(2) Numerical imagination in the sciences does not take on these delirious forms; it has the advantage of resting on an objective basis: it is the substitute of an unrepresentable reality. Scientific culture, which people often accuse of stifling imagination, on the contrary opens to it a field much vaster than esthetics. Astronomy delights in infinitudes of time and space: it sees worlds arise, burn at first with the feeble light of a nebular mass, glow like suns, become chilled, covered with spots, and then become condensed. Geology follows the development of our earth through upheavals and cataclysms: it foresees a distant future when our globe, deprived of the atmospheric vapors that protect it, will perish of cold. The hypotheses of physics and chemistry in regard to atoms and molecules are not less reckless than the speculations of the Hindoo imagination. "Physicists have determined the volume of a molecule, and referring to the numbers that they give, we find that a cube, a millimeter each way (scarcely the volume of a silkworm's egg), would contain a number of molecules at least equal to the cube of 10,000,000—i.e., unity followed by twenty-one zeros. One scientist has calculated that if one had to count them and could separate in thought a million per second, it would take more than 250,000,000 years: the being who commenced the task at the time that our solar system could have been no more than a formless nebula, would not yet have reached the end."[92] Biology, with its protoplasmic elements, its plastids, gemmules, hypotheses on hereditary transmission by means of infinitesimal subdivisions; the theory of evolution, which speaks off-hand of periods of a hundred thousand years; and many other scientific theses that I omit, offer fine material for the numerical imagination.
More than one scientist has even made use of this form of imagination for the pleasure of developing a purely fanciful notion. Thus Von Baer, supposing that we might perceive the portions of duration in another way, imagines the changes that would result therefrom in our outlook on nature: "Suppose we were able, within the length of a second, to note 10,000 events distinctly, instead of barely 10, as now; if our life were then destined to hold the same number of impressions, it might be 1,000 times as short. We should live less than a month, and personally know nothing of the change of seasons. If born in winter, we should believe in summer as we now believe in the heats of the Carboniferous era. The motions of organic beings would be so slow to our senses as to be inferred, not seen. The sun would stand still in the sky, the moon be almost free from change, and so on. But now reverse the hypothesis and suppose a being to get only one 1,000th part of the sensations that we get in a given time, and consequently to live 1,000 times as long. Winters and summers will be to him like quarters of an hour. Mushrooms and the swifter-growing plants will shoot into being so rapidly as to appear instantaneous creations; annual shrubs will rise and fall from the earth like restlessly boiling water springs; the motions of animals will be as invisible as are to us the movements of bullets and cannonballs; the sun will scour through the sky like a meteor, leaving a fiery trail behind him, etc."[93]
The psychologic conditions of this variety of the creative imagination are, then, these: Absence of limitation in time and space, whence the possibility of an endless movement in all directions, and the possibility of filling either with a myriad of dimly-perceived events. These events not being susceptible of clear representation as to their nature and quantity, escaping even a schematic representation, the imagination makes its constructions with substitutes that are, in this case, numbers.
IV
Musical Imagination
Musical imagination deserves a separate monograph. As the task requires, in addition to psychological capacity, a profound knowledge of musical history and technique, it cannot be undertaken here. I purpose only one thing, namely, to show that it has its own individual mark—that it is the type of affective imagination.
I have elsewhere[94] attempted to prove that, contrary to the general opinion of psychologists, there exists, in many men at least, an affective memory; that is, a memory of emotions strictly so called, and not merely of the intellectual conditions that caused and accompanied them. I hold that there exists also a form of the creative imagination that is purely emotional—the contents of which are wholly made up of states of mind, dispositions, wants, aspirations, feelings, and emotions of all kinds, and that it is the characteristic of the composer of genius, of the born musician.
The musician sees in the world what concerns him. "He carries in his head a coherent system of tone-images, in which every element has its place and value; he perceives delicate differences of sound, of timbre; he succeeds, through exercise, in penetrating into their most varied combinations, and the knowledge of harmonious relations is for him what design and the knowledge of color are for the painter: intervals and harmony, rhythm and tone-qualities are, as it were, standards to which he relates his present perceptions and which he causes to enter into the marvelous constructions of his fancy."[95]
These sound-elements and their combinations are the words of a special language that is very clear for some, impenetrable for others. People have spoken to a tiresome extent of the vagueness of musical expression; some have been pleased to hold that every one may interpret it in his own way. We must surely recognize that emotional language does not possess the precision of intellectual language; but in music it is the same as in any other idiom: there are those who do not understand at all; those who half understand and consequently always give wrong renderings; and those who understand well—and in this last category there are grades as varying as the aptitude for perceiving the delicate and subtle shades of speech.[96]