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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:
starting 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

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.

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