86 THE FACTORS OF THE MIND

hand,, the avowed identification of the abstract methods may
lead to an unconscious and unwarranted identification of
the concrete subjects : and thus, though the processes
designated by the numbers or the points are no longer
material but mental, the spatial terminology is still apt to
suggest a spatial and physical interpretation. Mental
factors are described as * mental forces3 or as < mental
energy ? ; and these phrases in their turn are subsequently
treated, not as bold metaphors, but as implying something
fundamentally kinetic.

It would appear, therefore, urgently desirable to trace out
the correspondence in clearer and more explicit terms.
Although in themselves non-spatial, mental conceptions,
I suggest, may nevertheless be legitimately given a spatial
representation if we accept the following principles. The
initial steps, it will be observed, are analogous to those
adopted in other sciences—in thermo-dynamics, for example
—where the language of analytic geometry is used in for-
mulating somewhat similar problems,

(i) The first step involves no difficulty. A point at the
end of a line, having a fixed origin and a specified direction,
may be used to represent, not only an actual line having the
same relative direction and the same proportionate length,
but also motion along that line, and (if the masses moved
and the time of the movements are assumed to be the same)
the forces implied byl such movements. Thus a line on a
map might be used to indicate, not only the distance from
Dover to Calais, but also the force required to move a vessel

1 I do not say the i forces causing such movements,5 By a force I under-
stand, not a perceptible push or pull (such as we ourselves might feel in a tug
of war), but a certain abstract algebraic function of mass and motion, lending
itself to convenient statements of equality (as in formulating the conditions
for two or more poised weights in equilibrium). Thus, instead of talking of
such and such a movement as produced by such and such a ' cause,' it would
be better to say that the movement appears as the necessary logical conse-
quence of some conceivable change that is logically prior. The point is
important in psychology, because of the popular associations still clinging
to the terms force and energy : these lead the student to think such phrases
as * mental force? or c energy' refer to a perceptible effort or exertion ;
whereas, at any rate in the present context (cognitive testing), they refer
merely to the relative efficiency of the mental process.