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This and other functions of laughter can be exaggerated so that it
becomes as the crackling of thorns under the pot, and prevents men
from taking anything seriously; but in due proportion its value is
very great as a lubricant against troublesome friction and a lightener
of the inevitable gravity and horror or life, which would otherwise
become portentous and overshadowing. True laughter, like true
speech, is a unique possession of man.
Those of man's unique characteristics which may better be called
psychological and social than narrowly biological spring from one or
other of three characteristics. The first is his capacity for abstract and
general thought: the second is the relative unification of his mental
processes, as against the much more rigid compartmentalization of
animal mind and behaviour: the third is the existence of social units,
such as tribe, nation, party, and church, with a continuity of their
own, based on organized tradition and culture.
There are various by-products of the change from pre-human to
the human type of mind which are, of course, also unique biologic-
ally. Let us enumerate a few: pure mathematics; musical gifts;
artistic appreciation and creation; religion; romantic love.
Mathematical ability appears, almost inevitably, as something
mysterious. Yet the attainment of speech, abstraction, and logical
thought, bring it into potential being. It may remain in a very rudi-
mentary state of development; but even the simplest arithmetical
calculations are a manifestation of its existence. Like any other
human activity, it requires proper tools and machinery. Arabic
numerals, algebraic conventions, logarithms, the differential calculus,
are such tools: each one unlocks new possibilities of mathematical
achievement. But just as there is no essential difference between
man's conscious use of a chipped flint as an implement and his design
of the most elaborate machine, so there is none between such simple
operations as numeration or addition and the comprehensive flights
of higher mathematics. Again, some people are by nature more
gifted than others in this field; yet no normal human being is unable
to perform some mathematical operations. Thus the capacity for
mathematics is, as I have said, a by-product of the human type of
We have seen, however, that the human type of mind is distin-
guished by two somewhat opposed attributes. One is the capacity for
abstraction, the other for synthesis. Mathematics is one of the
extreme by-products of our capacity for abstraction. Arithmetic
abstracts objects of all qualities save their enumerability; the symbol
TT abstracts in a single Greek letter a complicated relation between the