The Collapsible Triangle


A few months back, while researching the ring-finger piece, I came across something that I haven’t been able to get out of my head.  Not something in any of the source articles themselves, but rather in the pissed-off comments from people at the bottom.  Obviously, it is not remarkable that people on the internet were pissed — any article about gender difference being rooted in biology is going to have angry comments from feminists at the bottom, just like how any YouTube video of a Black guy wiping out is going to have poorly-spelled racist comments at the bottom.  What was interesting was the high incidence of comments cracking wise about religious sexism:  Adam and Eve, and God making the genders different, and the Pope saying that stuff about women being good listeners and all that.

The feminists weren’t accusing the scientists who conducted the studies, or the journalists who reported the findings, of being religious exactly — they were just declining to make a distinction, typing comments to the effect of “Duh why cant u just accept it God made you different ya right” as if dismissals of religious gender-difference arguments also functioned as dismissals of scientific gender-difference arguments.  This floored me.  Surely, whatever your views about gender, everyone knows that scientists are the opposite of religious people.


Well, it occurred to me that, like so much does in this universe, this may depend on where the observer is standing (philosophically speaking).  And the more I thought about it over the subsequent weeks, the more argument situations I found that this model applies to.

Picture it going on in physical space:  you are standing between two tall buildings.  You can plainly see that there is a good deal of physical space between them (obviously, since you are currently occupying that space).  Now get a few blocks away:  the distance between them seems shorter.  Now get miles away, so that the buildings are on the horizon:  the space between them has disappeared, to a point where they now appear to you to be one single building rather than two.  You and the two buildings actually form a triangle, but from where you are standing, it appears to you that you form a straight line.

Now apply that analogy to philosophy:

triangle one

I’ve written other articles pointing out the ways in which Academic Feminism appears to be similar to religious fundamentalism, of course.  But what hit me when I saw those comments is the fact that the same effect is going on at all three points on the triangle, not just mine (I know I’m not a scientist by profession, but I have a scientific worldview, and so for the purposes of this analogy I’m on the Science point of the triangle).  From the point of view of a Feminist, the groups “Scientists” and “Religious People” are collapsed into “People Oppressing Women By Arguing That They Are Inherently Different From Men.”  From the point of view of a Scientist, the groups “Religious People” and “Feminists” are collapsed into “People Who Ignore Empirical Evidence Based On What They Want To Be True.”  And from the point of view of a Religious Person, “Feminists” and “Scientists” are collapsed into “People Who Seek To Undermine Traditional Religious Beliefs, Customs, and Values.”

And it’s not like this is the only Philosophical Mexican Standoff (the thing in a movie where three people all draw guns on one another at the same time) where the analogy holds.  Once you start running with it, you can think of tons more.

triangle two

In this Collapsible Triangle, the Conservative Government combines “Liberal Teachers” and “Teenagers” into “Pot-Smoking, Sex-Having, Cynical, Unpatriotic Goof-Offs.”  The Liberal Teachers, in turn, see both the teens and the government as “People Who Hurt Others With Their Uneducated Aggressiveness.”  And finally, the teenagers simply see “People Who Are Always Telling Me What To Do.” 

triangle three

Assuming the Hawks and Hippies are in the same country, the Terrorists will see them both only as “Infidels” (or “Decadent Westerners” if it is the Imperial Communists from 50 years ago).  The Hippies will look at the Hawks and Terrorists/Communists and see “People Who Try To Solve Everything With Violence.”  And the G.I.Joe crowd will see only “People Standing In The Way Of Freedom” (or whatever).

It even works with art:

triangle four

The Bubblegum Pop fans will look at the Metalheads and Grungers and see only “Loud Guitar Music That You Can’t Even Dance To.”  The Alt kids will dismiss both Cock Rock and Dance Pop as “Mindless Drivel For The Masses.”  And the Metal Dudes will oppose both Alt and Pop as “Music For Pussies.”  (I’m sure there are a million ways to do this with various genres and sub-genres and sub-sub-genres of popular music, but this was the first one that sprang to mind.)

This model explains nothing about who is “right” regarding any of the issues to which it’s applied, of course.  It isn’t supposed to.  What it is supposed to do is help us examine the ways in which our philosophical oppositings aren’t as accurate as we think they are.  Now, I’m certainly not pulling from the P.C. Playbook here and trying to say that there are no opposites (“the tyranny of the binary,” as a '90s Humanities Professor would have put it).  Any of the hard sciences will inform you that the natural world has opposites coming out its ass (wherever that might be).

But philosophy is not a hard science (i.e., although it is often “hard” in the sense of “difficult,” it is not one of the hard sciences, e.g., physics, chemistry).  The hard sciences start with the external world and try to get information about it into our brains; philosophy starts with our brains and tries to get information about them into the external world (i.e., into books, whence into other people’s brains).  And the flaw in talking about beliefs having opposites is that it rests on the assumption that human thought behaves like objects in three-dimensional spacetime (i.e., physical “real life” as we are used to seeing it).  And this is rather arbitrary.  Yes, the brain is a physical object operating in three-dimensional spacetime, as are all of its component parts and impulses, even the really really tiny ones,  but thought itself — that is, being in the state of experiencing a thought — is not itself a physical operation, but rather the non-physical impression we get as a result.

This mistake is understandable, since it is quite literally impossible for us to think about anything behaving in any other way.  I am getting out of my depth here, but as I understand it, even Stephen Hawking et al cannot picture, say, objects operating in twelve-dimensional spacetime, but only perform the math that represents such operations (what we can picture mentally is limited by how we see, and although the brains of world-class physicists are very different from ours, their eyes are not).  That is the point of advanced math:  it is a symbolic system that allows us to communicate at a level beyond the sense that observation is capable of making (e.g., you cannot see negative five apples).

The Collapsible Triangle is a simple mathematical metaphor that can help people work out the kinks in their argumentative perception.  Somehow, scientists, feminists, and fundies (for example) really are all the opposite of one another, even though our minds, as trained by both the observable physical world and traditional argumentation, insist that "opposite" means there are only two of whatever’s going on.

In addition to helping us sharpen our own arguments, keeping the Collapsible Triangle in mind can help us disarm arguments unfairly leveled at us:  “Maybe this person who’s pissed at me isn’t actually pissed at me, but rather is under the impression that I’m the same as some other people who I’m not really the same as, so my first move should be to figure out which other people she/he has in mind and distinguish myself from them.”  You and the other person may still end up disagreeing about a lot, but at least you’ll both be directing the right arguments at the right person.

It’s also beneficial because it makes you more aware of “the enemy of my enemy is my friend” situations and the Machiavellian allegiance-switching that they demand:  in the ‘90s, feminists and spiritualists teamed up against logic, but then when the fundies got too powerful under George W. Bush, the rationalists and feminists teamed up against the Religious Right (and although no society has yet become matriarchal enough for this to happen on a grand scale, on certain college campuses it has become necessary for religious and rationalist students to work together to resist feminist tyranny).  This process is a pain to people who wish that one of the points on the triangle — i.e., their own — would just win already, but it is, I suppose, comforting to those who like the idea of society eternally shifting to remain “in balance.”

I’ll close by remarking on how strange it is (to me) that I can’t find this rubric reflected in Myth anywhere.  Most religions, legends, etc., divvied up their metaphysics either among many Gods with a panoply of duties and personalities (e.g., the Greek Gods, the Norse Gods) or between two, a “good” one and an “evil” one (e.g., Zoroastrianism, Judeo-Christianity, and yes I know these religions are monotheistic and hence have one official creator God, but despite this there is somehow always also an evil counterpart whom, despite being officially less powerful than the good God, the good God doesn’t just destroy for some reason, so monotheistic religions are actually dualistic).  To my knowledge, there has never been a mythos involving three and only three Gods, all cyclically waxing and waning in power, with the less powerful two always united against the third.  Honestly, it is staggering to me that this was never a religion.  Go figure.

There are groups of three all over mythology, of course (the three Fates; the three Graces), and plenty of individual three-natured divinities (the Catholic Trinity; the Greek/Roman Hecate/Trivia, whose feast day it turns out was just the other day, August 13th, the day I started writing this essay).  But those groups of three are all on the same side.  I can’t find any examples of groups of three that all war against one another via eternally shifting alliances, except in two mythologies, both relatively recent:  one is the three superstates of Oceania, Eurasia, and Eastasia in George Orwell’s 1984...

…and the other is the third-rate '80s toy line Battle Beasts.

I only knew one kid who played with Battle Beasts, and I guess I never gave him enough credit for being philosophically advanced.  At the time, I vastly preferred Army Ants, which involved only two opposed forces.

But I’m learning.

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