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Geometry aka logic as an analytic tool

[ by Charles Cameron — reflections on cognitive empowerment by selective noticing ]


I just realized that I take notice of details at the level of “geometry aka logic” which I would miss if I were more focused on content. In effect, I treat idiosyncracies and hiccups of expression — such as paradoxes — as indicative of condensed or distilled meaning.

What triggered this realization was the way my interest was aroused by this phrase:

The parallel universes may soon become perpendicular.

I found that today in an FP piece, Will June 30 be midnight for Morsi’s Cinderella story?


Paradox? Geometry? Contradiction? Figure of speech?

It’s the irregularity in the pattern used to describe the events in question that catches my eye here, however you care to name it. And something very similar is going on when I flag the weird juxtapositions of imagery and music in Taylor Swift, Sara Mingardo, JS Bach and a quiet WTF, or the koan-like tensions and reconciliations inherent in such inseparable pairs as war-and-peace in Of dualities, contradictions and the nonduality.

Here’s the full paragraph, discussing the increasing polarization of the Egyptian public, and some ways in which “the current situation differs more in degree than in kind from the recent past”:

Second, violence is on the table. The parallel universes may soon become perpendicular. Of course, Egyptian politics has had its victims over the past two and a half years, but violence has seemed episodic and almost self-limiting since those who have deployed it have paid a heavy political price. Nobody advocates violence now, but many expect it and it is not uncommon to hear from both sides that they will not shrink from self-defense. And the line between self-defense and offensive action can become thin for each camp for opposite reasons. The opposition is hardly centrally controlled and rogue elements have already been involved in attacks on Brotherhood offices as well as those of its political party. For the Brotherhood, its discipline has led it to prepare for what it sees as defensive action in a manner that understandably appears threatening to outsiders (especially after the events of December 2012 when Brotherhood cadres constituted themselves as a vigilante force to confront those demonstrating at the presidential palace).

Okay, so I’m already reading the article, ergo I must already have been interested enough in what’s going on in Egypt to click through to it. So why the fuss about paradox and geometry in what is, after all, only one turn of phrase in a piece whpose subject already interests me?


I’m still feeling my way towards and understanding of how my mind works, how I pick up on things, how I populate my mind with rich and interesting memories, how I make my small and large creative “leaps” — my means of collecting and connecting dots, if you will. Because there’s a cognitive skill there that I haven’t seen taught, and I believe it offers an “outside the box” alternative mode of monitoring topics of interest.

You know, of course, that most every time you read the words you know, of course, that it’s a dead giveaway that the speaker or writer is skimming quickly past a cherished assumption that he or she wouldn’t want you to examine too carefully? Of course you do. It’s one of those psychological “tells” that should alert you, like a facial tick, a hesitation, or that curious (and paradoxical) tight grip on one arm of the chair with one hand while the other rests almost disdainfully relaxed and gracious on the other, in El Greco’s masterful portrait of a Cardinal, now in the Metropolitan in New York:

How very telling that sort of detail can be!


And intersections.

I talk quite a bit about juxtapositions and parallelisms, because they’re the elements of “creative leaps” (and Sembl / Hipbone moves) and I “practice” noting them for my DoubleQuotes. But one way to clear the xlutter from mind is to concentrate on places where two fields intersect. I’m interested in apocalyptic, for instance, so I take particular note when someone from a Christian apocalyptic POV (Joel Richardson, Joel Rosenberg, eg) writes about Islamic eschatology, or when someone from an Islamic apocalyptic POV (Sh. Safar al-Hawali, eg) writes about Christian eschatology. Reading wherever I notice this kind of overlap means that I learn in two contexts — effectively doubling my knowledge value — where most reading that’s not “targeted” this way only allows me to learn in one…

Again: parallelisms, overlaps, paradoxes, perpendiculars, contradictions — these are all “formal properties” of a given text rather than “contents” — that’s the level of abstraction at which you can make the details sing.


Hey, I’m not alone. As I was cleaning this post up, Adam Elkus tweeted a link to a post about the CTO of Intel, Intel Labs: Assuring Corporate Immortality by Rob Enderle, which contains this phrase:

This is very orthogonal thinking

There we go! The word orthogonal is so important to me, and is so often on the tip of my tongue but out of reach of immediate memory, that I have a file on my computer consisting solely of the words “opposite oblique orthogonal congruent incongruous antithetical obtuse parallel asymptotic perpendicular right angles” — so if I can remember any one of them, I can easily find “orthogonal”.

Very orthogonal thinking — terrific!

9 Responses to “Geometry aka logic as an analytic tool”

  1. Norm DeLisle Says:

    Have you seen Scott Kelso’s “The Complementary Nature”? The book treats contradictory/complementary variations as dynamic processes.  See http://goo.gl/OLl6D

  2. Charles Cameron Says:

    I hadn’t — that and his Dynamic Patterns both look v interesting — many thanks!

  3. Curtis Gale Weeks Says:

    Just a point of curiosity.  What would be orthogonal to orthogonal thinking?  This may or may not be a koan; could be a trick question.

  4. Charles Cameron Says:

    Subract three, Curtis, then think of the thought you first thought of.

  5. Curtis Gale Weeks Says:

    Sorry, I might have been thinking of Schrödinger’s cat while smoking my hookah.  Bother.

  6. Charles Cameron Says:

    I understand kitties are very popular on the web — Schrödinger’s, or the Cheshire?

  7. Curtis Gale Weeks Says:

    Lol my name’s not Elkus, so I’m no expert on kitties.  But when you’re smoking a hookah, there’s not much difference in cats — until there is.

  8. Michael Robinson Says:

    It’s one of those psychological “tells” that should alert you, like a facial tick, a hesitation, or that curious (and paradoxical) tight grip on one arm of the chair with one hand while the other rests almost disdainfully relaxed and gracious on the other, in El Greco’s masterful portrait of a Cardinal, now in the Metropolitan in New York: …

    Or equally, such seeming lifelike ‘psychological’ tells may have absolutely nothing to do with the painter El Greco’s direct observation of a particular Cardinal ca. 1600, but be part of the established conventional formula for a particular type of ecclesiastical portrait based on an earlier celebrated model; the same combination of relaxed right hand and left hand had clutching the arm of the chair occurs first in Raphael’s Portrait of Julius II (1511-12) and subsequently became part of the ‘conventional formula’ appropriate for the seated formal  portrait of a senior ecclesiastical dignitary. 

  9. Charles Cameron Says:

    LOL, okay, Michael, thanks for that! — but you’ve just moved the direct observation back a few painters, no? And later painters in the series presumably pick up on that detail and continue it because it is telling, no? Somewhere there’s an eye for telling detail, and somewhere that detail is telling enough to set up its own slipstream.
    I have to say that El Greco’s cardinal’s hands are more elegantly relaxed and tightly gripping, respectively, than Raphaels.  But then I’ve been a crazed lover of El Greco for more than a half-century now.

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