188 THE PRINCIPLES OF SCIENCE 



terms of alterations in the (molecular) groupings of unaltered 

 (atomic) particles, now including electrons and nucleons. In biology 

 the fluctuating appearance of heritable traits is similarly referred 

 back to the fluctuating combinations of "atomic" genes ( and, today, 

 to the sequences of "atomic" base groups in DNA molecules). And 

 so on and on. 



The invariance expressed in a conservation law is, in very strong 

 form, just such a recognition of continuity as passes with us as knowl- 

 edge. And then, quite naturally, recognition of what invariance de- 

 mands will count with us as explanation. So it is that we couple the 

 atomic theory with conservation laws to explain the occurrence (or 

 nonoccurrence) of certain qualitative appearances, corresponding 

 to particular states or structural arrangements. Leibniz considered 

 atomism a theory flagrantly, and unacceptably, in violation of the 

 dominant concept of continuity. But we find no irremediable incom- 

 patability between the discreteness of atoms and the element of con- 

 tinuity so prominent in the conservation principles. Continuity and 

 discreteness are, after all, only imaginary conceptual polarities never 

 wholly separated in practice. We use them to designate modes of 

 thought (e.g., particle theories and field theories) in which one or 

 the other polarity seems dominant. The separation of the polarities 

 may then be highlighted by occasional spectacular conflicts of such 

 theories— ^.g., the ancient strife of atomist with Stoic, the modern 

 strife of morphologist with neo-Darwinian— but no scientific theory 

 fails to embody and unite, in some degree, both polarities. 



Beginning with (common-sense) concepts of discrete objects, 

 scientists may go on multiplying "things": galaxies, stars, planets, 

 atoms, electrons, photons, etc. But ultimately they seek somehow to 

 re-establish the spatial continuity these concepts will seem to set at 

 nought. Thus, for example, having begun by conceiving a sharp 

 boundary between stationary pipe and fluid e\'erywhere flowing at 

 some bulk velocity, ultimately we conceive ( and find ) a gradient of 

 flow velocities bridging the gap between a maximum value, along 

 the axis of the pipe, and a minimum, next to its walls. Analogous dis- 

 sipations of abrupt discontinuities occur at the furthest reach of 

 scientific thought. 



Newton first attacks the problem of celestial dynamics with a con- 

 cept of mutually attracting discrete bodies. Rebelling against the idea 

 of action at a distance, ultimately we seek to re-establish continuity 



