Pretend games
The mathematician Felix Klein (1849-1925) had a gift for visualizing both problems and their solutions in a concrete way. He was thus able to relate a Platonic solid, the icosahedron, to the solutions of algebraic equations of the fifth degree. Another instance of his particular talent occurred in 1871 when, by focussing on a conic section (e.g. a circular or eliptical disk) bearing either intersecting or nonintersecting linear segments, he was able to induce to coexist within projective geometry seemingly mutually incompatible euclidean and noneuclidean (Lobachevski; 1826 and Riemann, 1868) geometries.
Could there be any relation between a mathematician’s imaginings such as the afore-mentioned classic example, and “pretend games” of children? In such games, the players agree upon some rule. It defines the universe of the game. Kids are happy from abeyance of their self-imposed rule: nothing is more strict than a world of fantasy. Which goes some way toward explaining the intolerance of similar behavior in adults, quickly labeled as insane — unless their “pretend game” stays within the confines of the mind (as in the gedanken experiments of scientists) or of the bedroom
In like manner as projective geometry — a move to integrate both euclidean and noneuclidean geometries into a new, coherent whole —, pretend games make their players project themselves, out of everyday reality, elsewhere: into another being, with a different gender or identity; into another environment. By tradition, adult pretend games have been fenced into special reserves in time and in space.
The best known example is Carnival and its masks, whether in Cologne, Venice, Rio de Janeiro or the Mardi-Gras festivities in New Orleans. The temporary indulgence only serves to call attention to the ordinary intolerance of such behavior, of such transgressions of the ordinary social order.
To pretend: “X was a pretender to the throne of Ruritania. Y pretended she was Anastasia. Z pretended he could heal by mere imposition of the hands.” In all such cases of pretending, imposture lurks. The pretender tries to make other people share the delusion and believe too in an assumed identity, in the mask he or she has chosen to wear. Indeed, sometimes this works and people are conned and are fooled into doing so: “to pretend” derives from the Latin verb tendere with the meaning “to stretch.” Pretentiousness stretches the imagination. Pretence is tolerated actually only, as we saw, in special times such as Carnival; and in special places, such as the mind and the theater stage, besides erotic play in the bedroom.
In spite of being ruled out from ordinary social interaction, pretend games are a tool to scientific thought. I know empirically that the sky is blue. As a scientist, I trust light scattering to be the explanation. However, it is a normal impulse on the part of any scientist to raise the question: what if scattering were to vary, not as the wavelength to fourth power, but as its inverse, say? What would other consequences be, besides the sky turning red (but bluish at sunset)?
True, such fantasies are deemed by some irresponsible and irrelevant. Hypothesis non fingo famously wrote Newton. However, even though he meant for his style of science to conform with an exclusively inductive model, the hypothetico-deductive style of scientific argument had a field day after his time (and the Master of the Mint himself in private indulged in flights of alchemical fancy, intent as he was upon elucidating the ultimate truth of matter).
Flights of fancy? Scientific communities at various times were at best ambivalent toward them. In general, they are frowned upon, censored, repressed. Hence, an individual scientist harboring a “crazy idea” is even more careful than usual in divulgation. Success will redeem what would otherwise have appeared as a fantasy of his imagining only.
We need a history of the scientific imagination. There are times when such excursions become looked upon more favorably. Perhaps, our present period is such a time. The “Butterfly Effect” on the worldwide weather pattern may well be emblematic of our episteme. We have just witnessed the vogue of chaos theories, which may be taken as one of the signs of a collective escapism, away from the dreary seriousness of predictable linear, deterministic phenomena. Historians studying the alternance of seriousness and play in science may find a more or less regular recurrence of seriousness and play, of times when scientists are tolerated in the playroom more than they usually are.
Flights of fancy? They include rebellion too. Whereas society severely constrains the Carnival spirit, science encourages the kindred spirit of derision, directed against authority. It nurtures the playful wearing of a mask, it will tolerate thought, so long as it is genuine, giving itself the most outrageous vestments.
Challenging an accepted norm is both the daily bread and the Sunday cake in scientific life. Science thrives on discussion and controversy, institutionalizes them in allocation of resources and in publishing (under the anonymous mask of reviewers and referees), in seminars and conferences (the presentation is followed by a discussion), or in the Ph. D. ceremony (with the participation, in one form or another, of a devil’s advocate). Moreover, the advancement of knowledge often proceeds with the elision or erasure of earlier work, whenever a gadfly of a scientist takes exception to it out of disrespect, simply because there has been little room for dogmas and sacred cows in science ever since the Renaissance.
There is the challenging of an accepted norm. But there is also challenging as the accepted norm, by which I mean episodes in which a scientist dares others to a predefined performance, to jump through a hoop: a mathematician such as David Hilbert, André Weil or Paul Erdös issues a conjecture; some committee challenges fellow-chemists to synthesize a molecule picked as an iconic emblem for a conference (congressane, in a true story of the 1960s); or another group of scientists, such as an academy, sets-up a prize to be awarded to the first person to succeed in some predefined difficult achievement.
Flights of fancy? They are strongly encouraged in the devising of hypotheses. There are many examples and, usually, the scientific imagination is likened to that of the artist or the novelist: John Tyndall wrote in that vein in 1874, to mention just this example. However, the scientific realist demands some form of control over the imagination. And this is the role of experimental procedures.
There are quite a few other aspects, such as role-playing, humor and wit, the little cartoons and signs which adorn laboratory space, jokes and hoaxes, which come under the province of this topic of science as play. They deserve close study too. I might devote myself to it in the near future.
Thus, I should like to devote the next stretch in this lecture to examining a single question, because it underlines everything I have said so far.