This post is meandering philosophical whimsy that goes nowhere. If you don't get off on that sort of thing, best stop reading now.
Suppose you were looking at a map, or satellite photo. If you saw a straight line, you could be sure it had been drawn by a human hand, not by natural forces. Rivers, coastlines, mountain ranges, all curve and squiggle in irregular ways. But some roads and boundaries are straight lines. They were drawn by human hand. Or alien hand, like Martian canals.
But not all roads and boundaries drawn by human hand are straight lines. In England, if you see a road that's a straight line, you can be fairly sure it's a Roman road (or modern). As for the rest, the Anglo Saxon roads: "the rolling English drunkard" made them. They weren't planned and drawn by one hand at one time. They were drawn by many hands (or feet) at many times, and meander all over the place.
So when I saw David Beckworth's graph of the the Euro monetary base, and how straight the line looked, my reaction was immediate. "That's a Roman road; it's not Anglo Saxon". Somebody must have deliberately made it straight.
There are straight lines in physics. At least in Newtonian physics. Are there any straight lines in economics?
My basic answer is no. Everything in the economy is drawn by human hand. But nearly everything is drawn by many hands at many times. Economics roads are Anglo Saxon roads. If we see a straight line in economics, it means it's a Roman road, deliberately made straight by some single hand. Like an exchange rate that some central bank has decided to fix.
Here are some exceptions: The Long Run Aggregate Supply Curve is vertical; the BP curve in Mundell-Fleming is horizontal; the demand curve facing an individual seller in a perfectly competitive market (like the supply curve facing the individual buyer) is horizontal; the budget line is a straight line.
But all these exceptions seem to be a special case. When we draw the LRAS as vertical, we are saying there is zero relationship between P and Y, in the long run. Likewise with individual sellers' and buyers' demand supply and budget lines in perfectly competitive markets. And the BP curve for a small open economy in a competitive world market for loanable funds. There is zero effect of the individual's purchases or sales and the prices.
There are constants in physics that are not zero. Are there any constants in economics that are anything other than zero, or one?
Plus, no econometrician ever observes any of these straight lines, just by looking at the data. The straight lines (if they are straight) have to be estimated, by holding all other things constant. We would only observe them with the naked eye if all the other things were in fact constant, which they never are.
Economists may draw straight lines, but that usually means nothing except they don't know which way it curves.
I can't think of any processes that would tend to make an Anglo Saxon road in economics -- an unplanned road drawn by many hands -- a straight line. By sheer fluke it might be straight, if all the individual meanderings exactly cancelled out in aggregate. But the chance of that happening would be almost zero. If we see a straight line it is almost certainly a Roman road, that a single hand decided to draw straight.
I sometimes hear it said that economics is a "linear" subject. There are two meanings of the word: straight lines; and a plot that starts at the beginning and goes on to the end, with A causing B causing C....etc. In neither of those senses is economics a linear subject. It's all curves; and there's lots of feedback and simultaneous causality.