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James Gillray: Political Mathematician’s, Shaking the Broad Bottom’d Hemispheres (1807)

"There are good reasons I'm not a civil engineer."

Frequent offenders (er, readers) here will have noticed my fractured relationship with most things mathematical. I am nobody's mathematician, not even my own, a condition that baffles about as much as it delights me. I understand that I really should not revel in any utter ignorance, but I get some satisfaction in recognizing this difference. I'm clearly not the standard issue. I recognized early that my MannerOfThinking was apparently insufficient to accumulate the requisite inventory of procedures and rules to support even a modest mathematical practice. Further, one apparently needed to exhibit something like a genuine interest in concepts that, quite frankly, never made much of an impression on me. I could never quite find interesting answering or even asking mathematical questions, ones intended to definitely decide something.

I have sometimes, though, gazed longingly across the chasm, wondering if I might someday and somehow stumble upon some spare proficiency in something mathematical.
I pick up a book or, these days, binge watch a promising fresh set of videos, thinking to myself that I might yet prove myself to be a reasonable man, one open and perhaps even capable of conventional reason. Then some question gets asked, one about likelihood or volume, and I wonder how the mentor, the author or video performer, even knew how to ask that question in that manner. Then I reencounter that MannerOfThinking question, one which for me remains a question without a tangible answer. Mathematics seems to demand of its practitioners a unique relationship with this world, one framed by an extensive internal library of procedures and models which might be combined to answer questions, indeed, to even ask coherent questions. The rest of us, with me most prominent, will not recall the formula for calculating volume and most likely will not even recognize a situation where a volume calculation might solve something, let along know what to do with an "answer" stated in square or cubic anythings. We do not parse our world like that.

We're not stupid, either, just, perhaps, differently practical. My friend Mark, who is a certified mathematician and a physicist sent me a link to a video which purported to explain how a 90+% accurate diagnostic test might prove incapable of correctly diagnosing the presence of some illness. [Here's that
link.] What followed was a completely coherent explanation I could not follow. It provided a guided tour through another universe from the one I inhabit, one where anyone might seem to just know how to think about something so obtuse and abstract as to defy actual analysis, except it doesn't, not in this example. The teacher, who seems authentic and sincere seems to be pulling models out of his trousers or someplace, examples which I realize I would have never retained even had I been previously exposed to them. I do not casually apply Bayes Rule in my daily life, and not only because I couldn't. I can't see the relevance of Bayes Rule. I cannot comprehend how its used, what it's FOR. Explanations prove boring.

My friend thought it essential for everyone to understand how to determine how likely they are to actually have a disease should they receive a positive result from a diagnostic test. I contended that what we really need might be a cadre of trustworthy mathematicians who might help a mere civilian interpret such results. The video reported that most doctors cannot properly determine the likelihood of a false positive result, and I'm not surprised. Few doctors, I suspect, maintain the MannerOfThinking such calculations expect. If they could retain those arcane procedures for calculating such things, they might have become mathematicians rather than physicians, like I might have become a number cruncher rather than a writer, though the world might well have been richer had I managed to pass muster as a number cruncher.

Fact is, I do not need to calculate such things, just like I do not need to perform my own dentistry. I have access to specialists who, ahem, specialize in those arcane MannersOfThinking such pursuits require. I do not offer this defense to in any way diminish the role the number crunchers perform nor merely to deflect residual guilts I might have always felt about being excluded from that clan, but just to state that I finally understand that I will never be able to relate to that alien way of relating to this world. I'm not stupid. Just different.

As synchronicity would have it, I this week stumbled across an article about an obscure but important twentieth century mathematician, Alexander Grothendieck. [Link
here.] The story told of his first exposure to mathematics as a child resident in a Nazi concentration camp and how his first impression was that math's definitions were all messed up. He contended that the standard definition of a point and a line just complicated solving problems. Unlike the rest of us who experienced his reaction, he went on to influence changes to the very language traditionally used to think about mathematical relations. He later became a recluse and lived on a diet of foraged dandelion soup. Changing a profession's vocabulary might prove the riskiest but most influential contribution that only a few might ever appreciate. I fled, instead, to inhabit a more convivial universe.

Five years ago, I wrote a piece introducing the concept of MannerOfThinking [Link
here.] In it, I revered a teacher friend who chose the profession of introducing students to the mathematical MannerOfThinking and, indeed, introduced me to the concept if not the practice. In that essay, I emphasized just how hard he and his students found it to assimilate the mathematical MannerOfThinking. Only some succeeded, but those who managed to experience the shift, forever after inhabited a different world than the one they'd inhabited before. They couldn't go back, either. MannerOfThinking is not knowledge, not intelligence, but a unique parsing of surroundings and experience. As I told my physicist friend, when I need to buy some sand, I do not first calculate the volume of the space I intend to fill because I will not in that moment recall how to perform that calculation, indeed, I will not in that moment even think about calculating. I'll instead think I might only need one bag, but I'll buy two just in case, and thereby have some leftover for when The Muse needs some sand within which to root some plant starts. There are good reasons I'm not a civil engineer. I maintain a different MannerOfThinking here.

©2022 by David A. Schmaltz - all rights reserved

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