Monday, November 24, 2008

There are more ways of being wrong...

...than being right.

Here is a sequence of numbers: 2, 4, 6, 8. These might be, for example, the distances from the star (in some arbitrary units) of the four known planets in your planetary system. Predict what will be the next number in the sequence. Express mathematically the rule you use for your prediction. Go ahead. I'll wait.


Ah, surely you guessed that the next number was 10, and the rule was X+2, where X is the previous number. Are there other rules that work for the given sequence? Well, yes, there is at least one alternative: -(1/44) X3+(3/11)X2+(34/11) works equally well, although the rule is rather more obtuse.

If one were going to invest in research to look for a new planet further out in your solar system, where would you put your money? Of course, you'd spend your time looking at D=10. A simple application of Ockham's Razor: Don't assume a more complicated explanation when a simpler one will suffice. And if indeed you find a planet at D=10 you will feel happily justified and go looking for the next planet at D=12. You will be confident that you have discovered "the Law of Planetary Distances."

But what if after diligent searching you find no planet at D=10. So you say, "Just for the hell of it let's look at D=8.91, which is the next number predicted by the second rule." And what if you find a planet at that distance. Whoa! Clearly, the stunning agreement of observation with the more complicated prediction suggests that Ockham's Razor let you down. The simplest rule did not suffice. (How useful the formula will be for the next step in the series remains to be seen.)

At this point you would probably start looking for a simple set of fundamental laws of nature from which you might derive the complex formula. You will be especially gratified if your new fundamental laws explain something in addition to planetary distances. You are still guided by Ockham's Razor, but willing to let nature have the last word.

There are lots of ways to be wrong, and fewer ways of being right. There are dozens of mutually contradictory religions, for example, but only one science. There is no conceivable way to falsify a supernatural truth system -- such as a religion or Intelligent Design -- since whatever is observed or not observed can be ascribed to the will of an inscrutable supernatural being. A scientific hypothesis can be falsified by finding a single reproducible counterexample (a planet at D= 8.91 exposes the inadequacy of the original hypothesis). There is an irony here. Systems with no conceivable way of confirmation or falsification often claim immutable truth. The one system that holds its hypotheses to the fire of exact reproducible experience claims nothing more than reliability -- and looks forward to refinement.

(More tomorrow. I take the numerical example above from Nicholas Humphrey's Leaps of Faith, of which more later.)