What size map do you need to model terrain perfectly?

Lewis Carrol’s Sylvie and Bruno Concluded contains a short(er) story containing an interesting concept: the only way to perfectly map a territory is for the map to be the territory itself. This is fairly self-evident; a scaled down model is just that, a model. For the model to be the thing, and not a model of the thing, it must be the thing. (See also: the map-territory relation and whatnot).

It also seems self-evident that there is some loss in accuracy in a model of a thing. If you apply this, take into account the “rational actor assumption” [TODO: write that blog post], and sprinkle in part 1 (TLDR: things are complex*) you land on something like Beer’s words from The Heart of the Enterprise (1979):

The case is that we constantly take a high-variety system, slash down its variety in order to penetrate its invariance, get the wrong answer – and then project that wrong answer onto the system, which we subsequently insist is as it is not – and never was. There are two realms of life in which this process appears with bizarre frequency. The first is in politics. Before joining in a laugh against politicians, we should recall that each of us is a citizen, and has a political standpoint of some kind… . The second realm is inter-personal relationship. Most people seem to be extremely incautious about falling into this trap. Speaking personally, and given that hardly anything that happens any longer occasions me much surprise, I am nonetheless repeatedly astonished to hear my behaviour described and my motives ascribed by others – even close friends. In politics and human relationships alike, we have no choice but to hold in our heads low-variety models of high-variety realities. We also have no choice but to attenuate the variety of new states of the system, since this is proliferating too fast for anyone to accommodate. Then obviously we shall make terrible mistakes in our judgments. Witness: ‘How could a socialist government in Britain allow its economic policy to be dictated by the International Monetary Fund?’ The answer is: with no trouble at all. Witness: ‘All I can say is that what he has done is completely out of character’. The answer is: it isn’t.

There yet remains one choice, however, that we can make, once we are alert to these risks. Given that incoming information has too much variety to be assimilated, and that we have no choice but to cut that variety down, we can either casually select aspects of the new variety generated that reinforce the low-variety model in our heads, or we can actively search for manifested states of the system that clash with that model, and constantly adjust it. Of course, it is far more ‘comfortable’ to do the former. Then the variety of the model shrinks, because the selection of inputs to it focusses more and more on its own most salient features; and this in turn leads to more astringent selection of inputs in the future, since the model in our heads tells us that many manifested new states are simply irrelevant. After this process has well and truly set in, it is only a matter of time before the unthinkable happens. It was unthinkable because the shrivelled model in our heads become incompetent to encompass it. To understand this (and perhaps variety analysis is an aid to that understanding) might be to change a vote, to preserve a marriage, to save a friendship, to cross generation gap, or to avert a strike.

My attempt to attenuate: most people are rational & well-intentioned; the world is too complex for anyone to truly understand (model in their minds). We should seek to understand well-enough before passing judgment on others. “I don’t understand” is a lot better than wrong.

*some would disagree, but “complex”~=“variety”