It can not be too strongly emphasized that this is a statistical law,
not a biological law. It must not be applied to predict the character of
the offspring of any one particular mating, for it might be highly
misleading. It would be wholly unjustified, for example, to suppose that
a certain man got three-tenths of his nature from his father, because
the Law of Ancestral Heredity required it: in point of fact, he might
get one-tenth or nine-tenths, none or all of a given trait. But, when
dealing with a large population, the errors on one side balance the
errors on the other, and the law is found, in the cases to which it has
been applied, to express the facts.[51]
While, therefore, this Galton-Pearson law gives no advice in regard to
individual marriages, it is yet of great value to applied eugenics. In
the first place, it crystallizes the vague realization that remote
ancestry is of much less importance than immediate ancestry, to an
individual, while showing that every generation has a part in making a
man what he is. In the second place, it is found, by mathematical
reasoning which need not here be repeated, that the type of a population
may be quickly changed by the mating of like with like; and that this
newly established type may be maintained when not capable of further
progress.
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