THE PRINCIPLES OF SCIENCE 191 



counter with such a case is always something of a surprise— so gen- 

 eral is our success in distinguishing substantially independent parts. 

 To mark our surprise we usually give a special name to the "co- 

 operative phenomenon" that redresses the balance of sum and 

 whole. But, however it may surprise us, such a phenomenon does 

 not dismay us: frequently it represents nothing more than some 

 element(s) intrinsic to our problem, but purposively ignored in our 

 first sketch of a solution. 



Consider the "perturbations" of planetary orbits. The word may 

 be seriously misleading: what we call perturbations are no more 

 than artifacts of our own approach to the problem of calculating a 

 planetary orbit. Ordinarily we begin with the simplifying assumption 

 that planet and sun can be treated as completely independent of all 

 other bodies in the system. This assumption yields a tractable two- 

 body problem, but of course it is an oversimplification: there must 

 also be gravitational attractions among planet, sun, and all other 

 planets in the system. Directly to attack the total problem is hope- 

 less: even a three-body problem defies exact mathematical analysis. 

 We proceed then by solving the central two-body problem, and later 

 re-introduce ( as "perturbations" ) the generally minor systemic inter- 

 actions previously ignored. And our success in thus reconstituting 

 the whole from its parts is at least partially attested by the exquisitely 

 accurate predictions we found on our celestial mechanics. 



This instance has nothing unique about it. Thus we first approach 

 the problems of nuclear physics with concepts of independent parti- 

 cles. However, among "particles" present in the narrow compass of 

 the nucleus there might well be strong interactions. These do indeed 

 manifest themselves in the difference between the mass of the nucleus 

 and the sum of the masses of the particles of which we suppose it con- 

 stituted. We call this difference a "mass defect," but we readily under- 

 stand that the "defect" arises simply from the interaction of particles 

 we formerly treated as wholly independent. Quite similarly, in chem- 

 istry we begin the study of molecular structure with a conception of 

 bonds having characteristics dependent only on the identities of the 

 two atoms directly linked by each bond. But ultimately we recognize 

 co-operative effects of "parts" in the context of the molecule as a 

 whole— systemic interactions for which we must make allowance, 

 e.g., as "resonance." 



How often we meet this situation in work with living organisms! 



