242 THE FACTORS OF THE MIND

algebra. And actually, as we have seen, there is now an
instrument of analysis which enables us to reason with
exactitude, and at the same time to avoid specifying, not
only the variables, but also the relations between them.
It carries the somewhat uninformative title of the ' theory
of groups,5 and has been defined as " a kind of super-
mathematics in which the operations are as unknown as the
quantities on which they operate." To parody Bertrand
Russell's famous definition, we might say that it consists of
sums in which the mathematician can never know what the
sums are about, nor what figures he is working with, nor
yet what mathematical operations he is supposed to be
performing, nor even whether his operations are mathe-
matical at all.

I have already noted the successful use of the method in
problems of quantum physics. There is little question in
my own mind that the theory of groups could be applied
with equal success to the analogous problems in psychology ;
for, if it is doubtful whether material processes are subject
to the laws of addition and multiplication, the doubt is
far greater when we turn to mental processes : in psychology
even more than in physics,1 " not only the actors, but even
their actions are unknown." Here, then, as it appears to
me, is a line of advance which the theoretical factorist might
well attempt in the near future.

Practical Implications.—My emphasis on relations, how-
ever, as forming the only concepts we can safely work with,
is not to be regarded as a conclusion for the theorist alone :
it has implications for the practical worker as well. In the
psychological clinic the notion that a child's mind is a
kind of substance with causal properties of its own—
* abilities3 and ' tendencies ? that can be summed up by a
few simple assessments—engenders very primitive modes of
examination and treatment. Teachers, parents, doctors,

is really a special case of the product theorem as relating to classes, which in
turn is a special case of the product theorem as relating to proportions. An
equation merely states a mutual implication. The root of an equation
defines a class. Multiplication by a selective, operator is equivalent to the
operation of selecting a class. And so on.
1 Eddington, loc. cit* sup*