Good & Evil. God & Satan. Life & Death. Flesh & Stone. Ideal & Real. Isn’t every culture filled with dualities?
One, two, three … Every human culture can count to three. Ancient Chinese artists knew that if you subdivide larger groups into smaller groups, the viewer’s eye/mind system can take it in. Put three geese here, four nearby. The viewer will see three-geese plus slightly more than three: 3 + (3+1) = 7!
(Don’t tell me that few ancient Chinese took algebra. Stone age children learned that much algebra just by being what they were and looking around. It’s easily established that simple calculations go faster than counting. Besides, counting can miscount past three. Simple calculations are much faster and infinitely more reliable. We all do it. Even the kid who’s failing algebra does so only after making a few simple calculations that assure him that he’s safe to do so, and perhaps better off.)
The first group of geese in our Chinese scroll forms a polygon (a triangle) no matter how the geese are clumped. Ditto for the second — only there the polygon has four angles and four edges. See the two together: it’s another triangle.
A painting with seven geese can’t be taken in; a painting where the seven form a triangle of two unequal components can be “seen” by a six year old. Artists don’t waste their time with eight. It’s too much for the human mind. Maybe God could see it, but few of our representations are ever really for Him.
(We’re told of Eight Wonders of the Ancient World. There’s an eight. So what am I talking about? Seven is the minimum number greater than the two threes we can see. Eight is the minimum number greater than that. Therefore, each of our primitive minds automatically understands: an astounding number.
It’s like raining for forty days and forty nights. Or fasting for forty days and nights in the desert (or wandering or praying). What the “forty” means is a number greater than you can reliably count, calculate, or comprehend. The Romans said a “thousand.” We say millions. It means the same thing! It’s nothing but a linguistic form of inflation.
The experienced backgammon player doesn’t have to count his moves. Odd numbers go to an opposite color point; even rolls stay on the same color. Six is a single quadrant away: just go to the same relative point. The novice chess player soon sees how the queen’s power radiates over the board; only the experienced chess player sees how the knight can feint here, only to suddenly appear there! The chess player is still sub-dividing his world into manipulable components.
Now: is reality divided into triangles and lines and the little inverted-Ls of the chess knight? Are numbers “true”? Is there an identity between how we see and how the “laws” of the universe actually function?
If not, might there at least be an analogy?
It’s my position that we can’t know altogether what’s true, but that we can know some part of how we perceive and understand things. Monists are forever seeing things as One. In general, the religious impulse is an urge to unify. It’s certainly my urge (or has been most of my life) (though not always).
But unification can only go so far. If you make everything the same, then you can’t tell anything apart. Information, as Gregory Bateson teaches, is perceived difference. No difference would be the thermodynamic heat death cosmologists have been frightening us with. Total entropy. The end of information.
Monists, like the Scholastic Realists are annoyed by people who see more difference than they, the Monists, like.
One / Many. Continuity / Discontinuity.
St. Thomas Aquinas saw “chair”; Abelard saw this chair and that chair. Aquinas saw “Man”; Abelard saw Alison, Geoffrey, and John. But Aquinas too could address John when he walked into the room. Bertrand Russell was one modern nominalist who annoyed twentieth-century monists by emphasizing the discontinuities of the universe.
Drivers-training vehicles have dual controls. On the road, the public is in the least danger with vehicles having only one set of controls: no matter how drunk a particular driver may be. Even democracies assign one captain to a ship. Even democracies have one executive “at the top.” Even modern democracies don’t want two hundred and fifty million people all talking at once. You couldn’t hear anybody.
I don’t doubt that in the earliest days of religion (My piece on Magic argues that) man first invented only one god. But then he found more than one trouble. And the one god wasn’t always handling it satisfactorily. By one or two thousand BC who could blame the Jews for wanting a Chief Executive? By then even the Chinese had come to believe that all their gods were merely facets of Hung Ti. From a polynomial standpoint, the Trinity of Christianity is a clear evolutionary advance over the simple monotheism of Judaism. Humans will never be emotionally or perceptually ready for George Gamow’s 1, 2, 3 … Infinity. Lao Tsu was as wise as Homo sapiens can (as a group) get when he wrote:
From One comes Two
From Two comes Three
From Three comes Many.
I’ve long taken the title of Gamow’s book to be a translation of those words from the Tao Te Ching. Though, for myself, I Christianize them: From Unity comes Duality. From Duality comes Trinity. From Trinity comes Infinity.
But let’s leave unity, trinity, and infinity alone for a moment. I mount this piece today because I suddenly saw a pedagogically graphic use for duality, one custom suited to my current teaching here.
I’ve been writing here and there about definition, about ambiguity. Take justice for instance. On the one hand, everyone has his own imagined ideal of justice: your enemies under thumb-screws; your daughter married to Prince Somebody; Palestine back in the hands of … name your group. On the other hand, we have OJ Not Guilty; the mass murder legally insane and not responsible, therefore Not Guilty of Counts 1, 2, & 3; your wife with a new boyfriend so now she gets the Rolls, the Steinway, both the house in Vermont and the condo in Monaco, plus $8,000 per month …
What you want versus what you get
Your ideal versus what the judge says.
I’ve already discussed the example of Work elsewhere:
The physicists’ specialized meaning of force through distance versus the common language’s multiple meanings of Monday to Friday … what you do in the garden … what you do in your work shop … what you’re doing when you push against a wall (even if the wall doesn’t move) … Do you think you can use that tool inside your own head when you notice an ambiguity? So what? you may be thinking. Take it a step further. Use it to distinguish useful ambiguities from deleterious ones.
In his Point Counterpoint, Aldous Huxley offers a masterful contrast between what the politician is thinking when he offers speeches about liberty and what the audience hears as meaning. Talking about Liberty the politician is thinkingLet corporations do what they want.
Limit liability for medical malpractice.
For God’s sake, don’t elect Labour.
while the audience is thinking
Sit around, drinking beer.
Stand around, in your undershirt.
Feel up who you want on the street.
If I remember correctly, Huxley made his reader aware that the politician knew exactly how his audience was misunderstanding his words. Whether or not that’s so I hope you see it.
The French invested in their Maginot Line; but the Germans invaded from their flank, through Belgium.
You can not-smoke and not-drink and not-do-drugs … have a body as ready for immortality as you can make it … yet get hit by a car, hit by a meteorite … You can have some quantum improbability occur right in the middle of your healthy heart.
Because we can perceive, because we can imagine, because we see ample evidence of our intelligence, we tend to think that we have all the information we need to make right decisions.
There’s a great moment in literature that I often recall in this connection: Joseph Heller wove a number of iterations in his Catch-22, bits of flotsam that gradually pattern and form a clear picture. We meet the character Snowden in bits and pieces long before we meet him.
Yossarian was a pilot. Snowden was a gunner. Throughout Yossarian’s thoughts are troubled by Snowden: Where are the Snowdens of yesteryear? … “I’m cold,” said Snowden. … “And Snowden lay dying in back.”
Their plane has been hit (while they’re dropping bombs of course: it’s WW II). Yossarian finally gets time to attend to Snowden. He finds a wound. He treats it. By the numbers, by the book: stop the bleeding, clean, disinfect, bandage. But Snowden continues his litanies: “I’m cold.”
And when he turns Snowden over, the remaining blood in Snowden falls out the huge hole in his back. Yossarian has been busy treating a minor wound, while Snowden’s life spills through a major wound. Not only Snowden flesh and Snowden fluids gush out of his back, but Yossarian can clearly see the stewed tomatoes Snowden had had for lunch!
But Yossarian had thought he’d been doing the right thing! Yossarian had been doing the right thing: he was dealing with what he saw. How could he have dealt with what he didn’t see?
That’s what we need science for: to keep looking, to never think we’ve got it all.
But society will never be run by science. Society is run by people too busy, too self-important for science: the people who give budgets and who take away budgets: the people who free Barabbas and condemn Jesus: people.
The “practical” people.
Oh, wait: I’m in terrible danger of being misunderstood there, understood too quickly, too easily, shallowly. (So what else is new?) (And I’m not writing this draft anywhere near perfectly yet either.) My point is not that the wrong party was in power … that if smarter people ran things … that if only the Communists had won, or Charles were still king, or if only Congress were two-thirds Libertarian … Homeostasis would still be the law even if the average IQ were 110 to 130, not 90 to 110. Homeostasis would still apply, as far as we can tell, if human intelligence doubled: some still greater intelligence would still be out of reach to the new majority. Those with 190 to 210 IQs would still gang up against the one or two with IQs of 260 … And Not Know They’re Doing It! (Or, they’d know it the way we know Godel, or Korzybski, or Mandelbrot … not really.
Walter Reed could have missed Snowden’s big wound. So could Einstein.
And I’m sorry, but so could God!
I have the inestimable privilege of seeing things that the group doesn’t see, doesn’t want to see, can’t afford to see — not and keep its flattering images of itself. Once upon a time I thought I had my intelligence to help my fellow man. now I realize that my fellow man will die of stupidity rather than admit to imperfect wisdom. My destiny was not secular savior after all. Rather I am a bit of ignored irony. I shouted Fire, and the society sat for more of the show.
People think their institutions are good enough for their intended purposes: so we back the institutions: as they dump the bleeding bodies of whistle blowers in the alley.
My university knows no more about my reading of literature than it did before I tried to share it starting in 1962. They were there to fill me with their old wine; they were not there to let me fill them with new wine. Communication flowed from top to bottom; it was not dual, not two-way.
Only feedback traditionally prepared for was heard.
The guns were aimed at Germany; not at Germans coming through Belgium.
Yossarian was not stupid. In the case of Snowden’s big wound, he was merely wrong.
But I’m sorry. I say our society is stupid. It still won’t hear me, refuses my warnings.
Doesn’t know it’s done so, is still doing so!
And now [extended 2007], the FBI arrested me (so my university’s not having to lisen is now official). The US Federal Court censored my site, the host destroyed the information: government and industry cooperating to destroy evidence when told of a citizen’s indictment.
Hey, Pogo: we’re not just the enemy; we’re the Nazis!
And the Nazis called themselves the good guys too: without a single intelligent discussion allowed: except for how to design rockets.