Dembski and Berlinski – Tossing Coins

A month or two ago, I was reading an exchange between William Dembski and David Berlinski regarding a key point of Dembski’s design inference – improbability – and got the impression that there was a basic disconnect in the exchange.

By way of background, Dembski has at least a couple of points he wishes to make in discussing probability scenarios. First, Dembski argues, and I understand Berlinski agrees, that the sheer logical possibility of an event occurring does not mean that it should be considered as a practical possibility within the realm of grounded science. Second, Dembski argues that an information-rich system arising through random natural processes is not a practical possibility, and can therefore be disregarded as a useful explanation for the origin of the system.

In order to illustrate this second point in this particular exchange, Dembski provides the following example:

“According to Mr. Berlinski, highly improbable events happen ‘precisely as many times as one might expect, given their probabilities.’ This claim is easily disproved by flipping a coin a thousand times. The probability of the sequence you get is around one in ten raised to the 300th power. How often should you have expected this sequence to occur? Not at all! With all the elementary particles in the universe furiously flipping coins for trillions of years, the expected waiting time for a given sequence places it well beyond the predicted heat death (or big crunch) of the universe.”

For this example, Berlinski takes Dembski to task:

“[Dembski’s] counterexample is a fair coin flipped 1,000 times. The particular sequence of heads and tails that results has the probability of roughly one in ten to the 300th power. ‘How often should [I] have expected this sequence to occur?’ Mr. Dembski asks. Not at all, he responds cheerfully. But the sequence has occurred, and the relevant record of heads and tails is there in plain sight. This persuades Mr. Dembski that, if left unspecified, unlikely events tend to occur more often than any assignment of probabilities would suggest.

I understand Mr. Dembski’s reasoning, but I reject it as unwholesome. He is stuck, after all, with an expectation – a particular sequence should not occur at all – that is in plain contradiction to the facts – a particular sequence has indeed occurred. This is not necessarily a fatal flaw, but it does suggest that something has to give. What has to give is the nice coincidence between what the theory of probability affirms and what the facts reveal.”

Reading the above one is struck with the simple logic of Berlinski’s point: Dembski is arguing that a particular string of numbers cannot be expected to come about through a random process, and yet here it is, having been generated by a random process. It appears that Berlinski may have indeed spotted a weakness in Dembski’s theory. But upon closer inspection, it turns out that Berlinski has simply identified a weakness in Dembski’s example.

Tweaking the Example

Here is what is going on: Dembski’s focus is on the second half of his example – the improbability of a random process generating a string of 1,000 heads and tails. Dembski’s contention is that given a specific string of 1,000 heads and tails, the probability of obtaining the same string through a random process is so negligible that it should be rejected as an explanation for the string’s existence.

The problem arises, however, because Dembski unfortunately formulated his example in such a way that the specific string in question was first generated through a random process. As a result, Dembski’s conclusion – that a random process could not generate the specific string – is in contradiction to the very example itself. The problem with Dembski’s example is not the string, nor is it his conclusion that we should not expect to see the string generated by a random process. It is simply that he has chosen the wrong given.

With one little tweak to Dembski’s example, Berlinski’s criticism is largely eviscerated: Let’s suppose that an individual sits down and chooses a specific string of 1,000 heads and tails. What is the probability that a random coin toss could generate this same string? Now instead of a random process on either side of the example, we have captured the real substance of Dembski’s design inference: an intelligent selection on the one hand, versus a random process on the other.

Berlinski is correct to take Dembski to task for an example that is less tight than it should be. However, the failure of Dembski’s example is one of semantics, not substance, and with a slight adjustment to the semantics, the substance becomes more clear, and Berlinski’s criticism on this particular point becomes less relevant.

Specified Improbability and Information Content

Yet there is a more subtle issue at work here. Berlinski challenges Dembski on the question of whether an unspecified probability is more likely to occur than a specified probability, and suggests that it is not. But this approach again focuses on the semantics of Dembski’s particular example, rather than on the underlying substance. Specifically, the information content in the string is critical. In our tweaked example, the individual selecting the sequence of heads and tails could repeat that task, again and again, by using intelligent input. In contrast, a random coin toss would not be expected to generate the same string in the first place, and certainly would not have the capability of generating it again and again.

Berlinski is fixated on the fact that random events do occur, and believes that, as a result, it is just as reasonable to expect a specified improbability to occur as an unspecified improbability. He thinks that Dembski’s position depends on the proposition that an unspecified improbability will occur more often than the laws of probability would suggest. But that is not Dembski’s point at all. Dembski’s argument is not simply about the improbability, but the specification, which to Dembski means information content.

Berlinski may be getting hung up on the fact that one coin toss sequence does not contain any more meaningful information than another. Our tweaked example above should solve that problem, but if that doesn’t persuade Berlinski, then we can tweak the example to a sequence of numbers that includes meaningful information: perhaps a series of primes, or a Morse Code message, or some other secondary information.

At this stage we get to the real heart of Dembski’s design inference, which is that (i) we know for a fact that meaningful information-rich sequences can be generated (and indeed are regularly generated) by an intelligent agent, while at the same time (ii) there is no expectation of, nor any reliable record of, random processes ever generating a similar information-rich sequence.

As a fan of Berlinski’s writing and his wit, I look forward to his continued involvement in the intelligent design debate. Certainly the exchange between Berlinski and Dembski covers more than the specific issues I have probed above, and Berlinski may in fact have cogent reasons for rejecting the design inference. But he will have to come up with a stronger argument than pointing out a few semantic weaknesses with Dembski’s coin toss.

Eric Anderson

November 14, 2003