148 IV. STRUCTURAL FACTORS INLANGUAGES
simple if one decides to follow the general rule; namely, either completely to reject or completely to accept provisionally, at a given date, a new system; use exclusively the structurally new terms; perform our semantic operations exclusively in these terms; compare the conclusions with experience; perform new experiments which the structurally new terminology suggests; and only then, as an independent enquiry, investigate how one system translates into the other. In those translations, which correspond to the transformation of frames of reference in mathematics, we find the most important invariant characteristics or relations which survive this translation. If a characteristic appears in all formulations, it is a sign that this characteristic is intrinsic, belongs to the subject of our analysis, and is not accidental and irrelevant, belonging only to the accidental structure of the language we use. Once these invariant, intrinsic characteristics are discovered, and there is no way to discover them except by reformulating the problems in different languages (in mathematics we speak about the transformation of frames of reference), we then know that we have discovered invariant relations, which survive transformation of different forms of representations, and so realize that we are dealing with something genuinely important, independent from the structure of the language we use.
History shows that the discovery of isolated, though interesting, facts has had less influence on the progress of science than the discovery of new system-functions which produce new linguistic structures and new methods. In our own lifetime, some of the most revolutionary of these advances in structural adjustment and method have been accomplished. The work of Einstein, the revision of mathematical foundations, the new quantum mechanics, colloidal science, and advances in psychiatry, are perhaps structurally and semantically the most important. There seems no escape from admitting that no modern man can be really intelligent in 1933 if he knows nothing about these structural scientific revolutions. It is true that, because these advances are so recent, they are still represented in very technical terms; their system-functions have not been formulated, and so the deeper structural, epistemological and semantic simple aspects have not been worked out. These aspects are of enormous human importance. But they must be represented without such an abundance of dry technicalities, which are only a means, and not an end, in search for structure.
A scientist may be very much up to date in his line of work, let us say, in biology; but his physico-mathematical structural knowledge may be somewhere in the eighteenth or nineteenth century and his epistem-ology, metaphysics, and structure of language of 300 b.c. This classifi-