But how much of actually clear comprehension does the number
thus expressed convey to the mind? We say that one place is 100 miles from
another; that A paid B 1000 dollars for a certain piece of property; that a
given city contains 10,000 inhabitants; that 100,000 bushels of wheat were
shipped from Duluth or Odessa on such a day; that 1,000,000 feet of lumber
were destroyed by the fire of yesterday,--and as we pass from the smallest
to the largest of the numbers thus instanced, and from the largest on to
those still larger, we repeat the question just asked; and we repeat it
with a new sense of our own mental limitation. The number 100
unquestionably stands for a distinct conception. Perhaps the same may be
said for 1000, though this could not be postulated with equal certainty.
But what of 10,000? If that number of persons were gathered together into a
single hall or amphitheatre, could an estimate be made by the average
onlooker which would approximate with any degree of accuracy the size of
the assembly? Or if an observer were stationed at a certain point, and
10,000 persons were to pass him in single file without his counting them as
they passed, what sort of an estimate would he make of their number? The
truth seems to be that our mental conception of number is much more limited
than is commonly thought, and that we unconsciously adopt some new unit as
a standard of comparison when we wish to render intelligible to our minds
any number of considerable magnitude.
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