Differentiation defines distinctions.
Integration joins commonalities.

In Biology

Entities differentiate for special functions and integrate for wholistic purposes.  Our cells are perfect examples.  As we are made of trillions of cells, we humans are complex entities who constantly differentiate and integrate on the physical level.

In Psychology

Sometimes, we confidently want to stand out and be recognized for our unique propensities, abilities and aspirations (Amelia Earhart photo below).  Individuals shoulder the risk/reward to specialize.  (Differentiation)

And during challenging times, we might want to huddle together with others for support, become a member of a loyalty clique, or enlist in an organization that collectively empowers its participants (Million Man March shown below).  Participants share the risk/reward when unified.  (Integration)

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 Scripture

The Tao te Ching says,

The ten thousand things carry yin and embrace yang.  They achieve harmony by combining these forces. 

Yang is a term describing an expressive capacity, or an outward pushing movement.  Yin is a term describing the receptive capacity, or an inward pulling movement.  First yin and yang are differentiated, then integrated.

Genesis says,

God divided the light from the darkness.  He named the light “day” and the darkness he called “night.  And the evening and the morning were the first day.

Light and darkness were differentiated and then the evening/darkness and morning/light were integrated into the first day.

When I read the story of creation in Chapter 42 of the Tao te Ching, I first noted the stark difference between its phrasings and the comparable phrasings of the creation story proffered in Chapter 1 of Genesis.  After I differentiated between the two versions of creation, I wondered if they could ever be integrated.  If this were to be possible, I would need to find a common denominator for the diverse stories.  This entire blog-book is about the journey of finding that common denominator and integrating the wisdom teachings of our ancestors.  (For more about this, visit A Puzzle of Creation Stories).  

In Calculus

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.

In each of these differentiated arenas, an alternation of differentiation and integration is being described.  One leads to the other and then back again, producing an ongoing process of reintegration.