Wednesday, January 1, 2014

Check Your Premises

I studied mathematics in school. And I loved the way Euclidean geometry started with some postulates and reasoned from them into theorems. Hopefully, you had this in your sophomore year of High School. The most controversial of these was his fifth postulate:
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Some thought this postulate should be derivable from the postulates. Over the course of centuries mathematicians came to understand that this postulate was either true or false based on the curvature of space. Positively curved space is what you find on a globe. Two lines of longitude may form two right angles with the equator, but they end up meeting at the north and south poles. (This is termed Reimannian geometry.) Another way this axiom is false is when you have negatively curved space. This is the space you see in pictures of black holes with those hyperbolic shapes. Einstein played with a lot of hyperbolic spaces when doing General Relativity. (This is termed Lobachevskian geometry.)

If you're near a black hole, on a globe, or on an ideal plane, Lobachevskian, Reimannian, and Euclidean models will match your observed reality, respectively.

We see this pattern of axiomatic systems repeated in other contexts. If you're better at Math than me, you can talk about Zorn's lemma and the Axiom of Choice: they work the same way. And I'm of the opinion that the existence and non-existence of God is one of those things that you can use to build two independent, logically consistent explanations for reality. Logic and proof about God's existence is not going to do anything but make you tired, you can only match up how well the system of thinking (axiomatic system) your come up with matches observed reality.

If you're still with me, consider another branch of mathematics you did not learn in grade school: Game Theory. Suppose we play checkers, chess, or poker. You can either win, lose, or tie. The winnings of any player come about pursuant to the losses from other players. These are the games we're most familiar with and they demonstrate the zero-sum games.

But there are other games in life that don't look like games. Life Insurance is a game where the insurance company bets that you won't die, and you bet that you will die. (I rather like the idea of corporate fat cats betting that bad things won't happen.) Casinos also make wagers, but they rig the odds so that your expected payout is less than the amount you wager. A few bettors may win big, but for the most part, only the house gets rich. The profits the casinos take from winning more often that the lose make this a negative-sum game.

Suppose Vikings invade a region to loot its goods. If the victims peacefully hand over the lolly and the Vikings leave with it, it's a zero-sum game. But if they rape, pillage, and burn, those incidental damages make this another negative-sum game.

How about free exchange between willing participants? You've heard business consultants tell folks to think win-win. Economists who know more than I claim that free trade creates more wealth than it consumes. 

Let's say I have a handful of radio parts, and you have a handful of grain. If you need some diodes, and I need food, we can exchange and we will both be better off. 

Our natural desire to get more value in exchanges like these motivate us to grind the wheat into flour, mix it with yeast, and bake it into bread. Or fashion those radio parts into a desirable gadget--a radio, or something more valuable. We exchange better things and we benefit more from the exchange.

Technology enables us to create value without taking from others. We start with some plastic, use electricity to heat it and extrude it into a particular pattern, then a few cents' worth of plastic become a part we can sell for dollars. Maybe a farmer uses that plastic part in his irrigation system to use less water and thereby sell more food more cheaply. 

I think that technological innovation makes free trade a positive-sum game. As it becomes cheaper and more ubiquitous, the things only GM could do when I was a college student are within the grasp of makerspace tinkers today. And will be within the grasp of third-world bohemian have-nots within a decade.

I was once scolded by a famous economist when I asked whether productivity gains could solve inflation. When I asked him, one could buy a 19" analog color TV for about a thousand dollars and watch three channels. He was right about inflation. Gold was selling for a couple hundred dollars an ounce and it is well over a thousand dollars an ounce today. BUT a couple hundred dollars will buy a much nicer television that receives much more interesting programming.

I said before that the destination of economic inequality is less important than the way in which we get there. Economic Inequality is a terrible thing if life is more like a negative sum, or zero sum game: Pirates raiding villages, or Politicians (both Republicans and Democrats) enriching cronies on the backs of everyone else, or Casinos making a few rich to distract while impoverishing the rest.

Our world is a mix of negative-sum, zero-sum, and positive-sum components. When economic inequality comes about from the first two, I am justly annoyed. When it comes about from positive-sum exchanges, I remember the last thing Moses brought down from the mountain.

Thou Shalt Not Covet.

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