Teasing out a solution
Newton’s half-niece was named Catherine Conduitt and she sent to Fontenelle her written recollections of Newton’s life. It includes the following story, which will serve me as an exemplum : In 1697, when Newton was Master of the Mint, upon coming home one day after a hard day’s work, found waiting for him at 4 PM the brachistochrone problem. He had solved it before going to bed: it was “child’s play” to the great mathematician.
The anecdote conjoins science and play, which is cause enough for selecting it for consideration here. But what kind of science? This is science as puzzle-solving. Newton was presented with a problem and he found a solution to it. Furthermore, by way of commenting on the intrinsic difficulty of the problem, he (or the onlookers) termed it “child’s play.”
Indeed, there is an association between play, as children are wont to do, and problem-solving. A puzzle consists of a question, a quandary which cannot be resolved at first sight. It has to be set apart. Hence, it deserves study and it needs some thought before it receives an answer. Etymologically, a puzzle is indeed the term for a problem being posed: the English word derives from the Latin verb ponere, whose original meaning was to “set apart.”
Among puzzles, there are jigsaw puzzles, games both children and adults play. They confront their player with two-dimensional fragments, each with a characteristic shape, from which to reconstruct an overall picture.
Real-life jigsaws puzzle are part of what archeologists do. They have to reconstitute for instance a Greek vase from a set of small pieces. Which brings up my second exemplum. As a child, Dorothy Crowfoot’s parents gave her the task of assembling, likewise from fragments, an ancient mosaic: later on, when she had become an X-ray crystallographer of proteins, she said that this early experience determined her life’s work, it gave her a taste for solving problems of comparable awesome complexity.
The Newton and Crowfoot exempla share the difficulty of the problem to be solved, the sheer complexity of the task to be accomplished. They are illustrative of many other problems as well, in the display of a dual ability, fixation on a problem i.e. volition; and a cognitive skill, guessing at the solution. What does guessing entail?
Guessing is a mental action common to many spheres. It connects science and gambling: the gambler guesses all the time. He or she will guess the outcome of a draw by lot: the gambler tells himself “which lottery ticket should I pick, which number in the roulette game ought I to put my money on, who is going to win the American presidential race?” But gambling is not all bad, it embodies also daring, being adventuresome, which can be turned into qualities by a scientific mind.
Guessing the solution of a science problem, as in the Newton or the Crowfoot anecdotes, is a bit more involved. It does not reduce to picking arbitrarily a number out of the blue. When putting together the solution to a problem, the scientist inspects each piece for its logical interconnectedness with its neighbors and, link by link, constructs a whole argument (or rebuilds a Roman mosaic). In so doing, the problem-solver faces complexity: a priori, the problem presents numerous potential configurations for its solution.
The scientist has to tease out a solution from such a hyperspace. The verb “to tease” meant originally “to pluck, to disentangle,” where the referred-to was very concrete, flax or wool. As such, “to tease” is related to another, related object “the clue” which, originally, Ariadne’s thread-like, was a rolled ball of string. The problem-solver, confronted with a randomly coiled knot posing an awesome task of unraveling, has this uncanny ability of teasing out a clue; which ultimately will be turned into a solution.
After this short reminder on textiles and problem-solving, which ought to make clear my strong belief in feminine hands as the original problem-solvers, let us return to guessing and guesses. I mentioned the interesting etymology of “tease.” That of “guess” is a bit more ordinary, it is merely a variant of the verb “to get”. Nevertheless, it finds its place in my argument. “To guess” is to get at a result, true. But how? The characteristic of the guess is the short cut. The economy of the effort is what made witnesses, such as Catherine Conduitt, describing Newton’s tackling of a problem as “child’s play.” The problem solver displays an admirable ability to obtain the solution, not so much by methodically building a logical chain, examining at each step all the possible alternatives, but by somehow grasping the whole concatenation in a single fell swoop. No wonder that philosophers, ever since Plato, have been left to evoke a divine revelation or a private daimon, a flash of intuitive clarity, to describe such Eurêka moments.
I won’t venture a guess as to how and where guesses are made, it may lead into infinite regression. It is more useful to consider outguessing. This feature of the guessing game arises from the superiority of some guesses to others. Some guesses are plainly wrong. Also, a set of guesses may be inferior to another. The gambler makes guesses which are statistically inferior to those of the bank.
Sometimes, we are lured into making the wrong guess. This is a key ingredient in many jokes. Riddles too are based on outguessing. I shall take as my example number 61 in the Exeter book of riddles:
“A woman, young and lovely, often locked me
in a chest; she took me out at times,
lifted me with fair hands and gave me
to her loyal lord, fulfilling his desire.
Then he stuck his head well inside me,
pushed it upwards into the smallest part.
It was my fate, adorned as I was, to be filled
with something rough if that person who possessed me
was virile enough. Now guess what I mean.”
In this typical case of double-entendre, we outguess ourselves i.e. we blind ourselves to the “intended” solution (“a helmet”) with the solution both obvious and lewd (“vagina”).
The epistemic lesson is the need to get underneath the obvious: the important meaning hides below the apparent meaning. The one solution to aim for is the secret solution. Guessing is not enough. One has to make the correct guess.
For instance, both Dorothy Wrinch and Linus Pauling were trying in the late Thirties and early Forties to guess at the structure of proteins, instrumentally, by building models. Pauling outguessed Wrinch. His theory, with alpha helices and beta sheets as the well-ordered structural modules, was correct. Her cyclol theory, with rings as the well-ordered structural modules, turned out to be incorrect.
There is an element of play in guessing. The play comes, as in the Pauling-Wrinch rivalry, from one-upmanship: each scientist tries to outwit and to outguess the others in the field. But competition is only part of the explanation. The playfulness, and this is a more general argument, has to do with the incompleteness of science. At any time, any given problematic phenomenon stirs up at least two classes of solutions, pertinent and non-pertinent (Wrinch’s cyclol theory was non-pertinent). It can even be the case that the latter obscure and hide the former for a time.
Scientific research, just like the child in a treasure-hunt, just like the gambler aiming for the jackpot, identifies with playing to the extent that it makes guesses, not only about how to best solve a problem, but also about which problem it is most important to solve. To play, in this epistemic sense, is to aim for a goal unidentified previously. When Linus Pauling started dabbling in biochemistry in the 1930s, little did he suspect that he would specifically elucidate the structure of proteins.
Scientists do not play only at outguessing one another. They also play with a number of toys. This is the next topic I shall address.