Aside: Differentiation and Integration

Differentiation and integration are words that represent procedures performed in the Calculus.  A brilliant mathematician and author, David Berlinski, wrote beautifully about this paradoxical duality in his book, A Tour of the Calculus:

The miracle of the calculus is that in the realm of the real numbers, the passage from local to global and back again is both possible and necessary, so that whenever differentiation reveals a white-hot collection of local points, places glowing in their full particularity, integration recovers a global picture, a panorama.  And whenever integration produces a panorama, a region wide characterization, there is always a countervailing process by which those white-hot local points may be recovered and thus discovered anew.

Differentiation and integration are words that have meaning in developmental psychology as well.  Here are two quotes combined from The Principles of Psychology by Herbert Spencer:

Consciousness can neither arise nor be maintained without the occurrence of differences in its state.  It must be ever passing from some one state into a different state.  In other words — there must be a continuous differentiation of its states.

In being known, then, each state must become one with certain previous states — must be integrated with those previous states.  Each successive act of knowing must be an act of integrating.  That is to say, there must be a continuous integration of states of consciousness.

In each of these quotes, an alternation of differentiation and integration is being described.  One leads to the other and then back again, in a continuous process.