In the second case, with elimination of the hereditary factor, progress must be attributed to social causes, utility and imitation. From all time there have been minds which when face to face with practical problems knew better than others how to extract the essential, and neglect the accessory, in the complex of facts. The utility of abstraction is identical with that of attention, which does not require demonstration; it may be summed up in a single word: to simplify. As the process succeeds, it finds imitators. There is no need to admit at the outset any reflected and fully conscious abstraction: a happy instinct, guided by the needs of life, is sufficient at the commencement. Races that are poorly gifted in this respect, or little apt at imitating their betters, have never got beyond a low level. In effect, abstraction and generalisation are the nerve of all knowledge that transcends sensation. Is this mode of cognition useful? There can be no possible doubt as to the answer. 2. The rôle of inventors corresponds to the fact which, in transformist terminology, is known as spontaneous variation. By inventors, we mean those who are born with the talent or the genius for abstraction. It is superfluous to prove that such have been found, in considerable numbers. They are abstract thinkers by instinct, as others are musicians, mechanicians, designers. The biography of the great mathematicians abounds in examples: Pascal inventing geometry out of a few vague indications from his father; Newton divining Euclid’s demonstrations from the simple enunciation of the theorems; Ampère, before he could read or understand the use of figures, making long calculations by means of a few pebbles; Gauss, at five years old, rectifying the arithmetic of a workman, etc. If fewer analogous facts can be quoted from the other sciences, it is because mathematical precocity is frequent, and is more surprising. All that is the effect of innate disposition: this word serving only to recapitulate our ignorance of the causes which produce such minds. In the development of knowledge by abstraction and generalisation, the first cause—utility—may be likened to the part played by slow actions in geology; whether in the case of practical inventions, or of the constitution of an idiom, it is continuous, collective, and anonymous. The rôle of the great abstract thinkers, on the contrary, resembles the rapid and epoch-making actions.