Sunday, February 24, 2008

Affirmation and the Slow Learner

If the universe does not have a moral structure, or perhaps any structure at all, I might not be able to distinguish, disentangle or separate the wheat from the chaff, the gold from the dross, within the calcareous dome wherein resides my brain and presumably my thinking mind ( which assumption is itself very relevant and interesting.)

Through habit I become very accustomed and comfortable with the “thought-processes” of a certain “I” with whom I have very definitely become accustomed and am quite willing to regard as completely self-certain and natural and as original, authorial, and foundational. In some ways, (but in what ways?), I doubt I have a choice.

This “I” suffers its miseries, its vicissitudes, its lapses, its learning traumas, and moves on.

Right now, I am interested in considering these learning traumas, moments where I either am unable or somehow in some strange way unwilling to assimilate new or different “thinking” or “thinking materials.” ( At this level of consideration I would like to keep the notion of what is assimilated or unassimilated as general and abstract as possible, partially because I don’t know what’s what here, and partially because the nature of this “stuff” –whether it blocks or facilitates “thinking”—needs to be kept in question.)

Upon the introduction of some new material or subject for learning, I have had the sensation of drawing a blank…I don’t understand, and I so thoroughly do not understand that I can’t understand where the disunderstanding originates, what’s triggering it…I can’t find or formulate the kinds of questions which would give me a foothold, either. I am stumped.

I feel as if I may be like the two characters at the top of this post – I wonder if I am a drooling retard. But the real problem of stupidity and of feeling stupid or mentally incompetent has nothing to do with the problem these two suffer.

I might interpret this being stumped as a kind of basic flaw or failure of my intelligence. Or I might suddenly decide “I don’t like this ‘stuff’—it is not for me,” and place some sort of emotional distance between myself and the subject – avoid it, and give myself a kind of cushion against the failure. Or, I can through some kind of probing operation try to find the reasons why I resist the assimilation, why I feel there is something wrong with the “thinking material”, why it would be incorrect, why I sense it to be harmful or incomplete or somehow incongruous with the way I think “thinking” should be.

In other words, I can take seriously the idea that I am not flawed, that my thinking does not lack intelligence, and if there is a problem, it is with the thinking which is presented to me. There is a daring to this approach – I am pitting an apparent personal incapacity (often enough shown to be an actual personal incapacity), assuming my thinking to be shrewd and capable, against material of some proven worth and veracity, vetted by great and thorough minds, the masters and authorities of rationality in the history of science and mathematics.

I took calculus in the last year of high school, muddled through, and at the end of the year scored high enough on the exam so I could have received college credit. I felt somehow fraudulent about the whole performance—I wasn’t convinced I had learned anything or that I knew calculus. In the first year of college, I wanted to put off taking any mathematics, and so I did. At the start of the second year, I decided I had forgotten what I learned in the first calculus course—I continued to feel fake about it—so I enrolled to take it again. My intention was this time to attend to all the intricacies and details of the thinking I had more or less willingly skimmed on my first time through.

This is interesting to me – from the standpoint of philosophy I think the most provocative, controversial and in general undecidable material in all of calculus is the material given during the first part of the first semester. The student is presented with a thicket and no way to orient in it. I encountered this material with my fresh resolution to thoroughly think it through, understand and master it, and this resulted in some kind of crisis—a crisis of the “I”, of this “I” which I am quite willing to regard as completely self-certain and natural and as original, authorial, and foundational. Its foundation crumbled, and the bottom fell out, and I was adrift.

The possibility of thoroughly and completely understanding the material in the way I envisioned did not exist. I think it does not exist.

I resolved this through what I experienced as an effort of the will—I did not want to fail the course, I did not want to give up, or to restructure my life in such a way that I would avoid all further mathematics (a fairly common response among students I think – and I would be very interested to know if it is triggered by experiences similar to what I am trying to describe here.) The actual operations of calculus are simple—the algorithms of calculus—are easy—are child’s play-- to learn and perform. I resolved to attend to these and not allow myself to drift away into the cognitive and perhaps philosophical difficulties which seemed to present themselves…I resolved to not treat these as necessary to learning and understanding. I resolved to treat these as imaginary, rather than real, difficulties. And this resolution did the trick and I never encountered a crisis of the “I” again in my college mathematical career.


Probably most, or even all, modern mathematics develops through some encounter with these very difficulties which splinter off from calculus and move out in very diverse and eccentric directions… In other words, these difficulties are real, not imaginary…Resolving them into the imaginary was convenient for me, but not really a victory for my thinking… My suffering "I" moved on, but by in some sense collapsing and retreating... The crisis of the “I” was real, even if disturbing and unsettling to academic success. I consolidated the “I” by choosing to treat the subject through procedures which terminate, which also terminated the creative potential of the subject.


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