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 hopeless for an organism reacting directly to the stimulus _abc_, and yet be easily met by a free knowledge of _d_. One who knows that _l_, _m_, and _n_ will produce _d_, may by these means provide the missing factor, complete the sum of required conditions, _abcd_, and so obtain the end _M_. Such indirection might be used to obtain any required factor of the end, or of any near or remote means to the end. There is, in fact, no limit to the complexity of action made possible upon this basis; for since it is available in idea, the whole range of such knowledge may be brought to bear upon any individual problem. [Sidenote: Skill as Social.] § 44. But knowledge of this free type becomes at the same time _social_ or _institutional_. It consists no longer in a skilful adaptation of the individual organism, but in a system of terms common to all intelligence, and preserved in those books and other monuments which serve as the articulate memory of the race. A knowledge that is social must be composed of unequivocal conceptions and fixed symbols. The mathematical laws of the exact sciences represent the most successful attainment of this end so far as form is concerned. Furthermore, the amount of knowledge may now be increased from generation to generation through the service of those who make a vocation of its pursuit. Natural science is thus a cumulative racial proficiency, which any individual may bring to bear upon any emergency of his life. [Sidenote: Science for Accommodation and Construction.]