July 17, 2010 (ClubOrlov) -- Let’s face it, we, the civilized, educated, enlightened part of humanity like things to be straight. Let primitive tribesmen live in picturesque and practical round huts -- we require abstract boxes of steel and concrete clad in plate glass, with plenty of nice straight lines, true vertical and horizontal planar surfaces and lots of ninety-degree angles to please the eye. Let these tribesmen spend their days meandering up and down picturesque winding paths laid down by grazing animals -- when we build a road, we take a map and apply a ruler to it, and anything that’s in the way of that ruler, picturesque or not, must be dynamited and bulldozed because everyone knows that traveling in straight lines is more efficient.
This is good enough for most of us, and so we have come to regard straight lines as natural. In fact, in our world there are just two types of natural phenomena that give rise to straight lines: objects drop or hang down in straight vertical lines, and light beams travel in straight lines; beyond plumb lines and lines of sight everything is either a curve or a squiggle. But since most of our environment is artificial -- and crammed full of straight lines and flat horizontal and vertical surfaces -- we hardly ever have to confront this fact. Of course, the more scientifically astute among us know that straight lines are but a convenient fiction. We start with a conceptual framework of space that consists of x, y and z axes, and proceed to coerce our observations to fit this framework until the mismatch becomes too obvious to ignore, as with objects dropped from orbit, or with light from far-away galaxies that’s so warped by nearby galaxies that the image looks like a smear.
But the fiction is indeed very convenient. To start with, all straight lines are interchangeable and compatible. When we build, we tend to put things either on top of or next to other things, and if they involve straight lines, then no intricate fitting is involved -- we can just slap it together any which way and efficiently move on to our next box-building exercise. When we go to a lumberyard, what we buy is not so much wood as straight lines cut through wood. Trees know a lot more than we do about constructing maximally efficient structures out of wood, but we like straight lines, and so we cut through the strongest part of the tree -- the concentric rings of wood that make up the trunk—for the sake of making a perfectly straight stick. We could build beautiful, strong, long-lasting structures using round timbers grown to order (as some of us do) but generally we don’t because we are mentally lazy, always in too much of a hurry, and have made a fetish of straight lines.
Quite unsurprisingly, our preference for straight lines carries over into the way we think about relationships between things -- the mental models we construct of our world. For instance, we consider it a matter of moral rectitude and straight dealing that the price be linearly proportional to the amount of stuff we get: if you pay twice as much, you should get twice as many potatoes. Quantity discounts are acceptable and sometimes expected, but pricing on a curve is generally seen as underhanded. We mistrust curves. Stepwise functions are fine, though, because they are made up of straight line segments. We can put up with having tax brackets, but try taxing people based on a nonlinear formula, and there is sure to be a tax revolt. Were the potato market a product of biological evolution rather than of human artifice, it would perhaps work like this: the price would be some nonlinear function that’s directly proportional to the customer’s net worth, and the number of potatoes dispensed would be some nonlinear function that’s inversely proportional to his net girth. Place your moneybags on one sliding scale, your flab-bags on the other, and some potatoes come out. Such a natural regulatory mechanism would prevent fat, rich gluttons from out-eating the rest of us, but it cannot be, for we have a very strong cultural preference for a simple linear relationship between price and quantity.