“I am not a number! I am a free man!” So begins one of the filler songs on one of the top 5 metal albums of all time. But I come here today not to extol the virtues Bruce Dickinson or to ruminate on the fact that galloping bass-lines are best bass lines.
No, today I’m here for something much more interesting – Math!
Let’s take a look at second grade arithmetic. Here’s a refresher on the equivalence properties of equality:
- The Reflexive Property tells us that an A is (equal to) an A. Oh, now I’m sad again.
- The Symmetric Property tells us that if A is equal to B, then B is equal to A.
- The Transitive Property tells us that if A equals B, and B equals C, then A equals C.
Pretty straight forward, and if you want to do arithmetic or algebra, these are the rules that let you do it. But there are a lot of assumptions built into. For example, you can expand the Transitive Property of Equality to generate the Transitive Property of Inequalities, such that if A is less than B and B is less than C, A is less than C.
And that is useful and intuitive too. You can do some nice arithmetic and algebra with that too. But like both my graduate-level math classes and my collected works of HP Lovecraft reminded us, there is more to this universe than nice reasonable Euclidean space.
Take football. If Directional State beat Poly A&M last week, and Poly A&M beats Costal U this week, stands to reason Costal U has no hope against Directional State next week, right? After all, if DS > P A&M and P A&M > CU, so we know DS > CU. Just stands to reason, Transitive Property and wot not. All us learned gentlemen can see this.
And a any sports fan knows… That’s not the way it works. CU beats DS in, what, 35% of the games under this scenario?
It’s almost like you can’t apply the Transitive Property to a model when in reality it doesn’t apply. You can’t just apply theoretical rules, you have to look at the real universe and see if they apply before you can incorporate them into your model.
So let’s move to another domain and see if all the rules of basic arithmetic apply. A man, a woman, and their kid are going backpacking. Weight is the limiting factor, they can walk until any one of them is worn out. In a universe that is perfectly fair, but stupid, they all would carry the same load. In the real world, the kid would carry a day of food, a day of water, and emergency supplies. The woman would carry a bit more, and the man would carry the most. They then hike farther than in the stupid and fair world. Thus, the transitive property holds true in this model.
Here’s my first assertion for this series of articles: Assuming arithmetical property where they don’t actually exist in humanity is the root of most evil these days.
One place that it shows up* is in macroeconomics. Specifically, I’m thinking of the study of optimal tax policy. This is the study of how to structure taxes to maximize utility. Assuming arguendo that taxes will be a thing, how do you structure them so that the most good / least bad is done by them. There’s a lot of math, behavior economics, etc that goes into these analysis. And there are some beautiful curves telling you how to structure a tax policy.
And they are always wrong.
They all boil down to how much can I rob Peter to pay Paul. If a tax structure results in Peter having -3 happy points and Paul getting +5 happy points, that’s a net of +2 happy points. So that’s a winner right? (I’m going to call “happy points” by their common made up name, utils.)
No. There is no +2 utils floating around as the product of aggregation. There isn’t Peter+0 and Paul+2. There is only Peter-3 and Paul+5. This leaves a pissed off Peter and a Paul who is going to get trained in the fine art of rent seeking. Take it too far, and the Peters revolt. Take it too far the other way, and Paul becomes a parasite on society. Keep it right in the middle, and you can divide and conquer Peter and Paul for their votes.
Why does aggregation work for the backpackers and not for the taxpayers? Distance. Emotional distance, to be precise.
The backpackers are a family, but that was just an excuse to use a kid in the example. They could be a group of friends out for vacation, or a firm out to find gold in them thar hills. Human nature says that those we care about are those closest to us. Its
normal for you to care about yourself. Adam Smith has a great example about a man in Europe facing the loss of his finger and hearing about an earthquake in China. Which one does he care about more? The finger, even though he would know that that’s nothing compared to hundreds of deaths. It sounds cruel and heartless, but that’s just utopian thinking. In the real world, we all can identify with this idea. The closer you are to someone else, the more you care about them.
You might even care enough to take on their burden to make their life easier. In the real world, a parent would pay -3 utils to see their kid get +5 utils. The transitive property works because there is an emotional bond there.
But there are 300 million people in America. Any random American can only have a personal relationship with maybe a few dozen of them. Any system that assumes the aggregation utils among all Americans is going to be a cock up.
So ok, there’s one mathematical model with this flaw. Hardly the root of all evil. Well, step out of the math and into the real world. Race. Class. Religion. Political Party. These are all aggregation techniques. On rare occasions they are useful mental shortcuts. In most cases, they just erase the individual in your mind and replace them with a cardboard cutout called up from your own mental Hollywood. All cops are violent. All Southerners are racists. All progressives are stupid. All intellectuals are out of touch and dangerous.
These are common errors in thinking. And they are the root of all major humanitarian disasters of the last century. Except it was all blacks being violent, let’s roll out the drug war. All reactionaries are racists, let’s roll them off to the gulag. All low-income female workers are stupid, let’s sterilize them. All intellectuals are a danger, let’s hunt them down. The pattern repeats itself, and as we’ve seen, this pattern is dangerous. Any pattern that could lead to genocide, mass sterilization, or the drug war should be cut off before it can get anywhere near this scale of disaster.
So I hope here to have laid out a case that aggregation doesn’t apply on the large scale. But for individuals, they can have it apply to themselves and their small circle. This error is complex, but it reaches into some of the worst events in living memory. In the next article, I’ll discuss how a person could harness this insight to make themselves a better person. And in a twist that I’m sure would make all of you Jordan Peterson fans with clean rooms interested, this technique doesn’t require any change from anyone but yourself.