The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to StatisticsVenn, John
Philosophy
The Logic of Chance, 3rd edition: An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics
Venn, John
Chance; Logic, Symbolic and mathematical; Probabilities; Science -- Methodology
But then, as Mr Galton insists, if such agencies acted
freely and independently, though we should get the same
_kind_ of arrangement or distribution, we should not get the
same _degree_ of it: there would, on the contrary, be a tendency
towards further dispersion. The 'curve of facility' (v. the
diagram on p. 29) would belong to the same class, but would
have a different modulus. We shall see this at once if we
take for comparison a case in which similar agencies work
their way without any counteraction whatever. Suppose, for
instance, that a large number of persons, whose fortunes
were equal to begin with, were to commence gambling or
betting continually for some small sum. If we examine
their circumstances after successive intervals of time, we
should expect to find their fortunes distributed according to
the same general law,--i.e. the now familiar law in question,--but
we should also expect to find that the poorest
ones were slightly poorer, and the richest ones slightly
richer, on each successive occasion. We shall see more
about this in a future chapter (on _Gambling_), but it may
be taken for granted here that there is nothing in the laws
of chance to resist this tendency towards intensifying the extremes.
Now it is found, on the contrary, in the case of vital
phenomena,--for instance in that of height, and presumably
of most of the other qualities which are in any way characteristic
of natural kinds,--that there is, through a number of
successive generations, a remarkable degree of fixity. The
tall men are not taller, and the short men are not shorter,
per cent. of the population in successive generations: always
supposing of course that some general change of circumstances,
such as climate, diet, &c. has not set in. There
must therefore here be some cause at work which tends, so
to say, to draw in the extremes and thus to check the otherwise
continually increasing dispersion.
17. The facts were first tested by careful experiment.
At the date of Mr Galton's original paper on the subject,[3]
there were no available statistics of heights of human beings;
so a physical element admitting of careful experiment (viz.
the size or weight of certain seeds) was accurately estimated.
From these data the actual amount of reversion from the
extremes, that is, of the slight pressure continually put upon
the extreme members with the result of crowding them back
towards the mean, was determined, and this was compared
with what theory would require in order to keep the characteristics
of the species permanently fixed. Since then,
statistics have been obtained to a large extent which deal
directly with the heights of human beings.
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