Convergent and Divergent Problems
One of the most interesting sections in A Guide for the Perplexed is about convergent and divergent problems and how they relate to our perplexing human state.
Convergent problems have solutions that are verifiable, repeatable, and stable. The example Mr. Schumacher used in the book was bicycles: after many attempts at a two-wheeled vehicle, a design emerged that has been amazingly stable over time, and that is the bicycle. Computers, lamps, suspension bridges, and nuclear energy (for example) are also results of solved convergent problems. In general, convergent problems are the problems of the physical world–the laws of nature govern the solutions, and these solutions lie along one converging path. That is, the more you study a problem, the more it converges into a solution–one solution. People might improve on the bicycle’s design, but the basic design itself will not change, because there is really no other way to create a usable, efficient two-wheeled vehicle.
Divergent problems are problems that have more than one solution, or a complex mix of seemingly contrary solutions, or no solutions at all. The example Mr. Schumacher used in the book was education. Many people believe discipline is the key to educating children. Others believe freedom is the key. Who is right? If you have nothing but discipline, you end up with a prison. But if you have nothing but freedom, you end up with a jungle. Thus, neither solution is completely correct.
The more you study divergent problems, the more evident their paradoxical nature becomes: there is no one solution that will solve a divergent problem, and sometimes there is no solution at all. Understanding does not lead to one overarching solution; it leads away from it.
Divergent problems are the problems of humanity. The physical world is full of interesting, difficult problems, but they are all convergent problems–problems that, once solved, essentially become “dead” problems because they’ve given up all their mystery and are no longer interesting or useful to study. In the realm of humanity, this rarely happens. Questions about human concerns do not yield quite so easily. Discipline or freedom? Fate or determinism? Capitalism or socialism? Equality or justice? Agency or communion? Do we live for ourselves, or do we live for others? Should we spend more time working or more time playing? What is love? What is virtue? Is there an absolute morality and if so, is it definable? What is the nature of god? And on and on.
This is what Mr. Schumacher says about the divergent problem of education, which I believe can be applied to divergent problems in general:
Freedom and discipline here is a pair of perfect opposites. No compromise is possible. It is either the one or the other…Logic does not help us because it insists that if a thing is true its opposite cannot be true at the same time. It also insists that if a thing is good, more of it will be better. Here we have a typical and very basic problem, which I call a divergent problem, and it does not yield to ordinary, “straight-line” logic; it demonstrates that life is bigger than logic.
If divergent problems are bigger than logic, then, how can they be solved, if at all? The answer is that they must be solved at a higher level. Just as convergent problems are solved by observation and logic, which could be viewed as “higher levels of being” than the physical world (because the physical world can neither observe nor think), divergent problems must also be solved by a method of transcendence. In Mr. Schumacher’s words:
Divergent problems…cannot be solved in the sense of establishing a “correct formula;” they can, however, be transcended. A pair of opposites–like freedom and order–are opposites at the level of ordinary life, but they cease to be opposites at the higher level, the really human level, where self-awareness plays its proper role. It is then that such higher forces as love and compassion, understanding and empathy, become available, not simply as occasional impulses (which they are at the lower level) but as a regular and reliable resource. Opposites cease to be opposites; they lie down together peacefully like the lion and the lamb.
Why is it important to understand the nature of divergent problems? Mr. Schumacher explains:
It is important for us to become fully aware of these pairs of opposites. Our logical mind does not like them: it generally operates on the either/or or yes/no principle, like a computer. So, at any time it wishes to give its exclusive allegiance to either one or the other of the pair, and since this exclusiveness inevitably leads to an ever more obvious loss of realism and truth, the mind may suddenly change sides, often without even noticing it. It swings like a pendulum from one opposite to the other, and each time there is a feeling of “making up one’s mind afresh”; or the mind may become rigid and lifeless, fixing itself on one side of the pair of opposites and feeling that now “the problem has been solved.”
The pairs of opposites, of which freedom and order and growth and decay are the most basic, put tension into the world, a tension that sharpens man’s sensitivity and increases his self-awareness. No real understanding is possible without awareness of these pairs of opposites which permeate everything man does. (italics mine)
In my own words, if we don’t understand the divergent nature of our human psyche, of our need for both freedom and justice and both order and equality, then we are destined to oversimplify life situations and be facile thinkers about the most important of all topics: our own humanity. And we fail to develop that one, primary transcendent capacity that we all carry as a seed inside of us: wisdom. And if we don’t cherish and use our wisdom, then we will, indeed, fall short of our full human capacity.
I suppose I like this idea of divergent problems so much because it sort of encompasses everything I write about: critical thinking, personal agency, self-development, and the great need to honor our complex, messy, infinitely layered inner worlds. Again, Mr. Schumacher really says it best:
Everywhere society’s health depends on the simultaneous pursuit of mutually opposed activities or aims. The adoption of a final solution means a kind of death sentence for man’s humanity and spells either cruelty or dissolution, generally both…
Divergent problems offend the logical mind, which wishes to remove tension by coming down on one side or the other, but they provoke, stimulate, and sharpen the higher human faculties, without which man is nothing but a clever animal. A refusal to accept the divergency of divergent problems causes these higher faculties to remain dormant and to wither away, and when this happens, the “clever animal” is more likely than not to destroy itself.
We are complex by our very nature. Many attempts have been made to reduce human nature to cause and effect, thereby denying the higher faculties of the human mind. (Because these faculties aren’t measurable and predictable, some say, they don’t exist, or exist only as reactions to environmental stimuli.) Disturbingly, some of these attempts–scientific determinism being a primary example–have gained a powerful foothold in the sciences as well as in popular thought. The categorizing of problems into convergent and divergent puts these debasing theories largely to rest, which is a great victory for our humanity. Even those who want to disagree about the divergent nature of human problems would be hard-pressed to come up with a better explanation, I think. It may cause some people anxiety to think of human problems requiring “higher faculties” to solve, because 1) the development of these higher faculties takes time and effort, and 2) acknowledging their necessity eliminates the possibility of reductionistic, black-and-white thinking. But to deny that fact seems, to me, absurd–and indeed, has led mankind down all sorts of absurd paths, which you need only look around you to see.