with the natural motions of bodies. We
can conceive such a performance to be accompanied by an almost entire
failure to grasp its essentials. It would then be necessary for nearly
the whole situation to be repeated in order to induce in the monkey the
same action and expectation. He would require a similar form, color, and
distance. But he might, on the other hand, regard as practically
identical all suspended and freely swinging bodies capable of affording
him support, and quite independently of their shape, size, time, or
place. In this latter case his skill would be applicable to the widest
possible number of cases that could present themselves. Having a
discerning eye for essentials, he would lose no chance of a swing
through looking for more than the bare necessities. When the
physicist describes the pendulum in terms of a formula such as
t = 2pi[squareroot(l/g)] he exhibits a similar discernment. He has
found that the time occupied by an oscillation of any pendulum may be
calculated exclusively in terms of its length and the acceleration due
to gravity. The monkey's higher proficiency and the formula alike
represent a knowledge that is free in the sense that it is contained in
terms that require no single fixed context in immediacy. The knowledge
is valid wherever these essential terms are present; and calculations
may be based upon these essential terms, while attendant circumstances
vary _ad infinitum_. Such knowledge is said to be _general_ or
_universal_.

There is another element of freedom, however, which so far has not been
attributed to the monkey's knowledge, but which is evidently present in
that of the physicist. The former has a practical ability to deal with a
pendulum when he sees it. The latter, on the other hand, knows about a
pendulum whether one be present or not. His knowledge is so retained as
always to be available, even though it be not always applicable. His
knowledge is not merely skill in treating a situation, but the
possession of resources which he may employ at whatever time, and in
whatever manner, may suit his interests. Knowing what he does about the
pendulum, he may act from the idea of such a contrivance, and with the
aid of it construct some more complex mechanism. His formulas are his
instruments, which he may use on any occasion. Suppose that a situation
with factors _a_, _b_, and _c_ requires factor _d_ in order to become
_M_, as desired. Such a situation might easily be hopele