Numerical Imagination

Under this head I designate the imagination that takes pleasure in the

unlimited--in infinity of time and space--under the form of number. It

seems at first that these two terms--imagination and number--must be

mutually exclusive. Every number is precise, rigorously determined,

since we can always reduce it to a relation with unity; it owes nothing

to fancy. But the series of numbers is unlimited in two directions:

sta ting from any term in the series, we may go on ever increasingly or

ever decreasingly. The working of the mind gives rise to a possible

infinity that is limitless: it thus traces a route for the movement of

the imagination. The number, or rather the series of numbers, is less an

object than a vehicle.



This form of imagination is produced in two principal ways--in religious

conceptions and cosmogonies, and in science.



(1) Numerical imagination has nowhere been more exuberant than among the

peoples of the Orient. They have played with number with magnificent

audacity and prodigality. Chaldean cosmogony relates that Oannes, the

Fish-god, devoted 259,200 years to the education of mankind, then came a

period of 432,000 years taken up with the reigns of mythical personages,

and at the end of these 691,000 years, the deluge renewed the face of the

earth. The Egyptians, also, were liberal with millions of years, and in

the face of the brief and limited chronology of the Greeks (another kind

of imagination) were wont to exclaim, "You, O Greeks, you are only

children!" But the Hindoos have done better than all that. They have

invented enormous units to serve as basis and content for their numerical

fancies: the Koti, equivalent to ten millions; the Kalpa (or the age

of the world between two destructions), 4,328,000,000 years. Each Kalpa

is merely one of 365 days of divine life: I leave to the reader, if he is

so inclined, the work of calculating this appalling number. The Djanas

divide time into two periods, one ascending, the other descending: each is

of fabulous duration, 2,000,000,000,000,000 oceans of years; each ocean

being itself equivalent to 1,000,000,000,000,000 years. "If there were a

lofty rock, sixteen miles in each dimension, and one touched it once in a

hundred years with a bit of the finest Benares linen, it would be reduced

to the size of a wango-stone before a fourth of one of these Kalpas had

rolled by." In the sacred books of Buddhism, poor, dry, colorless, as they

ordinarily are, imagination in its numerical forms is triumphant. The

Lalitavistara is full of nomenclatures and enumerations of fatiguing

monotony: Buddha is seated on a rock shaded by 100,000 parasols,

surrounded by minor gods forming an assemblage of 68,000 Kotis (i.e.,

680,000,000 persons), and--this surpasses all the rest--"he had

experienced many vicissitudes during 10,100,000,000 Kalpas." This makes

one dizzy.



(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." 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."



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.