In a prior post the order of a deck of cards was used as an example of specified complexity. If a deck is shuffled and it results in all of the cards being ordered by rank and suit, one can infer design. One commenter objected to this reasoning on the grounds that the specified order is no more improbable than any other order of cards (about 1 in 10^68). In other words, the probably of every deck order is about 1 in 10^68, so why should we infer something special about this deck order simply because it has a low probability.
Well, last night at my friendly poker game I decided to test this theory. We were playing five card poker with no draws after the deal. On the first hand I delt myself a royal flush in spades. Eyebrows were raised, but no one objected. On the second hand I delt myself a royal flush in spades, as well as every hand all the way through the 13th.
When my friends objected I said, “Lookit, your intuition has led you astray. You are infering design — that is to say that I’m cheating — simply on the basis of the low probability of this sequence of events. But don’t you understand that the odds of me receiving 13 royal flushes in spades in a row is exactly the same as me receiving any other 13 hands. ” In a rather didactic tone of voice I continued, “Let me explain. In the game we are playing there are 2,598,960 possible hands. The odds of receiving a straight flush in spades is therefore 1 in 2,598,960. But don’t you see, the odds of receiving ANY hand are exactly the same, 1 in 2,598,960. And the odds of a series of events is simply the product of the odds of all of the events. Therefore the odds of receiving 13 royal flushes in spades in a row is about 2.74^-71. But, and here’s the clincher, the odds of receiving ANY series of 13 hands is exactly the same, 2.74^-71. So there, pay up and kwicher whinin’.”
Unfortunately for me, one of my friends actually understands the theory of specified complexity, and right about this time this buttinski speaks up and says, “Nice analysis, but you are forgetting one thing. Low probability is only half of what you need for a design inference. You have completely skipped an analysis of the other half — i.e. [don’t you just hate it when people use “i.e.” in spoken language] A SPECIFICATION.”
“Waddaya mean, Mr. Smarty Pants,” I replied. “My logic is unassailable. ” “Not so fast,” he said. “Let me explain. There are two types of complex patterns, those that warrant a design inference (we call this a ‘specification’ and those that do not (which we call a ‘fabrication’). The difference between a specification and a fabrication is the descriptive complexity of the underlying patterns [see Professor Sewell’s paper linked to his post below for a more detailed explanation of this]. A specification has a very simple description, in our case ’13 royal flushes in spades in a row.’ A fabrication has a very complex description. For example, another 13 hand sequence could be described as ‘1 pair; 3 of a kind; no pair; no pair; 2 pair; straight; no pair; full house; no pair; 2 pair; 1 pair; 1 pair; flush.’ In summary, BarryA, our fellow players’ intuition has not led them astray. Not only is the series of hands you delt yourself massively improbable, it is also clearly a specification. A design inference is not only warranted, it is compelled. I infer you are a no good, four flushin’, egg sucking mule of a cheater.” He then turned to one of the other players and said, “Get a rope.” Then I woke up.