In my reading of J. M. Coetzee’s The Lives of Animals, I find an interesting discussion about Wolfgang Köhler’s study of the mentality of apes. Coetzee’s novella and the ensuing opinion pieces by Marjorie Garber, Peter Singer, Wendy Doniger, and Barbara Smuts provide various perspectives on the issue of animal rights. But, from reading about Köhler’s study, I am struck by something else which is subordinate to the novel but of paramount importance to my day-to-day work.
Köhler’s subject is a chimpanzee named Sultan. In an attempt to examine how apes respond to a challenging problem, Köhler arranges for a bunch of bananas to be hung in Sultan’s cage from a wire such that they are three meters above the ground. He leaves three wooden crates inside the cage. Now, as Elizabeth Costello in the book hypothesizes, Sultan can think several thoughts:
- Why is he starving me?
- What have I done?
- Why has he stopped liking me?
- Why does he not want these crates any more?
- What miconception causes him to believe that it is easier for me to reach the banana hanging from the wire than it is to pick it up from the floor.
From the perspective of solving the problem, all these thoughts are wrong. The right one, of course, is “How does one use the crates to reach the bananas?”
I commiserate with Sultan, because every day I think of “wrong” thoughts – wrong ways to attack a research problem; syntactically correct, but functionally inefficient ways to write code; wrong assumptions in a derivation; starting with a useless hypothesis; right paths to the wrong solution; wrong paths to the right solution. Sometimes, this becomes endlessly frustrating, and I often wonder how one is supposed to “think the right thought”, in the context of problem-solving.
Motivation alone does not do it: Sultan may become hungrier by the minute, but his brain must know beforehand that a crate can be stood upon. I could be incredibly motivated by an approaching deadline, but I can’t solve a problem, if I don’t know the underlying theory.
Knowledge wedded to motivation is also insufficient at times: Sultan might know that he can stand upon a box, but he needs to remember a previous experience of having stood up on something in order to reach for something else. I was once asked a complicated probability question in a 10 minute oral exam. Approaching the solution from first principles would have been nearly impossible (for me at least.). I could solve it only because I knew how to begin, having previously practiced several problems which had been formulated similarly.
Next, is the ability to form connections. We can only go so far by referring to old problems. To generate new problems and to solve them, one must be able to connect the motifs from old problems with those in the new problem, and to extrapolate the old ideas up to a point where they convey some new information. This, of course, requires a certain amount of innate intelligence.
But this is still not the whole story. Intelligence is used to form connections by taking recourse to logic (If A then B, then C, and so on). But it is also used to jump over obstacles, to see the solution before we have arrived at it, by means of intuition. If Sultan has never seen a box before, has never stood upon something before, could there be any way in which he would just “guess” that the top of a stack of crates is closer to the bananas? This phenomenon occurs all the time in some fields of mathematics. The mathematician guesses – by a process that is sometimes logical and sometimes not – that the answer to the problem is X, and then proceeds backwards to prove that X is the correct answer. Of course, he has to be rigorous and check whether X is the only possible answer or just one of a number of possibilities. A great many mathematical results are proved in this way. I have a new-found admiration for the restraint necessary in such situations – the ability to not get carried away by the intuited solution, to not confuse cause and effect. Last week, in a fit of inspired guesswork, I wrote down a certain result and then proceeded to prove it. It turned out that the result was correct, but due to haste, carelessness, and inexperience, one of the arguments in my proof was completely bogus! I didn’t realize it until I explained it to a friend who pointed out the embarrassingly obvious error.
For a faculty that we exercise so much and so often, it is ironic that thinking the right thought should be so hard.