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On Authority

 Some Flaws in the Analogy   Gödel's Theorem   An Example

## What Is Law?

A while ago, I'd been looking at Gödel, Escher, Bach again, and had also been thinking about law—probably because I'd run into one of its many absurdities, that's normally what makes me think about it—and out of the juxtaposition of the two popped the following idea.

Law is an attempt to delineate the complex boundary between right and wrong using only rectangular shapes.

Here's an example of the kind of complex boundary I have in mind. (If you've read Gödel, Escher, Bach, you may notice that this looks an awful lot like part of figure 18 in Figure and Ground.)

Suppose you had to explain to someone which parts of this figure are black without actually showing them the figure. (And suppose, if necessary, that you don't know the boundary is just a Koch curve.) One way to go about it would be to lay out Cartesian coordinates and then describe the black area as a series of rectangles. For example, the first rectangle could be the region { x < a }, the second the region { a < x < b and y > c }, and so on. The series would then give a better and better approximation to the black area.

Of course, one could also describe the black area in other ways, for example, as a series of polygons, but rectangles are just the thing for the analogy I want to make. You can see from my prose description above that a rectangle is really just a set of conditions joined together by logical operations (“and”, in this case), with each condition applying to a different dimension, or aspect, of the situation. Law, or indeed any system of rules, is exactly the same thing. Here's an example from the instructions for Form 1040.

Qualifying Child for Child Tax Credit. A qualifying child for purposes of the child tax credit is a child who:

• Is claimed as your dependent on line 6c, and
• Was under age 17 at the end of 1999, and

:

So, that's the analogy I wanted to make. There are several more things about it I'd like to discuss, but I'll put them into subessays instead of continuing here.