is not denied – and more recently, has been affirmed on the basis of the evidence – and there is no commitment to a particular age of the Earth or the Universe, nor to the actual mechanism of Evolution, apart from affirming that it is due to the action of Divine Providence..

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At the beginning of the Twentieth Century, when an atheistic version of Evolution – (natural selection acting on random mutations) – was confidently being promoted as an alternative to God, questioners were routinely silenced by the response, "Ah, but you do not realise how long a million years really is. In fact, the Earth is millions of years old, which gives plenty of time for Natural Selection to operate." There was a popular saying: "If you got a roomful of monkeys with typewriters, and left them for long enough, eventually they would type out the Complete Works of Shakespeare." Sounds convincing, doesn't it?

The theory was actually put to the test at Rothamstead, the leading Plant Breeding Nursery of England. Crops were grown in plots provided with a pole on top of which was a radioactive source. The radiation was intended to increase the rate of mutation, and the favourable ones would be used to yield new, improved strains of crop. The project ran for many years, but not a single improved strain emerged, although there were some deformed specimens produced, useless for further propagation. Eventually this project was discontinued. Compare it with modern techniques of Genetic Engineering – what the philosophers would call Intelligent Design. Progress is now so rapid and comprehensive that it is literally rather frightening to consider what technology can already achieve by this method – let alone what could be realised in the future.

Are you going to say that the Rothamstead project was terminated far too quickly? That we simply have no idea how long a million years really is? That was indeed the catch-phrase in the heady days of Darwinism. So let us go back to the monkeys and the typewriters, and consider how long a random mutation would actually take to emerge.

Let us, for the sake of argument, forget about how the monkeys and typewriters got there in the first place. We must be kind to these atheists. Let us (to keep the arithmetic simple) assume a room containing one hundred typewriters, and that the monkeys type at the rate of two keyboard strokes per second. Let us see how long it would take to arrive, by random typing, at just the one phrase 'To be or not to be.' Not an onerous task compared with the complete works of Shakespeare, one might be inclined to say. The maths is not difficult. It is not University Level. In Ireland, it is taught in the Junior Certificate (Ordinary Level) syllabus, suitable for average 13-year olds. It is not even restricted to the Higher Level syllabus.

The alphabet has 26 letters. Taking Capital and small case, that gives 26 x 2 = 52 possibilities. Add the Space Bar, the comma and the full stop. That is the bare minimum for typing English prose. That makes 55 possibilities. To hit the right key for the first letter is a probability of 1 in 55. Having hit it correctly, the probability of then hitting the second letter correctly is 1 in 55 x 55, or 55 squared – 55 to the power of two. That's 1 in 3025. Having hit these two correctly, the probability of hitting the third key (in this case, the space bar) is 1 in 3025 x 55 = 55 to the power of 3 = 1 in 166,375. And so on. Notice how quickly the numbers begin to build up. Non-mathematicians do not have a good intuition about this. Some will know the legend of the grains of wheat on the chessboard, that outwitted the King of Persia. If we could fold double an ordinary (large!) sheet of paper fifty times, the stack would reach to the Moon. For a monkey to type just the first six characters correctly would take us to 55 to the power of 6 possibilities – just over 20,000,000,000 – one in twenty billion.

Now in the phrase we have chosen, there are 18 keystrokes to hit correctly. The probability of hitting these is 55 to the power of 18. Your pocket calculator will perform this calculation as quickly as you can press the keys. It comes to 1 in approximately 21,209,401,370,000,000,000,000,000,000,000. But if we have 100 monkeys, that makes it 100 times more probable – only 1 in 212,094,013,700,000,000,000,000,000,000. That is two hundred and twelve thousand and ninety-four trillion trillion.

Now – how long would it take the monkeys to hit this combination? At two strokes per second, how many strokes would that make in a year? (We have already allowed for the 100 monkeys). It comes to 2 x 60 x 60 x 24 x 365 = 63,072,000 – just over 63 million strokes per year. To find the number of years it would take to type every combination, divide that number into the first figure. Now let us be fair and suppose that the monkeys hit the right combination halfway through the list. Divide the total by 2. So the number of years it would be expected to take is 212,094,013,700,000,000,000,000,000,000 ÷ 63,072,000 ÷ 2 = 6,725,457,055,000,000,000,000 years. Rounding to one significant figure, that is seven billion trillion years.

How long has the universe been in existence? The current Standard Theory of cosmology and particle physics gives an estimated age of just under 14 billion years. So how many of our universes would have to run before one monkey hit that phrase? It is seven billion trillion divided by fourteen billion: half a trillion, or five hundred billion.

So it would take, given our starting premiss, five hundred billion universes to hit just that one phrase by a random sampling of the possibilities.