te 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. For example, we say that A has a
fortune of $1,000,000. The impression is at once conveyed of a considerable
degree of wealth, but it is rather from the fact that that fortune
represents an annual income of $40,000 than, from the actual magnitude of
the fortune itself. The number 1,000,000 is, in itself, so greatly in
excess of anything that enters into our daily experience that we have but a
vague conception of it, except as something very great. We are not, after
all, so very much better off than the child who, with his arms about his
mother's neck, informs her with perfect gravity and sincerity that he
"loves her a million bushels." His idea is merely of some very great
amount, and our own is often but little clearer when we use the expressions
which are so easily represented by a few digits. Among the uneducated
portions of civilized communities the limit of clear comprehension of
number is not only relatively, but absolutely, very low. Travellers in
Russia have informed the writer that the peasants of that country have no
distinct idea of a number consisting of but a few hundred even. There is no
reason to doubt this testimony. The entire life of a peasant might be
passed without his ever having occasion to use a number as great as 500,
and as a result he might have respecting that number an idea less distinct
than a trained mathematician would have of the distance from the earth to
the sun. De Quincey[50] incidentally mentions this characteristic in
narrating a conversation which occurred while he was at Carnarvon, a little
town in Wales. "It was on this occasion," he says, "that I learned how
vague are the ideas of number in unpractised minds. 'What number of people
do you think,' I said to an elderly person, 'will be assembled this day at
Carnarvon?' 'What number?' rejoined the person addressed; 'what number?
Well, really, now, I should reckon-