Fully Understanding

I have been lately digesting an enormous amount of material on biological systems and urban systems.  For both systems, I am interested in their health.  The focus in biology has been on cancer and understanding the signaling mechanisms whose aberrations allow uncontrolled cell growth.  Within cities, I have been exploring urban resilience, including historical narratives in the US for the last four centuries.  Both of these endeavors were motivated by very different opportunities.

Nevertheless, serendipity has intervened as usual and I find myself contrasting the two domains.  The scale of both humans and cities are mind boggling – 50 trillion cells in a human body and 10-20 million people in a city.  Of course, the 50 trillion cells have much less discretion than the 10-20 million residents in a city.  Thus, the two systems may be more comparable in complexity than the difference in the two numbers might lead one to believe.

For example, getting all the cells in a human body to walk in one direction would be much easier than convincing all the inhabitants of a city to walk in the same direction.  The owner of the human body simply has to start walking and all his or her cells follow along.  There is no comparable entity in a city.  On the other hand, getting all the citizens in a city to vote would be much, much easier than getting all the cells in a body to express any intention except birth, growth, and death.

It seems that cells in a human body and citizens in an urban area may not be very good analogies of each other.  However, they both are really difficult to fully understand.  There are too many levels and far too many interactions to be able succinctly describe the essence of either system.  Of course, you could make the same argument about a rabbit or a tree.

This begs a definition of “fully understand.”  It would seem that the definition depends on why one is trying to understand something.  I cannot imagine that anyone really wants to understand everything about a human, a city, a rabbit, or a tree.  Are weight, volume, density, and molecular structure of interest?  How about the current charge of every electron in every atom of every molecule of every substance in a city?

Clearly the notion of understanding is very much intent determined, as are other constructs such as complexity, cognition, and emotion.  We have invented many constructs that are useful such as gravity, energy, and heat.  These are among our ways of labeling regularities in the universe as we experience them.  They help us to predict that things will fall, motion requires something to drive it, and days with higher temperature feel warmer.

But we do not – and cannot – fully understand these phenomena.  Yet, we can employ these constructs and various principles, e.g., conservation and continuity, to engineer useful processes and devices.  Our limited understanding has pragmatic value.  What do we lose by recognizing these limitations?

Much of what we characterize as rigorous research is laced with equations, theorems, and proofs.  However, we can only prove things within the confines of these artificial worlds that we have created.  We can only prove things in our model worlds.  We cannot prove theories in the physical world.  The best we can do is find evidence that supports theories as plausible, as well as be on the lookout for disconfirming evidence.

Optimal solutions in model worlds are, at best, pretty good solutions in the real world.  We have no way of knowing the best answer in the real world.  We make a wealth of assumptions to force reality into a set of equations.  These assumptions are almost never true, but they can be good enough to enable useful outcomes.  The primary value is in these outcomes rather than the equations.

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