Shuffle and deal a deck of 52 cards into a single line, for example. There are 52! - that is, factorial 52 - that is, about 8x10

^{67}possible sequences of cards. So for a well-shuffled deck, it is fairly safe to say that nobody else will ever have seen that sequence before. In fact, the probability of that sequence arising is about 1.2x10

^{-68}. That is an incredibly small probability – and yet, there it is, in front of you! Which just goes to show that low probability events happen all the time. If you had a deck of 100 different playing cards, you would have over 10

^{150}permutations, which means that the chance of any particular sequence of cards arising would be less than the UPB of 10-150. And yet, all you have to do for such an improbable event to occur is deal the cards.

This response to the UPB featured in the BBC Horizon programme about Intelligent Design, that I reviewed some time ago. However, it misses the point that Dembski makes in relation to the UPB. Dembski never suggests that improbable events don't occur. The UPB relates to whether or not a specified improbable event will occur by chance. The difference is important.

To explain this, take the sequence of cards that you got in the last part of the experiment, and write it down. Now, pick up the cards, shuffle them properly and deal them again. What is the likelihood that you get exactly the same sequence as you wrote down? Actually, it's exactly the same as the probability that you got it in the first case – 1.2x10

^{-68}. But whereas you know when you deal the deck of cards you are going to get some sequence of cards, you certainly don't know that you are going to get a specific sequence of cards. So for you to obtain the same sequence would be a specified event of low probability, as distinguished from an unspecified event of low probability, which was what we had with the first sequence of cards dealt.

Now imagine a magician, who with great ceremony shuffles a deck of cards, and for good measure encourages onlookers to cut and shuffle the deck as well. He then deals the cards in the way described above, and presents a random sequence of cards. That random sequence is no less improbable than dealing all the cards out in order of suit and value. But the audience would fail to be impressed, of course, because there was “nothing special” about that sequence – that is, more formally in Dembski's terms, it is not a specified sequence. But if the magician deals the cards by suit and value, then people would be impressed – because the sequence of cards dealt obviously is specified.

Our instinctive reaction when presented with such a feat with a deck of cards is to conclude that there is trickery – in other words, the pattern in the cards is there by design, not chance. The event is a low probability event that is specified – magicians attract audiences for this sort of trick precisely because we don't shrug our shoulders and say: “Well, the cards were bound to come out in a sequence, and each sequence is as improbable as any other.” However, there is a small possibility that a deck of cards dealt at random will come up with a sequence that is significant – perhaps suit by suit, or value by value – let's say that 90% of card sequences dealt are significant in some way. So the probability of getting a “significant” or “specified” sequence is 10 times greater (actually, this isn't quite right from a statistical point of view, but I think it will probably do). That would mean that the probability of dealing a sequence which was significant was about 10

^{-67}. This is still an incredibly low probability – however, Dembski sets the UPB – the point at which the occurrence of a specified event can be confidently assigned to intention rather than chance is a lot lower – namely, 10

^{-150}.

On the other hand, people would not be impressed by a magician presenting a sequence of cards that we were unable to clearly distinguish from a random sequence. The concept of specification is one that we are intuitively happy with, and arguing against Dembski's approach on these grounds either represents a failure to interact with what he has actually written, or a willful misrepresentation of his argument. Neither is commendable.

I hope to write more shortly about our intuitive sense of specification, and how this relates to the information content in organisms, in future posts. But I'm sure I've said that sort of thing before ....