We are reminded, too, of Kekulé of Bonn puzzling over the constitution of benzene, trying in vain to satisfy six carbon atoms with six hydrogen atoms when they wanted fourteen. In the evening as he sat by the fire, his wearied brain refused to rest, and he seemed to see the four-handed carbon imps dancing with their one-armed hydrogen partners on the floor. Suddenly six of them joined hands in a ring and the problem was solved. Since then the benzene sextet has been dancing through hundreds of volumes and has added millions annually to the wealth of Germany. Professor Hilprecht of the University of Pennsylvania has told how a Chaldean priest, custodian of the "Temple Library", appeared to him in a dream and showed him how to put together the fragments of a cuneiform inscription which he had for a long time been striving in vain to translate.
Then there was Stevenson in Samoa, writing for dear life, but not failing to give credit to his "brownies" for doing a large part of his work for him. But the brownies do not work unbidden, and they will not make bricks without straw. Poincaré insists upon the necessity of the preliminary period of conscious effort without which these subliminal inspirations never come and the subsequent period of verification, development, and application, without which they are fruitless. Such ideas came to him most often in the evening or morning when he was in bed and half awake. He did not regard the operations of his unconscious mind as merely mechanical. On the contrary, it is distinguished by the power of choice, selecting and presenting to the conscious ego only those combinations that seem profitable and important. This choice is made, in Poincaré's opinion, under the guidance of the artistic instinct.
The usual combinations are precisely the most beautiful; I mean those which can best charm that special sensibility which all mathematicians recognize but at which the profane are tempted to smile. Among the numerous combinations which the subliminal self has blindly formed, almost all are without interest and without utility. For that reason they have no action upon the æsthetic sensibility and never come into consciousness. Only those that are harmonious and consequently both useful and beautiful are capable of moving that special sensibility of the geometrician of which I spoke, and which, once excited, calls our attention to them and so gives them the chance to become conscious.—"Science et Méthode", p. 58.
Poincaré, if we may believe what he says on this point, was a poor chess player and absolutely incapable of adding up a column of figures correctly. But the reader should beware of the common fallacy of reversing a proposition of this kind and assuming that if he, too, makes mistakes in addition he has the mind of a great mathematician. Poincaré's memory was, however, exceptionally good, especially for figures and formulas. On returning from a walk he was able to recall the numbers of the carriages he had met. When he was in the Polytechnic School he followed the courses in mathematics without taking a note and without looking at the syllabus provided by the professor. He was a rapid mental calculator, using auditive imagery rather than visual. He associated colors with the sound of words.[4]
In this connection may be quoted an anecdote told by M. Jules Sageret:[5] At a conférence in the Superior School of Telegraphy the director called upon him to discuss a very difficult problem in the propagation of the electric current. Poincaré complied and solved the problem without taking any time in preparation. After the conférence the director felicitated him on the solution. "Yes," said Poincaré, "I found the value of x, but is it in kilograms or kilometers?"
Poincaré did not find it profitable to work more than two hours at a time. His custom was to stay at his desk from ten o'clock to noon and from five to seven in the afternoon, never working in the evening after dinner. He drank wine at meals, but never smoked. He went to bed at ten and rose at seven, but did not sleep soundly.
He was a blond, five feet five inches in height and weighed 154 pounds. His head was unusually large, especially in breadth. His eyes were myopic and unsteady. He stood stoopingly with his wrinkled forehead upturned. He spoke somewhat slowly and with a distraught air, as though he were thinking of something else, even though he might be at the time interested and keenly observant. He talked English and German readily and read Latin and Italian. He was fond of music, especially Wagner.
Of the absent-mindedness that had been characteristic of him from youth, many stories are told. Like most mathematicians he was fond of walking while thinking, his fingers opening and closing in an unconscious gesture. One day on his return from a walk he was surprised to find that he was carrying a wicker cage, new and happily empty. He could not imagine how he had got it, but retracing his steps he found upon the sidewalk the stock of the basket maker whom he had innocently despoiled.
When as an engineering student he made a trip to Austria, his mother was afraid he would drop his portfolio sometime without noticing it. So, realizing doubtless that his memory was auditory, she sewed little bells on it. The plan was successful. His mother found on his return that he had brought back in his valise not only the portfolio but also an Austrian bed sheet neatly folded, which, some morning, he had mistaken for his night clothes.
These and similar anecdotes were told by M. Frédéric. Masson when he welcomed M. Poincaré into the Académie Française, January 28, 1909,[6] and it must have been a trifle embarrassing to the new member to listen to such a minute analysis of his life and character addressed to him in the second person. How deftly the director of the Academy mingled eulogy and raillery may be seen from a quotation: