pulled every which way but going nowhere

equilibrium and homeostasis

Now that publication’s done and I’ve somewhat decompressed from Santa Fe, things might start getting a bit back to normal. After some really interesting conversations with Ben Rechts (whose ‘stack is great, btw), he convinced me that the distinction between the engineering (and medical) concept of “homeostasis” and the economic (and physical) concept of “equilibrium” is really important to make.

It’s quite a subtle distinction, and there’s quite a bit of overlap – by definition, a system that’s in equilibrium is going to remain in the same state.  The big difference is that using the word “equilibrium” implies that it’s in some way the lowest-energy state of the system (either locally or globally), whereas “homeostasis” is something that requires continuing input of energy to maintain.  As one might put it in a medical context, there are two ways that your blood sugar can remain constant – either your endocrine system is working to balance the metabolism of glucose, or you’re dead.

As always, the way to get your head round tricky concepts is to look at the metaphors and jokes people use, and take them literally.  Economics textbooks (and even more so, finance textbooks discussing the concept of arbitrage) will often talk about the impossibility of having half the water in a lake being six inches higher than the other half.  Although implicitly we’re meant to understand that the water molecules are people, the gravitational forces are their incentives to maximise utility and the movements are transactions, this isn’t the focus of the metaphor at all - we’re meant to imagine a flat pool of water with nothing going on.

This sort of thing reliably drove Austrian economists crazy, and it’s hard to say they didn’t have a point. An economy in equilibrium is one in which there are no transactions, but how can you have an economy without transactions? And why, other than the fact that the mathematical toolkit is so damned convenient, would anyone think that the best way to understand truths about the economy is to consider a state which it could never actually be in?

Stafford Beer’s description of homeostasis in “Designing Freedom”, on the other hand, involves a fanciful description of men balancing on platforms, all holding fishing rods connected to elastic bands and trying to work together to keep a tennis ball in the middle of a circle.  It’s actually so lovely that I can’t bear to edit it down, so I’ll just reproduce it here, and then come back to the point I was going to make on Friday.

If the men on top of the poles do their respective jobs properly, they will pull correctly on the elastic. The ball—which marks the output state of the system—will bob about for a bit, and then be still. The dynamic system is doing its work, and producing stability. If the men are inefficient, and cannot make up their minds how to pull on the elastic (especially if they keep passing the buck), then the ball will bob about for ages, and may never settle. This system is unstable. However: if we assume goodwill and reasonable efficiency on the part of the two men, so that they behave like proper elastic connexions, the ball will soon stop bobbing about. The time it takes to stop is called the relaxation time of the system.

Well, this picture is a bit too simple for our needs. So let us erect a lot more poles (try to imagine about forty of them) arranged in a circle, where our original elastic connexion marks a diameter. Now let us join all the new men on the top of these poles to the system, by giving each one a piece of elastic and tying the other end to the central knot. These new members of the institution are not all equally proficient, or loyal, or hard-working; and we can represent that by giving some of them thin pieces of elastic, and some of them thick pieces. The ball was disturbed while we did that, and I think we can bet that the relaxation time will now be extremely long. In fact, and this is really rather interesting: the harder all the men try conscientiously to manipulate the system so that it settles, the more unstable it is likely to become. Just imagine the chaos. “Hey, George, stop pulling a minute;” “Harry, you pull a bit harder.” And so on; In fact if all of forty men are each trying to give instructions to each of the others, we shall have 1,560 communication channels trying to speak all the time. You are right: it isn’t going to work.

The reason is that this system as a whole has too many possible states. I am not talking now about the solitary output state, but about the vast number of configurations which the organization itself can assume. Every one of those men on the poles may behave in a great many alternative ways; and these are permuted together to reveal the total richness of possible organizational behaviour. If we consider the total number of behavioural configurations that are possible, we have a measure of the system’s complexity. Let us turn this perception into a formal definition. The number of possible states of a system is called its variety. This will be a most useful word for us, so may I repeat: variety means the number of possible states.

Suppose that each man can do only one of two things, which is an absurd simplication after all. Then between them they can produce more than a million million possible sets of conditions for the system. It is too many; and the tennis ball will never be able to settle. At least, it will in theory .But in practice the world is not going to leave the system alone for long enough. Just imagine those poor men feeling they have almost exhausted the possibilities after a week’s work, when the cat comes into the garden, and takes a playful swipe at the ball with its paw. It is back to square one.

All our major societary institutions are high-variety systems; all of them need to have a finite relaxation time; but all of them are subject to constant perturbation—which is the word to use for the unexpected interference of the cat’s paw. How do they cope? There is only one way to cope, and all institutions use it—although they use it in many forms. They have to reduce the variety of the system. Here are some of the ways.

They may put in four more taller poles, and connect ten of the shorter ones to each. The man on the tall pole gives instructions to his ten subordinates. That reduces the total system variety, but it also interferes with the short-pole men’s freedom to do the best they can. It is in this way that freedom starts to be subordinated to efficiency; but the only alternative—which we must face—is total anarchy.

Second, they may put in a lot of rigid connexions, called rules, between the elastic threads, so that the system looks like a spider’s web. That also reduces variety. But that confounded cat keeps coming around, and spoiling the whole effort. Or suppose that the child of the house comes into the garden and takes a tremendous crack at the ball with a tennis racket. Then the system may not have the resilience to take the strain, and may collapse altogether.

A third variety reducing method used by institutions, for example banks and insurance companies, is to shoot the cat. This works, but is no fun if you are the cat. In any case, you had better not shoot the son of the house.