13 March 2013

The Inductive Detective


Sherlock Holmes and Dr. Watson went on a camping trip. As they lay down for the night, Holmes said: “Watson, look up into the sky and tell me what you see”
Watson: “I see millions and millions of stars”
Holmes: “And what do you conclude from that?”
Watson: “Well, astronomically, it tells me there are millions of galaxies and potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarter past three. Meteorologically, I suspect we will have a beautiful day tomorrow. Theologically I can see that God is all powerful, and that we are small and insignificant part of the universe. But what does it tell you Holmes?”
Holmes: “Watson you idiot! Someone has stolen our tent!”

In the annals of literature, no character is as renowned for his powers of ‘deduction’ as Sherlock Holmes. But the way Holmes operates is not generally by using deductive logic at all. He really uses inductive logic. First he carefully observes the situation, then he generalize form his prior experience.

We don’t know exactly how Holmes arrived at his conclusion, but perhaps it was something like this:
1. I went to sleep in a tent, but now I can see the stars.
2. My intuitive working hypothesis, based on analogies to similar experiences I have had in the past, is that someone has stolen our tent.
3. In testing hypothesis, let’s rule out alternative hypotheses:
a. Perhaps the tent is still here, but someone is projecting a picture of the stars on the roof of my tent. This is unlikely, based on my past experience of human behavior and the equipment that experience tells me would have to be present in the tent and obviosly isn’t.
b. Perhaps the tent blew away. This is unlikely, as my past experiences lead me to conclude that that amount of wind would have wakened me, though perhaps not Watson.
c. Etc.
4. No, I think my original hypothesis is probably correct. Someone has stolen our tent.
See, It’s induction.