Material Power Struggles:

If one defines power as the ability to get more power, or the ability to destroy someone else's power, then you can write differential equations to describe a power struggle. An example could be:


dx/dt = Ax - By
dy/dt = -Cx + Dy

Here y and x would be the power of different entities, and A-D are constants describing their relationship to each other. It could describe money (like a company investing in its own growth), or a battle (like armies shooting at each other).

The solutions to this equation are always exponential. Exponential functions are obviously not stable. So we get the conclusion that power struggles are unstable by nature; small differences in power become large with time.


Battle Math:

To describe a battle, you just get rid of the positive terms:

dx/dt = -By
dy/dt = -Cx

This basically means that the bigger one army is, the faster it kills the other army. C and B describe how good the armies are at killing each other. In the time domain, these look like shifted hyperbolic sines and cosines (where the graph is obviously only valid while both army sizes are positive). You can eliminate time, however, to get the following equation:

y^2 = (C/B)x^2 + R^2

Here, R is an integration constant. If you assume that the armies are equally skilled, and treat y as being the victorious army, then you get this simplified equation:

y0^2 = x0^2 + yf^2

Here, y0 and x0 are the initial army sizes, and yf is the final size of the y army (assuming that x loses and goes to 0). This means that the battle is described by a right triangle, where the hypotenuse is the initial size of the winning army, one leg is the initial size of the losing army, and the other leg is the final size of the winning army. It is just interesting to me that you can describe such a complicated situation with a triangle. I went into the map maker for Age of Empires 3 a few years ago and tested this equation by having blocks of riflemen shoot at each other, and the results always closely fit what the equation predicted. So, for instance, if one army has 100, and the other has 80, all else being equal, the 100-man army will utterly annihilate the 80-man army with 60 men left over. So, as said before, small differences in power (20 men to start with in this case) become large with time (60 men at the end).

From this kind of analysis, you conclude that in war, outnumbering your enemy has a greater relative effect than skill or technology (for example, to compensate for being outnumbered by twice as much, the smaller army would have to be 4x better marksmen). You also conclude that you want all your army to work together at once to kill the enemy. Anything you can do to break up the enemy army into pieces is going to be enormously helpful. If there is a large conflict with many different theaters, and you need to choose where to send a small number of reinforcements, then sending them where the battle is least certain will have the greatest benefit (better than sending them to a place where you're clearly winning or losing).

The fact that numbers matter so much could be why people have such a strong tendency to conform. It could be perhaps that there were many internal conflicts in our evolutionary history, where our ancestors needed to choose one side or the other, and the ones who picked whatever side seemed most popular were better at surviving.


Money as Power:

Money clearly fits the definition of power described at the beginning, since you can use money to make more money. The fact that companies or economies tend to grow exponentially fits the mathematical prediction of the model.


Money Vs Violence

If there were a man with a lot of money and a man with a gun in close proximity to one another with no other outside factors, then obviously the man with the gun has advantage over the man with money. Unless the man with money uses his money to buy force (like his own gun, or body guards), then his money is entirely useless in a competition against force. So, clearly, force is the superior kind of power. Money is only power so long as force is not allowed to come into play (such as a societal consensus that violence is bad, enforced by police).

It is usually desirable to limit the opportunity people have to use force, both because it's dangerous, and also because frequent robbery destroys all incentive to invest.


On the Morality of Power:

In a role-playing game, you can increase your character's stats, equipment, and skills without limit. In some games, you might be able to take on whole armies single-handedly at a high level. Such a thing is obviously impossible in real life, since there is a limit to how high one can increase one's stats (a bullet can always kill you no matter how much you can bench press). So, how is it that humans in real life increase their power beyond their own muscle?

It seems to me that power among humans comes from the appearance of power. Without consensus by his soldiers that he is their legitimate authority, a general has no more power than any of his soldiers. Without consensus about the value of money, then a rich man has no more power than a poor man. People gain power by having it given to them by other people. Thus, who has power is a moral question. Whatever/whoever people believe has power is what actually has power.


On the 1st and 2nd Amendments:

This train of thought leads me to believe that simple speech can be a political act. Expressing one's likes and dislikes, if one convinces others to think the same way you do, will influence who they give their power to. How are people going to organize a new political structure if they can't even express their desire for things to be different? So, it makes sense that speech was protected under the 1st amendment. It also makes sense that the people who currently own us are so zealous in censoring speech.

As discussed before, violence is the most fundamental source of power, so it makes sense that is amendment 2. To understand its importance, imagine the following. There is a president who lost an election, but he said, "F*ck you. I'm the dictator now." Suppose he had the support of the army, and suppose that the population was unarmed. What should they do? Vote again? This train of thought makes it clear that political power cannot exist without at least the credible threat of violence.


Why Is Power Limited?

The first thing noted at the start of this essay is that power struggles are unstable. You expect whoever is best at acquiring power to acquire more and more with time. So, why don't we live under an absolute and permanent tyranny? I think the main reason is because men are mortal. When a man acquires a great deal of power, he still dies, and his power is likely distributed amongst children who likely don't all possess his same level of skill.

So, if power is growing over long periods of time, it is not an individual man acquiring the power, but some organization which preserves its purpose with time and which maintains meritocratic leadership. If the organization either forgets its purpose, or the leadership is bad, then the power will be lost. So, perhaps simply maintaining purpose and quality of leadership are the main things to consider when trying to acquire power in a multi-generational project.

One disturbing conclusion of this train of thought, however, is that supposing there were an organization which maintained its unity of purpose and meritocratic leadership over many generations, you'd expect it to conquer the world and establish an unending tyranny.

The exponential nature of the accumulation of power may be the reason for the Pareto distribution.


A Prediction By Oswald Spengler:

Oswald Spengler published "The Decline of the West" in 1917. While reading the book, I wrote down everything that seemed to be a prediction, and checked at the end how many of his predictions came true. According to my judgment, he has +90% accuracy, which is very impressive for such an ambitious work.

One of the things he predicted was that the West would continue to be ruled by money and become increasingly corrupt until there was a transition to rule by force. He did not explain exactly why this happens, however, other than that, "..people become sick to death of money politics."

I was thinking about what causes the historical pattern that civilizations transition from rule by force, to rule by money, and then back to force. I have come up with a hypothesis.

In rule by brute force, people are dissatisfied because the force is arbitrary. The people (or respected rulers) establish laws which are respected so that rulers can't be arbitrarily capricious. The establishment of this law, however, depends on a general moral consensus of the population, otherwise it could not be enforced. Oswald Spengler would probably argue that this moral consensus IS a civilization, and the development of this moral consensus is what his book is about.

Law, however, is a static thing. But money can be used to beget more money. So, so long as the law restricts force and protects money and property, it leads the way eventually to rule by money. It is the nature of power that it tends to accumulate with time. So, eventually, the society becomes so unequal that the people would prefer a return to rule by force over rule of law. I suppose this happens when the people begin to view robbery as being just as legitimate as making a purchase (or perhaps purchasing as being just as illegitimate as robbery).

Or setting aside the force/money discussion for now, perhaps the pareto distribution is the cause of most/all societal upheavals. Because of the nature of power, you expect that in a stable society, power becomes increasingly concentrated with time. Eventually, it passes the threshold where people would rather overturn society and make a new set of rules than maintain the old system. Since a person's power is really nothing other than the appearance of his power, if it becomes known that most people don't want him to have power, then that is the same thing as him losing power. So, with every system yet discovered, society eventually becomes unequal to the point where most people would rather topple it and start over, and that's always what happens.