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A Reactionary Rant by The Famous Brett Watson, 12-Jan-2002.

The Mathematics of Monkeys and Shakespeare still ranks as the most popular document of all time on Nutters.org. It's probably been getting more hits per week than everything else combined. I've written more on the subject before, in the form of More Monkey Business, but that document is way too long and involved for most tastes. I'll try to learn a lesson from this and specifically not attempt to address every possible objection to every possible argument this time.

Although nobody has ever pointed out a flaw in my mathematics, many people leap on the "conclusion" of The Mathematics of Monkeys and Shakespeare as being unsupported by the corpus of the essay, and to a large extent, this is quite true. The essay was originally an email to a person that I met on the 'net. He put to me the difficult question as to what evidence I thought there was for the existence of God. Why believe in God at all? From an evidential perspective, I believe that the argument from probability makes a strong case for believing in God. This conclusion is not inescapable, however, and I admit as much in the "Postscript" of my essay, which I reproduce here for your information.

If you read the thesis above, you will agree at least that if the universe did arise by chance, it must be truly infinite and in the continuous process of trying out new alternatives. That, and the universe as we know it is an incomprhensibly unlikely fluke. I find it much simpler (and much more "natural", I might say) to suppose that there is a God who is greater than the universe who made it, much like I made this document.

You can believe that the universe is an accident if you want to, and nobody is ever likely to be able to prove you wrong on that point. The mathematics I present is simply intended to put that belief into perspective for those who are still deciding whether or not God exists. Of course, if you're already committed to a naturalistic world view, where everything that happens happens because of the laws of physics, then you've already written "God" pretty much out of the picture, and any non-zero probability will do to fill in the gap, no matter how small.

It's people who have taken this stance of committed naturalism who most often criticise my essay. Most such criticisms arrive by email, but some are published on the web. I'm going to pick on one particular web-published criticism today, mostly for the sake of my own convenience. It's fairly representative of the kinds of objections that I get, and it's called Statistical Monkey Business, by Aaron Krowne.

Before getting down to the business of addressing the specific points raised in Aaron's critique, I'd like to point out a debating technique that I've seen evolutionists employ — probably unwittingly more often than not — in arguments against creationists or apologists for anything other than naturalism generally. I don't have a clever name for the technique, so I'll describe it here.

I first noticed the technique when I read some responses to Michael Behe's excellent and thorough work, "Darwin's Black Box". In this work, Behe carefully describes the biochemical details of certain vital functions, like blood-clotting. He shows how amazingly complex such apparently simple systems are at the biochemical level, and how breaking any one link in the biochemical chain can have catastrophic results for the biological function in question. He puts forth the challenge to evolutionists generally to explain how such a system (where a complex system is in place, and the disruption any one link can break the function) can arise one piece at a time in a slow and gradual manner.

This would seem like a knock-out blow to me. Can evolutionists show a viable biochemical sequence of small steps between distinct but supposedly related biological systems? The typical answer is to dismiss Behe as having overlooked the obvious. They don't need a linear set of modifications between one and the other, they say, because it may not have happened that way. In the same way that an arch requires scaffolding when it is being built, but supports its own weight when complete, these biochemical systems may well have had scaffolding around them in the past which rendered this objection irrelevant.

What they never ever do, of course, is provide details how that scaffolding could have worked at the biochemical level. It's like Behe has given them a really hard challenge, saying, "you claim this has happened; here are the facts of the matter, now explain how your system worked." In response, they claim that the process happened by some much more round-about method, and omit the explanation part. In my opinion, this is a magician's technique: distraction. It's a way of preventing people from noticing that you haven't really answered the question, and it's certainly not good science. I claim that Aaron Krowne's critique of my essay also contains such distractions. I leave it to you, dear reader, to judge the extent to which that claim is valid.

Aaron's first objection is that of "probabilistic independence of events". My hypothetical monkeys are strictly independent of each other, and one keypress is strictly independent of the next, but in the physical universe nothing is perfectly independent in this way. I note in the first instance that this doesn't stop statisticians from taking themselves perfectly seriously when they use the same kind of "independent event" model in their calculations. Why is this so? Because, in many cases, whatever "dependence" exists between the two events is so small as to be negligible. Dependence can be validly ignored when it doesn't have a significant impact on the outcome. It's fair to point out that I've used a model of independent events, but this in itself is no big deal unless dependence is significant to the results.

The exact nature of the objection is somewhat confused by Aaron's example of a baby learning to speak. If we consider a baby as a random event generator (like the monkeys in my essay), then the chances of it ever uttering a Shakespearean quotation is pretty darn low. But it would be very odd to consider a baby as a random event generator, because they aren't even remotely like that. Real live monkeys aren't all that much like random event generators either, but for the purposes of illustrating a mathematical problem using something other than numbers, monkeys and typewriters are a reasonable choice, I think.

A human baby, on the other hand, has spectacular learning capacity. We expect a human baby to pick up language as a matter of course, because that's what human babies do. We would be inclined to think that there was something wrong with a human baby that did not pick up language skills. We don't expect a baby chimpanzee to learn to talk (or type, for that matter), despite whatever other similarities may exist with human babies.

A human baby does, as Aaron suggests, reside in an environment where it experiences dependent events and feedback, but this would be irrelevant if it weren't for its innate capacity to react to that feedback in a manner that allowed it to acquire language abilities. Every other object in the baby's environment is exposed to the same kind of stimuli as the baby, but only the baby reacts to those stimuli in such a way that it eventually acquires the ability to publish essays on the Internet.

Aaron has completely ignored the "intelligence" involved in his example, concluding instead that "we have significantly accelerated how fast complex patterns like communication can arise in a dependent universe." Dependence is a factor in his example, no doubt, but is it the key factor? Replace the human baby with a chimpanzee and you get all the same dependencies but none of the results. I would argue that the example shows how intelligence can be a vital ingredient to the production of "complex patterns like communication".

Others have suggested that I'm ignoring the effects of "Natural Selection", which may have been what Aaron was really driving at here. This is true, but Natural Selection (in the form of "differential reproduction") only applies to things which can reproduce. My mathematical objections are still completely valid, even with the omission of Natural Selection, when applied to "chemical evolution", being that stage of the process that goes from non-life to life.

It's entirely likely that the kinds of events necessary for chemical evolution would have a large number of dependencies, and that a model of "independent events", such as I have used, is not a very good model of the process. Dependencies would change matters, either for better or worse, but it's unlikely that they would change the fundamentally exponential nature of the problem. Rather than speculate about it, however, I would like to actually perform a mathematical analysis of the probabilities in chemical evolution, but the supposed process of chemical evolution has never been defined in sufficient detail to analyse mathematically! I will be happy to include dependencies in my analysis if anyone can specify exactly what those dependencies are.

Aaron's second objection is that "improbable does not equal impossible". This objection comes in two parts: a semantic quibble, and an attack on my underlying assumptions. I dismiss the semantic quibble as immaterial. Aaron (and others who have raised this objection) would have me use "impossible" only in the strict sense of "having a probability of zero", or "can not happen under any circumstances". As the objectors have rightly noted, I have here used it in the slightly less strict sense of, "cannot reasonably be expected to happen", or "utterly impracticable". This distinction does not affect my conclusion, and the dictionaries of the English language which I have checked recognise such usage. Even so, I anticipated that I would face pedantic objections of this sort, and carefully weighed up the use of the word at the time, ultimately deciding that "impossible" was necessary to drive the point home.

The objection relating to my underlying assumptions is a little more interesting. Aaron correctly identifies that my argument "assumes that all useful analysis of life belongs within the scale of 17 billion years." As Aaron concedes, I didn't pick this number entirely arbitrarily: it is the approximate "age of the universe" as currently accepted by mainstream (evolutionary) science. Yet Aaron declares the age of the universe to be irrelevant on the grounds that we can speculate about as much additional time and space (in the form of other universes) as is needed to solve the problem. Astute readers will notice that I allowed for this kind of "out" in my Postscript (quoted earlier) in the form of an "infinite universe", although "arbitrarily many universes" will do just as well.

Granted, I do make the assumption that Aaron suggests. Why do I make that assumption? I make it because it's as generous as I can be with the figures relating to available time and space whilst staying within the bounds of "science". I don't necessarily believe that the scientific mainstream is right about the age of the universe, but I'm taking what they claim is a fact of science ("the universe is about seventeen billion years old") and applying it to another alleged fact of science ("life evolved without the input of an intelligent creator"), and hoping to demonstrate that the two are somewhat incongruous.

Surely an appeal to other universes beyond the reach of scientific knowledge cannot be considered a scientific objection to my thesis? It's metaphysical — pure speculation. I recognise that many people hold this belief, which is why I spoke of committed naturalists earlier, but I can see no compelling reason to prefer a naturalistic view over a supernaturalistic one, particularly when discussing matters that the parties agree is beyond the ken of science! Aaron states that the possibility of multiple universes with differing laws of physics is "not ruled out by known science", but the same applies to the possibility that the universe was created by divine fiat, so how does this help his argument?

In conclusion, Aaron criticises the lack of connection between my conclusion and the corpus of my work, whilst at the same time making the passing comment that, "science is a process - the only sure process - for gaining knowledge about the world." This is a statement of belief, not logically connected with the corpus of his work, not supported by facts in the corpus of his work, and not even strictly adhered to in the corpus of his work. Aaron has demonstrated some degree of epistemological awareness in another essay, so this apparent lapse is disappointing.

As to whether or not Aaron's objections really do expose flaws in my argument, let the reader be the judge.