[The enigmatical motto of Marischal College, Aberdeen: They say; what say they; let them say.] It expresses the three stages of an undergraduate’s career. “They say”—in his first year he accepts everything he is told as if it were inspired. “What say they”—in his second year he is skeptical and asks that question. “Let them say” expresses the attitude of contempt characteristic of his third year.

Theories thus become instruments, not answers to enigmas, in which we can rest. We don’t lie back upon them, we move forward, and, on occasion, make nature over again by their aid.

A strange enigma is man! Someone calls him a soul concealed in an animal.

All the events which occur upon the earth result from Law: even those actions which are entirely dependent on the caprices of the memory, or the impulse of the passions, are shown by statistics to be, when taken in the gross, entirely independent of the human will. As a single atom, man is an enigma; as a whole, he is a mathematical problem. As an individual, he is a free agent; as a species, the offspring of necessity.

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made I ended up in the domain of mathematics.

I am always wandering around in enigmas.

I recall my own emotions: I had just been initiated into the mysteries of the complex number. I remember my bewilderment: here were magnitudes patently impossible and yet susceptible of manipulations which lead to concrete results. It was a feeling of dissatisfaction, of restlessness, a desire to fill these illusory creatures, these empty symbols, with substance. Then I was taught to interpret these beings in a concrete geometrical way. There came then an immediate feeling of relief, as though I had solved an enigma, as though a ghost which had been causing me apprehension turned out to be no ghost at all, but a familiar part of my environment.

It did not cause anxiety that Maxwell’s equations did not apply to gravitation, since nobody expected to find any link between electricity and gravitation at that particular level. But now physics was faced with an entirely new situation. The same entity, light, was at once a wave and a particle. How could one possibly imagine its proper size and shape? To produce interference it must be spread out, but to bounce off electrons it must be minutely localized. This was a fundamental dilemma, and the stalemate in the wave-photon battle meant that it must remain an enigma to trouble the soul of every true physicist. It was intolerable that light should be two such contradictory things. It was against all the ideals and traditions of science to harbor such an unresolved dualism gnawing at its vital parts. Yet the evidence on either side could not be denied, and much water was to flow beneath the bridges before a way out of the quandary was to be found. The way out came as a result of a brilliant counterattack initiated by the wave theory, but to tell of this now would spoil the whole story. It is well that the reader should appreciate through personal experience the agony of the physicists of the period. They could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays, and Fridays they must look on light as a wave; on Tuesdays, Thursdays, and Saturdays, as a particle. On Sundays they simply prayed.

Round about what is, lies a whole mysterious world of might be, — a psychological romance of possibilities and things that do not happen. By going out a few minutes sooner or later, by stopping to speak with a friend at a corner, by meeting this man or that, or by turning down this street instead of the other, we may let slip some great occasion good, or avoid some impending evil, by which the whole current of our lives would have been changed. There is no possible solution to the dark enigma but the one word, “Providence.”

The history of chemistry is properly divided into the mythologic, the obscure, and the certain. The first period exhibits it from its infancy, deformed by fictions, until the destruction of the library of Alexandria by the Arabs. —The second, though freed in some measure from these absurdities, yet is still clothed in numberless enigmas and allegorical expressions.— The third period commences at the middle of the seventeenth century, with the first establishment of societies and academies of science; of which the wise associates, in many places uniting their efforts, determined to pursue the study of Natural Philosophy by observation and experiments, and candidly to publish their attempts in a general account of their transactions.

The one who stays in my mind as the ideal man of science is, not Huxley or Tyndall, Hooker or Lubbock, still less my friend, philosopher and guide Herbert Spencer, but Francis Galton, whom I used to observe and listen to—I regret to add, without the least reciprocity—with rapt attention. Even to-day. I can conjure up, from memory’s misty deep, that tall figure with its attitude of perfect physical and mental poise; the clean-shaven face, the thin, compressed mouth with its enigmatical smile; the long upper lip and firm chin, and, as if presiding over the whole personality of the man, the prominent dark eyebrows from beneath which gleamed, with penetrating humour, contemplative grey eyes. Fascinating to me was Francis Galton’s all-embracing but apparently impersonal beneficence. But, to a recent and enthusiastic convert to the scientific method, the most relevant of Galton’s many gifts was the unique contribution of three separate and distinct processes of the intellect; a continuous curiosity about, and rapid apprehension of individual facts, whether common or uncommon; the faculty for ingenious trains of reasoning; and, more admirable than either of these, because the talent was wholly beyond my reach, the capacity for correcting and verifying his own hypotheses, by the statistical handling of masses of data, whether collected by himself or supplied by other students of the problem.

The wounded surgeon plies the steel
That questions the distempered part;
Beneath the bleeding hands we feel
The sharp compassion of the healer’s art
Resolving the enigma of the fever chart.

This is, in truth, the first charm of chemistry, and the secret of the almost universal interest excited by its discoveries. The serious complacency which is afforded by the sense of truth, utility, permanence, and progression, blends with and ennobles the exhilarating surprise and the pleasurable sting of curiosity, which accompany the propounding and the solving of an Enigma... If in SHAKPEARE [sic] we find Nature idealized into Poetry, through the creative power of a profound yet observant meditation, so through the meditative observation of a DAVY, a WOOLLASTON [sic], or a HATCHETT; we find poetry, as if were, substantiated and realized in nature.

This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is seen to be an enigma only as an individual: in the mass he is a mathematical problem.

Through the naturalist’s eyes, a sparrow can be as interesting as a bird of paradise, the behaviour of a mouse as interesting as that of a tiger, and a humble lizard as fascinating as a crocodile. … Our planet is beautifully intricate, brimming over with enigmas to be solved and riddles to be unravelled.

Ye daring ones! Ye venturers and adventurers, and whoever of you have embarked with cunning sails on unexplored seas! Ye enjoyers of enigmas! Solve unto me the enigma that I then beheld, interpret for me the vision of the loneliest one. ... O my brethren, I heard a laughter which was no human laughter.