Monday, January 9, 2012

Why Is the World Four? Part 0

A very peculiar favorite book

In that peculiar period of my life when I went to graduate school to study things I was sort of interested in, dropped out to make money doing R&D on things I really wasn't interested in, and then returned to grad school to study things I actually was interested in, I was fascinated with William Irwin Thompson’s extended essay, At the Edge of History: Speculations on the Transformation of Culture. At a guess, I re-read it ten times, but it may have been twenty.*

The part of At the Edge of History that I have reread the most is a the fourth chapter, "Values and Conflict Throughout History." It's typical Thompson, i.e. it begins in one small, narrow, interesting place, rockets to a view of the whole world, and then gently deposits you back into your world. As a child, I remember reading a kids-sf novel in which a mouse finds himself sent up on a sounding rocket and becomes so enthralled with the experience that he keeps trying to get the human scientists to pick him for another ride (it was long ago, and the book was old then, written well before Gagarin and probably before Sputnik. ) That's kind of what Thompson does to you when he's on his game; there's a nifty little bit of intellectual cheese to nibble on, right through this—CLANK. THUNDER. WHOOSH. OH MY GOD IT'S THE WHOLE WORLD SPREAD OUT IN FRONT OF ME … and then forever after, you wish you could see that again, and whenever the giants in the white coats come by, you jump and dance and beg for another ride on the rocket.

Or if you're a much saner mouse than I am, whenever you see that sadistic bastard in the white coat you hide under something and hope he goes away. It's kind of a matter of taste and temperament. Once I became one of those white coat guys, I was always looking for mice who volunteered among my test subjects (or students, as I believe the Human Services department prefers they be called).

In any case, Thompson's "Values and Conflict Throughout History" leads off with an initial reference to John Marshall's famous ethnographic film The Hunters, (the link is to a trailer – imdb here if you find The Hunters more interesting than what I'm going to talk about further on down, which I think is entirely likely), a movie that we are lucky to have; Marshall, while quite young, gained the trust and apparently the liking of some of the last true hunter-gatherers on Earth, and was permitted to film four of them on a 13-day hunt in the early 1950s. (That tribe have all long since been forced to give up their traditional way of life; it's doubtful that there can ever be another movie like The Hunters for seeing how the whole human race lived until a geologic eye blink ago).

The four men on the hunt, Thompson argues, are not just any four dudes that were up for a hunt when they called for volunteers. He dubs them the Headman, the Huntsman, the Shaman, and the Clown, and argues that they represent four types that are fundamental to a human society that is going to accomplish anything together (and bringing down a giraffe by wounding it with a poisoned arrow and then tracking it till it drops, days later, is quite an accomplishment!) He sees them as the cells of a double, cross-cutting dichotomy:



Social Position

By "operational" Thompson seems to mean "getting stuff done day to day" and by "ideational," relating to or working with ideas/visions/dreams. So clockwise around those four, we have the High King, the High Priest, the Low Comedian, and Working Joe.

Thompson goes into a fascinating direction from that: he argues that larger and more complex societies keep re-subdividing each of the four categories into further powers of four, so that, for example, once there's an organized church, you replace the Shaman with an organization that will have Bishops (operational-high), Theologians (ideational-high), Mystics (ideational-low), and Scribes (operational-low), or once the Huntsman has become the military, the huntsmen subdivide Generals, General Staff, Warrior Heroes, and Common Soldiers.

As Thompson points out, the Trojan War story embodies this very well: the Greeks have Agamemnon, Odysseus, Achilles, and Ajax in those roles. We might without much violence to the idea also say Kirk On the Bridge, Spock, Kirk While Beamed Down, and then Bones/Scotty/Chekhov/Sulu/Uhura in a five-way split of the Warrior Hero/Achilles gig.** Or Thompson doesn't say it, but if you've ever been in an academic department, you will immediately recognize the Chairman, the Tenured Theoretician, the Departmental Stalwart, and the Poor Bloody Grad Student.

If you're a science fiction or fantasy writer, there's a lot of potential for figuring out imaginary societies on this basis, and if you're not but you write fiction, it's also a quick way to come up with a cast. I've used it off and on for all kinds of things.

But the most interesting thing of all to me is something Thompson says very early on in his essay:

This model of four seems to be a persistent one; it recalls the rule of four in the Indian caste system, Plato, Vico. Blake, Marx, Yeats, Jung, and McLuhan . So many people look out at reality and come up with a four-part structure that one cannot help but think that it expresses the nature of reality and/or the Kantian a priori pure categories of the understanding. But whether the [four part] structure exists in reality or is simply a projection of the categories of the human mind, is, of course, the traditionally unanswerable question of science. Since the mind is part of nature, we make a mistake when we imagine that the act of perception is through a window in which we are on one side and nature on the other. We are in nature, so there is no reason that subjectivity and objectivity should be so dissonantly arranged; it is more than likely that the key in which the nerves and the stars are strung is the same.

And there's my jumping off point; in the decades since I first read that, I've encountered at least a dozen other major theories underlain by a quadripartite division, and have seen that same splitting into four crop up over and over. And whether this is a case of a kind of theory for which I have a fetish, or it is actually a reflection of reality, despite what Thompson says, is not a completely unanswerable question; it's just not answerable with the kind of certainty that we have about, e.g., the atomic weight of vanadium or the range of possible dates for the birth of Genghis Khan. Rather, it's a question that demands a plausible answer —and I think I have one.

And hence the question at the top of this piece: Why is the world four?

Quadripartite divisions abound.

Modern politics often uses the basic division of Radical, Liberal, Conservative, Reactionary, which you can draw like this:

Basic orientation


Position about existing order

Aristotle said there were four causes of anything —by cause he meant ways of explaining them:

With regard to information source


With regard to time
and for those of you who slept through humanities class, essentially formal means by definition, material means by ingredients or substance, efficient means by process that brings it about, and final means by purpose.

The Four Gospels fit into a double dichotomy:

Main concern about Jesus



as do the four seasons:

Days are

Longer than nights

Days are

as do the four Beatles


Amiable doofus

Main musical position in group

Northrop Frye divided up literature into four forms:


Change or reversal

World seen as fundamentally
Romance or pastoral
Satire or anatomy

Medieval and Renaissance physicians believed we were governed by four Humors, or fluids:

Essential temperature


Essential mood
Choler (Yellow Bile)
Melancholy (Black Bile)

When four guys set out to rescue Princess Leia, they take along:

Led by


Han Solo
Obi-wan Kenobi
Takes orders
Luke Skywalker

And when four guys (and a whole lot of men in tights) set out to oppose the wicked usurper and serve the true king, they are

Physical Type

Small and fast

Mental Type
Robin Hood
Friar Tuck
Will Scarlet
Little John

And of course this would all be incomplete if I didn't at least mention the ancient four elements:




I have no doubt at all that I'll be getting some mail reminding me of all the ones I left out, too.

Now …. why? Why is the world four?

Here's my guess:

Notice that that four is always a double dichotomy. So to completely describe one of these foursomes, you need to record:

4 cells, plus
2 dichotomies.

Now, a basic principle ever since Alan Turing is that you can't think about something or solve problems related to it unless you have an empty bin or register to move the thoughts in or out of, so if you're going to think about a foursome, you also need

1 empty register (basically your scratch pad).

4+2+1 = 7.

Number of ideas most people can hold in the head at one time: 7. Some below-average but not actually disabled people go down to 5 —and don't think very clearly and get lost when they try. Some very bright people go up to 9, which is to say they can work with three empty registers and therefore work very fast.

I think that double dichotomy—two splits of the world into two categories—is the most complex idea we can easily hold in our heads and operate on all at once. For anything more complex we have to add registers somehow—writing down, memorizing and moving things in and out of memory consciously, etc. So the answer is

The world is four because that's as complex as we can get in our heads all at once, and to be useful, an idea has to not overflow our heads; and the best ideas tend to be more complex.

And that has a few interesting applications. Suppose a species of aliens is kind of dumb and all they can handle is one dichotomy; that would be 2 cells, 1 dichotomy, and 1 empty register, or 4.

It seems to me that's about as smart as most dogs and cats I've known; they can act on a single category (good people/bad people, people who kick me at the dinner table/people who drop food, etc.) and they can move people between them, or align with one side or other. (To dogs and cats we might also add ferrets and perhaps some voters).

And what if we go the other way? A triple dichotomy requires
8 cells
3 dichotomies
1 empty register

or the ability to hold 12 things in mind. Would such a being see us the way we do dogs? i.e. nice enough, sometimes surprisingly smart, but, well, you know. Still a dog.

In general the formula is that where the number of dichotomies is d, the number of registers required to have one of these ideas about it is 2d+d+1. Supposing you had an alien for whom d was = 5; they would have 38 registers. Would we be able to talk to them at all?

Anyway, many interesting things fit into these foursomes, and the foursomes have interesting properties all their own. That's why I've numbered this blog entry as Part 0. I know I'll be back to cases and points of interest about this topic, many times, though probably rarely will I write two of these back to back.

And now that you know what I mean when I write Why is the world four? you can either sensibly hide under the food dispenser, or hop around and see if I will send you up in a rocket.

* Nowadays At the Edge of History seems to be most widely available as part of a double volume published by the Lindisfarne Institute, which Thompson helped to found, if you find yourself so curious you have to look for it. Even that edition was twenty years ago, and I was afraid that when I opened the book again —I hadn't done so in four or five years —the magic might finally have faded. But when I sat down to review it for this essay, before I quite knew what I had done, an hour and a half had gone by and I had read about fifty pages, so I would say that for at least one person, the old magic is still there.

** Yes, that makes Kirk while beamed down the Clown. See how well this works?