One of the comments on my post about The Esssence of Heuristics went like this:
“An excellent example of a heuristic is a hammer.”
Ecstasy is your friend: it picks you up at the airport.
Non heuristics that can help an expert solve a problem, without being a guarantee – an abridged list:
* Newton-Raphson Algorithm
It was posted anonymously. I generally don’t publish anonymous comments that are argumentative, because opponents who yell things and run away bore me… but this one is helpful. The writer is a little confused, but I bet other people are confused too, in the same way.
He offers a list of things that he claims are non-heuristics (he doesn’t explain why so I guess he thinks they are “obviously” non-heuristics), and suggests that they meet my definition. I think he’s trying to make two points: either my definition of heuristics is wrong because it admits non-heuristics, or it’s trivial because then everything would be a heuristic and therefore the idea conveys no information.
Well, the first point is easily handled. By definition, each thing on his list is heuristic (because he has declared that they help without guaranteeing in some scenario which he seems to have in mind). There is no contradiction, he’s simply mistaken by calling those things non-heuristics.
As to his second point, that’s where the real confusion lies. I think he is mixed-up because he expects heuristics to have some essential nature that identifies them. But what makes something a heuristic is not its essential nature, but rather its relationship to the problem and the problem-solver. We say that anything that may help you solve a problem has “heuristic value” for you with respect to that problem. But if it is infallible (and also if it halts) then we don’t call it a heuristic. We call it an algorithm. For instance, long division is a guaranteed way for dividing one rational number with a finite number of digits by another such number. However, long division is just a heuristic if we were to apply it to splitting the check at a restaurant. It doesn’t guarantee that everyone will feel that they are paying a fair share.
How about instead of heuristics we think about weapons? Would it be absurd of me to suggest that a weapon is any fallible method of attacking your enemy or winning a battle? Someone might reply “But James, are pickles really weapons? Sand? Wind?” The answer is: they can be, depending on your situation. But you don’t need to catalog all possible weapons. Instead you study the art of combat and learn to spot the things that will help you. Myamoto Musashi wrote exactly about this in 1645:
We cannot speak intelligibly about heuristics without identifying the problem, the problem-solver, and the dynamics of the situation. You can make a list of anything you want, Mr. Anonymous, but can you answer my next questions, which are: what specific problems are you talking about for which these are heuristics and how specifically are they heuristic? Or if you think they aren’t heuristics, what specific problem do you think they can’t help with and why not?