Modes of Thought and Development

posted May 06, 2004

Den Beste has a post up I have to point to, because as near as I can tell without somehow reaching into his mind, we share to a high degree the rare form of thinking he refers to.

It is peculiarly well-suited to software engineering (which I believe he has done some of, though I can't find a link quickly). You can never, ever, ever quash all bugs in advance, but this sort of thinking allows you to spot the fundamental architectural failings far enough in advance to be able to do something about it, and those are the hardest bugs to fix after the fact. Many is the time I would appear to be zoning out, or drawing random, barely-labelled squiggles on paper, and then pop out with something very near The Answer.

One of the reasons that the holistic view is so useful in software engineering is that for all the (true) talk about how one little error can bring an entire program crashing down, it is the architecture that is much harder to get right, and much harder to fix if it is wrong. Proper testing methodologies can catch errors in the details, and there are so many details that no matter how detail oriented you are, you will get some things wrong. There are no equivalent tests you can do for your architecture. Thus, one of the relatively rare, even in the computing world, holistic systems thinkers can get much farther on a large program, even alone, then any number of details people can get.

Warning: The following paragraphs may be potentially insulting, offensive, or arrogant... but it is the way I feel. I could probably do this OK in person, but the text may rub you the wrong way.

But that's not really what I wanted to write about. I wanted to connect this to developmental psychology, specifically Piaget's four stages of development. They may or may not be literally correct but they are close enough to provide a vocabulary for what I want to say. (Note that I learned the names of the stages slightly differently then that link gives, and I will use the names I learned.)

Piaget's stages are very coarse, and advancing to each stage is a major leap in cognitive development. The second-highest stage is "concrete operational", "concrete" here as an antonym to "abstract", which has the following summary in the link given above:

As opposed to Preoperational children, children in the concrete operations stage are able to take another's point of view and take into account more than one perspective simultaneously. They can also represent transformations as well as static situations. Although they can understand concrete problems, Piaget would argue that they cannot yet perform on abstract problems, and that they do not consider all of the logically possible outcomes.

And the summary of Formal Operational (which I've always thought should have been "Abstract Operational" in contrast with "Concrete"):

Children who attain the formal operation stage are capable of thinking logically and abstractly. They can also reason theoretically. Piaget considered this the ultimate stage of development, and stated that although the children would still have to revise their knowledge base, their way of thinking was as powerful as it would get.

As an practical example, you can not teach calculus, or even really teach algebra qua algebra (as opposed to some mechanical operations you can perform to obtain answers without understanding), unless the child has progressed to formal operational. (As a side note, this is why I firmly believe that one-size-fits-all math education as we use now is fatally flawed; you must continuously test the child for when they reach formal operational, and only then try to advance them past arithmetic. Some kids will hit it in elementary school. Some kids... well, see below and extrapolate logically... and I strongly believe in the logical conclusion of this thought train.)

There are multiple valid ways of being in formal operational, and the holistic style is merely one of them. Details-orientation certainly has its place too, as well as other modes of thought.

But even though I am a holistic thinker, I can still respect the other modes of thought, and I have experienced respect for what I can do from details-oriented people and others. We all bring valuable skills to the table.

I wonder if Steven Den Beste is really encountering people who are so details-focused that they can't see what he is doing... or if he is encountering people who may well be in their 40s or beyond who have never made it to formal operational. It is this claim I wanted to warn about above, since claiming that goodness only knows how millions of adults are still functioning on a child's level is a somewhat controversial claim to make. On the other hand, I note with surprise a note on the bottom of the link from the University of Alberta I gave above the following (emphasis mine):

It is now thought that not every child reaches the formal operation stage.

I was not looking for that when I went looking for definition links; perhaps this has risen to the level of one of those open secrets of the science of psychology that few people outside of the discipline talk about but everyone inside knows. (Another one is men and women are totally different, and another one is intelligence is correlated to race, though please be extra sure you know what "correlation" means in the statistical sense before writing any angry letters to me... better yet, write them to the psychologists.)

Again, without meaning to be insulting, a concrete operational person who makes it into their 20s must simply not see the formal operational "level" of the essay. Thus, left with only the concrete points, they see errors in the concrete points, and believe that invalidates all value the piece may have, since what else is there? I experience this in other areas; for instance, visual arts may be aesthetically interesting to me but they only rarely touch my emotions at all, let alone transport me to other planes of existance. Yet I am willing to believe that some people react this way, since music can do that for me and it does nothing for them. Concrete operational people only know about the formal level as I know about visual arts transcendent nature: Hearsay.

The experience that finally made me seriously consider this theory was being a Teaching Assistant for Computer Science at Michigan State University. Now, MSU isn't a Top Five school for CS or anything... but the program is quite respectable and you'd think the people in the senior-level courses would be well into formal operational, right? And yet I would encounter people who are about to graduate with a bachelor's degree in computer science from a respectable University who were quite clearly still in Concrete Operational. It was... sobering.

It's impossible to be sure based on the sample that Den Beste has provided, though, since concrete operational and details-oriented look identical in small snippets.

One other thing is that his forests vs. trees comments really reminded me of my Seeing the Forests for the Trees posting a couple of months ago.


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