Sunday, June 14, 2009

Solving Complex Problems

We've encountered the observation before that solving really hard problems has to rely on an evolutionary trial and error approach. We might describe this as active inductive reasoning. In general, induction is just looking for patterns in data and formalizing them. The 'active' part means we're continually looking for more data. What actually happens, though is not so straightforward, and bears deeper inspection. For me, this is the crux of the "critical thinking" assessment debate, which anyone who reads this blog knows I've tried to refactor into more easily identifiable patterns of thought: deductive and inductive.

The cause for this iteration of that line of thought is two-fold: an article in the New York Times called "The Case for Working with Your Hands," from May 21, and a trip I took yesterday to Seagrove, North Carolina. In the article, Matthew B. Crawford describes how how left a high-paying career based on academic credentials and began fixing motorcycles full time. There are some beautiful descriptions of the inductive/deductive synthesis in his problem solving:
In fixing motorcycles you come up with several imagined trains of cause and effect for manifest symptoms, and you judge their likelihood before tearing anything down. This imagining relies on a mental library that you develop.
The possible cause and effect relationships are deductive rules that the successful mechanic accumulates in his mental library. But these rules are not enough to solve problems. These comprise only the theory. The imagining is the inductive process--positing solutions to test against the known facts and theory. But this is too simple a description, because there is cost involved:
There is always a risk of introducing new complications when working on old motorcycles, and this enters the diagnostic logic. Measured in likelihood of screw-ups, the cost is not identical for all avenues of inquiry when deciding which hypothesis to pursue. Imagine you’re trying to figure out why a bike won’t start. The fasteners holding the engine covers on 1970s-era Hondas are Phillips head, and they are almost always rounded out and corroded. Do you really want to check the condition of the starter clutch if each of eight screws will need to be drilled out and extracted, risking damage to the engine case?
What might seem in theory like a good line of inquiry may be expensive to carry out in practice. So over the whole deductive/inductive process operates an economic decision-making process that must weight possibly costs against probabilities of success. Because of the uniqueness of the situation, this may be guesswork--loose "deductive" rules we may as well call heuristics.

Theory is a powerful drug, however (witness the wars of ideology that continue into this century). The good problem solver knows when to ignore them, which according to the author is most of the time:
There probably aren’t many jobs that can be reduced to rule-following and still be done well. But in many jobs there is an attempt to do just this, and the perversity of it may go unnoticed by those who design the work process. Mechanics face something like this problem in the factory service manuals that we use. These manuals tell you to be systematic in eliminating variables, presenting an idealized image of diagnostic work. But they never take into account the risks of working on old machines. So you put the manual away and consider the facts before you.
The article itself is not a treatise on problem-solving, despite the quotes above. Crawford's thesis is that jobs like fixing motorcycles are not less than jobs like accountants and lawyers in their mental demands. In his words (taken from different paragraphs):
When we praise people who do work that is straightforwardly useful, the praise often betrays an assumption that they had no other options.

A gifted young person who chooses to become a mechanic rather than to accumulate academic credentials is viewed as eccentric, if not self-destructive.

The trades suffer from low prestige, and I believe this is based on a simple mistake. Because the work is dirty, many people assume it is also stupid.
Dr. Crawford comes to this line of thought after finishing a Ph.D. in political philosophy at University of Chicago and working as an executive director in a Washington think tank. Compare the problem solving process he encountered there:
It sometimes required me to reason backward, from desired conclusion to suitable premise. The organization had taken certain positions, and there were some facts it was more fond of than others. As its figurehead, I was making arguments I didn’t fully buy myself. Further, my boss seemed intent on retraining me according to a certain cognitive style — that of the corporate world, from which he had recently come. This style demanded that I project an image of rationality but not indulge too much in actual reasoning.
Later in the article he reflects on this distinction in thinking styles (emphasis added):
[M]echanical work has required me to cultivate different intellectual habits. Further, habits of mind have an ethical dimension that we don’t often think about. Good diagnosis requires attentiveness to the machine, almost a conversation with it, rather than assertiveness, as in the position papers produced on K Street. Cognitive psychologists speak of “metacognition,” which is the activity of stepping back and thinking about your own thinking. It is what you do when you stop for a moment in your pursuit of a solution, and wonder whether your understanding of the problem is adequate.
I think it would be an easy shot to wish that if only our captains of finance had taken this step back into metacognition..., but that would advertise a higher level of understanding about our current woes than I possess. Crawford's exposition is too graceful for that. The sense I get from reading the article, however, is aposite to both motorcycles and derivaties: complex problems are humbling, and if approached on their own terms (rather using than an ideological end-around, for example), cause us to grow through struggles within ourselves. This is the meta- part of meta-cognition. Crawford makes the fascinating observation that many professions--highly paid ones--do not easily allow for this sort of growth. He highlights the "moral trap" of the archtypical middle manager on page four.

An example of the anesthetic properties of theory over actual problem-solving is given in a Kafkaesque description of a job he held to write abstracts for academic journals (emphasis added):
My job was structured on the supposition that in writing an abstract of an article there is a method that merely needs to be applied, and that this can be done without understanding the text. [...] [I]t became clear [my instructor] was in a position similar to that of a veteran Soviet bureaucrat who must work on two levels at once: reality and official ideology.
Doing things by rote can solve some complicated problems, as computers routinely demonstrate. But of course in that case, the 'rote' solution can be quite complex, requiring millions of bytes of code. Simple prescriptions for complex problems are unfortunately common--any fixed ideology is a likely suspect--and seem to cause the kind of logical contortions described in the quote above.

I was reminded of the Times article because of a trip I took yesterday, to Seagrove, North Carolina. It's a unique place, a center for hand made pottery. I bought the piece shown below for $30 from William and Pamela Kennedy of Uwharrie Crystalline Pottery [email].

Mr. Kennedy told me that the technique he uses involves seeding the glaze with zinc, which begins to crystallize as it cools. Essentially, this re-creates in a kiln a geological process that might happen with rock far below the surface or near volcanism. At a different place, called Dirt Works, I bought a shallow bowl in the style shown below.

The master potter, Dan Triece, was kind enough to let us watch him work. His most common question is "how long does it take to make a piece?" His answer: about 3 years and fourteen minutes. You can figure out what he meant.*

Obviously there are problem-solving connections between the zen of motorcycle maintenance and hand crafting bits of clay into art. They are different problems, of course, but the differences serve to highlight the role of inductive reasoning.

With motorcycles, there are obvious empirical tests that have to be met. Does the thing run when I'm finished with it? Is it dripping oil? For the potter, physical reality also intrudes. Kilns affect the clay differently, depending on if they are electric or gas-fired or heated with wood. There is the chemistry and physics of glaze and high temperatures to reckon with, all of which may thwart the desired outcome. But it seems to me that beyond these physical limitations there are more possibilities for a distinct and obvious style to emerge with pottery than with motorcycle maintenance. This may be a blessing or a curse, but it seems to me that the inductive process becomes applied to solving problems in one's own mind in the artistic process. We might call this the "do I like it?" loop, which gets tested over and over again for the artist.

The underlying complexity of the physical problems to be solved PLUS whatever potential there is for creative expression together represent the challenge for the expert in any field, whether motorcycles or pottery or mythology or politics. In addition, there are the social complexities, like the one Dr. Crawford mentions, and for the artist the problem of finding an audience. These act like physical constraints in some ways--there are causes and effects--but maybe only in a Dr. Zeuss kind of way (you may puzzle until your puzzler is sore...).

What's the point? Shouldn't we have this sort of discussion with every student at a liberal arts institution? Shouldn't part of the curriculum include ideas about possible futures--not in the "what do you want to be when you grown up?" frame, but one informed by the psychology of happiness, the life experiences of experts in all sorts of fields (fixing engines included), an exploration of the styles of thought that resonate with the student (deductive, inductive, creative?), and at least some of the attempts of western civilization to answer the question "why am I here at all?"

If anything, the Times article ought to convince an educator that self-reflection is absolutely key to intellectual development. Take one more step, and we might conclude that we ought to be assessing thinking stills through reflection on the part of the student, and teaching that as a skill for its own sake. But there's more than that too. Developing one's intellectual maturity doesn't occur in isolation--it strikes me that the account given by Dr. Crawford illuminates what we might call an aesthetic maturity, a finding for one's self a place in the grand scheme. Perhaps this idea has too much baggage to get through a faculty senate that isn't populated with existentialists, but what do we gain by graduating nominally stellar thinkers who are unhappy with their lives? I think Dr. Crawford's implication is right on: preparing for a place in the "information economy" is not the only reason to seek higher education.

*three years to learn, after which it only takes fourteen minute to 'throw' the pot on the wheel.

No comments:

Post a Comment