Dirk Gently talks a lot about the impossibility of certain events that have actually happened. In “Dirk Gently’s holistic detective agency,” Dirk is much taken by a conjuring trick a professor performs at a high table dinner at one of the Cambridge colleges. Only he seems to realize that the particular trick is actually totally impossible, at least given what we know about the world. The professor makes a “salt cellar” disappear and then reappear in a 200-year-old pot that needed cracking open to get to the salt cellar (on pages 34-37 of my edition of the book). Dirk calls this event (p. 189) “completely and utterly impossible.” After asserting that, luckily, “there is no such word as ‘impossible’ in my dictionary,” in fact a lot of pages are missing, he rephrases this to “completely and utterly – well let us say, inexplicable … [I]t cannot be explained by anything we know.” What he means is that the model of the world that we have cannot explain this phenomenon. Because of this fact we should entertain a different model of the world. Indeed, eventually it becomes clear that the professor was able to travel back in time 200 hundred years, something our model of the world does not allow, and to have the salt cellar put into the pot when it was made. Dirk’s ability to think beyond the current model of the world made it possible for him to understand the seemingly impossible.

In “The long dark tea-time of the soul” Dirk goes further in claiming that he often prefers an impossible explanation over possible but highly improbable ones. Among a number of interesting patients in the ”Woodshead hospital,” there is a ten-year-old girl sitting in a wheelchair and murmuring constantly and “soundlessly to herself.” She is murmuring stock market prices, but yesterdays (with a precise 24-hour delay). She has no apparent access to outside news of any kind. Yet, the psychologists explains that “[w]ell, as a scientist, I have to take the view that since the information is freely available, she is acquiring it through normal channels.’’ This is happening on pages 121-123 in my edition of the book.

When told about this, Dirk is confronted with Sherlock Holmes’ (I guess really Sir Arthur Conan Doyle’s) statement that “[o]nce you have discounted the impossible, then whatever remains, however improbable, must be the truth.” Dirk responds with “I reject that entirely, the impossible often has a kind of integrity to it which the merely improbable lacks.” Applied to the present case of the girl in the wheelchair he states that “[t]he idea that she is somehow receiving yesterday’s stock market prices out of thin air is merely impossible, and therefore must be the case, because the idea that she is maintaining an immensely complex and laborious hoax of no benefit to herself is hopelessly improbable. The first idea merely supposes that there is something we don’t know about, and God knows there are enough of those. The second, however, runs contrary to something fundamental and human which we do know about. We should therefore be very suspicious of it and all its specious rationality.”

I like Dirk’s statement a lot, for two reasons. The first is that Dirk points out that we should be aware of model uncertainty. We should always entertain the possibility that the model that we have about the world is not completely correct, and sometimes new evidence should lead us to reconsider the model. This is somewhat comical in Dirk’s context, where we are really talking about the physics of the world (although of course physics models can also be wrong). The idea is much more important, however, in game-theoretic models (as used most heavily in economics), as these models are typically radical simplifications of the world. If a game-theoretic models leads to bizarre predictions (or policy implications), you should probably go back to the drawing board for a more appropriate game-theoretic model, rather than accept these predictions as truth. By the way, Dirk’s approach of questioning the underlying model based on possibly but highly improbable observations given the model, is a standard tool of statistics. Indeed, in statistics, we tend to reject a null hypothesis (our current model of the world) if the kind of data that we observe is sufficiently hard to explain with the null hypothesis; if the p-value is below the level of significance that you choose to begin with (you know, the often chosen of 5% for instance). So, while the way Dirk says this, may appear ludicrous, he is really just stating sound scientific reasoning.

The second part of Dirk’s statement that I like is that he puts human incentives even above physical laws (of a possibly flawed physical model). Why would this ten-year old girl maintain such a “laborious hoax” that is “of no benefit to herself”? Taking human incentives into account is what game-theoretic models (with a longer tradition in economics) are really good at. Douglas Adams would have made a great game theorist (or even economist ;).