The "Monkey Theorem"

First of all, let me state clearly that—at least up until now—I am a theist. I am an Orthodox Coptic Christian. I believe in the existence of one God, Jesus Christ our Lord and Savior. But I am not just taking this for granted, for my mind aches to find a logical understanding to religion and a divine model that does not have contradictions. Therefore, I started reading with interest books that discuss theism versus atheism, hoping to find some answers to some time-old questions about the divine. I came to read professor Antony Flew's book "There is a God. How the world's most notorious atheist changed his mind" and, although he defends the theism I believe in, had an objection to one of his arguments quoted from Dr. Gerald Schroeder, a renowned Israeli scientist and a PhD holder in nuclear physics. I do not claim to be a professional and experienced philosopher like professor Flew or a nuclear physicist like Dr. Schroeder. However, I hold a Doctorate degree in anesthesiology; I have some interest in philosophy of religion, mathematics and physics; and I trust my mind with logical explanations as far as my mind can comprehend. So, I present herein the reasons I object to Dr. Schroeder's argument, quoted by professor Flew, against the "monkey theorem" in order to defend theism.

I start by quoting what I read in professor Flew's book:

"I was particularly impressed with Gerry Schroeder's point-by-point refutation of what I call the "monkey theorem." This idea, which has been presented in a number of forms and variations, defends the possibility of life arising by chance using the analogy of a multitude of monkeys banging away on computer keyboards and eventually ending up writing a Shakespearean sonnet.

Schroeder first referred to an experiment conducted by the British National Council of Arts. A computer was placed in a cage with six monkeys. After one month of hammering away at it (as well as using it as a bathroom!), the monkeys produced fifty typed pages—but not a single word. Schroeder noted that this was the case even though the shortest word in English language is one letter (a or I). A is a word only i f there is a space on either side of it. If we take it that the keyboard has thirty characters (the twenty-six letters and other symbols), then the likelihood of getting a one-letter word is 30 times 30 times 30, which is 27,000. The likelihood of a getting a one-letter word is one chance out of 27,000.

Schroeder then applied the probabilities to the sonnet analogy. "What's the chance of getting a Shakespearean sonnet?" he asked. He continued:

All the sonnets are the same length. They're by definition fourteen lines long. I picked the one I knew the opening line for, "Shall I compare thee to a summer's day?" I counted the number of letters; there are 488 letters in that sonnet. What's the likelihood of hammering away and getting 488 letters in the exact sequence as in "Shall I Compare Thee to a Summer's Day?"? What you end up with is 26 multiplied by itself 488 times--or 26 to the 488th power. Or, in other words, in base 10, 10 to the 690th.

[Now] the number of particles in the universe—not grains of sand, I'm talking about protons, electrons and neutrons—is 10 to the 80th. Ten to the 80th is 1 with 80 zeros after it. Ten to the 690th is 1 with 690 zeros after it. There are not enough particles in the universe to write down the trials; you'd be off by a factor of 10 to the 600th.

If you took the entire universe and converted it to computer chips—forget the monkeys—each one weighing a millionth of a gram and had each computer chip able to spin out 488 trials at, say, a million times a second; if you turn the entire universe into these microcomputer chips and these chips were spinning a million times a second [producing] random letters, the number of trials you would get since the beginning of time would be 10 to the 90th trial. It would be off again by a factor of 10 to the 600th. You will never get a sonnet by chance. The universe would have to be 10 to the 600th times larger. Yet the world just thinks the monkeys can do it every time.

After hearing Schroeder's presentation, I told him that he had very satisfactorily and decisively established that the "monkey theorem" was a load of rubbish, and that it was particularly good to do it with just a sonnet; the theorem is sometimes proposed using the works of Shakespeare or a single play, such as Hamlet. If the theorem won't work for a single sonnet, then of course it's simply absurd to suggest that the more elaborate feat of the origin of life could have been achieved by chance.

My objection to this argument is that neither professor Flew nor Dr. Schroeder mentioned anything about the complete change of probability calculations when events are not independent.

First, the monkey experiment used flawed methods and is by no means an experimental proof that the [metaphorical] monkey theorem is wrong. If the theorem is understood literally, then it may be a valid experiment with correct methods, but the theorem never meant the literal meaning of the words. The metaphorical phrasing means that letters typed randomly can eventually result in a work of Shakespeare. This assumes that:

• The probability of a certain letter appearing in any trial is independent of all other trials; i.e. the probability of a certain letter appearing in any trial is not affected in any way by which letter appeared in any other trial.
• The probability of any of the letters appearing in a certain trial is exactly equal to the probability of all the other letters appearing in the trial. In statistical terms, the probability distribution should be uniform.

In this case, and only in this case, the probability of any letter appearing in any trial would be one out of thirty—referring to the assumptions of professor Flew when he mentioned this experiment in his book—and the probability of getting a one-letter English word would be 1 in 27,000.

Monkeys produced fifty pages of typed text. Assuming there are about sixty lines per page and about eighty letters (or characters) per line, then those monkeys produced 60 times 80 times 50 keystrokes, or 240,000 keystrokes. I chose the numbers 60 as the lines per page and 80 as the characters per line (CPL) after doing some Internet research and finding that older texts had about 57 lines per page, which is more than more recent texts, and that the standard CPL at the end of the typewriter ear was 72. I chose larger numbers to maximize the number of letters and make it easier for monkeys to produce a meaningful output.

If our assumptions were true, monkeys should have typed at least nine one-letter English words, given that the probability of getting one one-letter English word is 27,000 and that monkeys typed 240,000 characters. So, why couldn't monkeys produce any one-letter English word in those fifty pages? That's because our assumptions could not be verified. Sophisticated statistical analysis is needed to verify the assumptions and validate the results. Certain monkeys could have 'liked' the keyboard more than others and, therefore, contributed more to those fifty pages. Certain monkeys could have liked certain letters or certain sides of the keyboard to bang on more than the other letters or sides, and they could have certainly avoided certain letters. A monkey pushing down with its finger or toe on a particular keyboard key would repeatedly type this key for as long as the key is pushed. The repetition rate can be set to be slow or fast, resulting in fewer or more letters typed in a certain period of time, respectively. Certain keys or parts of the keyboard may have been covered with monkey excreta; professor Flew mentioned that monkeys used the keyboard as a bathroom as well. All these factors make the assumptions of the uniform distribution and the independent events very unreliable. The only way to validate these assumptions is to analyze the output statistically in a very sophisticated way, which I don't know whether it happened.

Now considering Dr. Schroeder's argument about the number of attempts needed to reproduce one of Shakespeare's sonnets, he actually made it easier by choosing the number of letters to be 26 rather than 30. I would have chosen 27 at least to count the space as a keystroke. Dr. Schroeder chose the number of attempts needed to reproduce one of Shakespeare's sonnets as an analogy to illustrate that the number of events needed to produce the universe—had it been produced completely randomly—exceeds every possibility we can comprehend. It is true, as Dr. Schroeder assumed, that the number of attempts needed to reproduce a Shakespearean sonnet is at least 26 to the 488th power, but only with the assumptions mentioned above; i.e. a uniform distribution and independent events. But is this an applicable analogy to what may have happened in the universe?

I would argue that the analogy is totally out of place. Events that happened and are happening in the universe are not completely independent. In the presence of a number of subatomic particles—electrons, protons and neutrons; components of the very initial plasma as far as I understand—and under certain circumstances, these particles may combine to form a hydrogen atom, the simplest of all atoms that exist, comprising of only one proton and one electron. There is a smaller possibility that two protons and two electrons combine with one or more neutrons resulting in helium, or that three protons and three electrons combine with four or more neutrons resulting in lithium, and it would be logical to assume that the probability of forming more complex atoms from these primitive building blocks is certainly smaller than that of forming simple atoms. But does this remain to be true after the formation of some hydrogen atoms? Certainly not, for it is now easier for a hydrogen atom to combine with a proton, an electron and two or more neutrons or with another hydrogen atom and two or more neutrons to form helium. As a matter of fact, nuclear fusion of hydrogen into helium is still happening everyday nearby in our sun. Then after the formation of helium, it is easier for other, more complex molecules to be formed and so on.

Not only this, but despite my lack of knowledge in this area I'd be bold enough to follow logic and basic knowledge and assume that the formation of these molecules changed the conditions of the medium in which the reaction happened, and this may consequently affect the reaction itself, either positively or negatively. In other words, the possibility of forming a hydrogen atom from the initial plasma is not constant, but rather changes with time as the conditions change. The same goes for all other elements. The point of all this is to argue logically that the assumption of independent events leading to the production of our universe is a wrong assumption, and any calculations made based on this assumption will consequently be wrong.

As for the assumption of different events having a uniform distribution; i.e. an equal chance of happening, I would also strongly object to this. Consider the initial plasma. In the very beginning, the possibility of forming a hydrogen atom is not the same as the possibility of forming the more complex helium or lithium atoms. With the formation of more hydrogen atoms, the possibilities of forming more hydrogen atoms will eventually decrease because of the consumption of the 'raw material' from which they are formed; i.e. the plasma. On the other hand, the probability of forming more complex atoms will increase because of the increase in the raw material from which they are formed; i.e.simpler atoms. Under all circumstances, it would be wrong to assume that the probability of forming various atoms is the same for all atoms.

The same argument goes for any other event in the natural history of the universe. Events are not independent, and are not equal in their chances of happening. Take as an example the arrival of humans to the island of Mauritius resulted soon in the extinction of Raphus cucullatus, also known as the 'Dodo bird'. Had this event not happened, the chances of survival of this bird would still have been near 100% as it had been for a very long time before humans had their encounter with it. The introduction of internal combustion engines, together with the industrial revolution, resulted in more carbon dioxide release into our atmosphere. This, combined with deforestation, is having significant effect on our environment and affecting our flora and fauna. The chances of survival of many species have not been the same after these events.

So, am I trying to argue that the universe could have been produced by mere chance? I am definitely not presenting this argument at all, but rather arguing against the examples and calculations quoted by professor Flew from Dr. Schroeder. I wouldn't use this particular argument in my discussions about the Divine existence. What calculations can be acceptable then? I can see no possibility of calculating or approximating these calculations with any degree of accuracy. The events seem to be enormous in magnitude, and the conditions in which these events happened are not known in many situations. We can only extrapolate from our current knowledge to try to understand how it was like at the time of birth of the universe and thereafter. So, can the "monkey theorem" be true? Could the universe as we know it have been produced by mere chance? Perhaps! I cannot argue strongly against this. I have to accept for now that this theory can be true. Refuting this theory is not the only way to argue against atheism. So, perhaps we should concentrate more on the strong arguments and less on the weak ones.

Finally, I'd like to say that it the 'divine model' as I call it that introduces contradictions and leads to debates about the existence of God. Each religion presents its own model of God. The model is a mere hypothesis that humans formulate based on their religious scriptures. No one so far has been able to verify experimentally the existence or non-existence of God. A hypothesis can and should be accepted as true as long as there is no logical objection to any of its assumptions. Therefore, I believe that the arguments should concentrate more on the divine model that we present and see if there are any contradictions in this model. If there is any, then perhaps our concepts about God are wrong, or perhaps there is no God at all! If we cannot come up with a coherent divine model, then we should always leave room for doubt. This will be my quest for as long as I live.

Addendum

I communicated with Dr. Schroeder by e-mail to present my argument. He kindly promptly responded within a day and this was his response:

"The events must be in order and not that you try and try to get the first and then lock that in and try ans try to get the 2nd etc. that would make it additive, as is a set used by R. DawKins which I discuss in my books. The actual is not additive it is multiplicative."

I will definitely refer back to Dr. Schroeder's books for more understanding of the topic. The reader can refer to Dr. Shcroeder's website for more information.