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What if we could use mathematics to figure out how to make ourselves happier? I submit for your consideration that it is, in fact, possible.  In this post, I construct a simple mathematical model of experiencing the world, and then derive some principles from the model which I believe are applicable to real life. Let’s begin! Consider the following graph of my happiness over the course of a day:

The day starts off well, and reaches a peak when I eat my breakfast of eggs and turkey bacon. Yum. I get into my car, and there’s a wreck on 15-501, so I’m late getting to work. My mood goes down, but it’s still positive. Upon arriving at work, I realize that I’ve fallen seriously behind in a big important project, so my mood falls. As I work harder and harder, I keep realizing how much more work I have to do. My mood plummets, until lunch time. A dozen buffalo wings provide a brief respite and put me in a better mood, but I’m still frustrated about work. I have time to think at lunch, though, and I realize  I can save myself some time if I take a new approach that I hadn’t though of.  My mood improves, and by the end of the work day I’m happy again.   After I get home from work, I relax by playing a game of Left 4 Dead with some friends, and my mood improves back to where it was.

The above graph was generated using a type of randomized noise function called Perlin noise. In other words, I modeled happiness as simply the summation of random waves. What better models can we use to describe and predict how people can become more happy? If happiness is a function of time, the simplest model says that we just choose to be happy all of the time. I would argue that the ‘choose to be happy’ model is too simple to be very useful.  Happiness isn’t a simple binary choice: It’s hard to choose to be happy when it’s cold and dark outside, and you feel tired, lonely, and hopeless about the future. Conversely, It’s easy to choose to be happy when it’s sunny outside, you’ve just enjoyed a nice meal with friends, and now you’re playing a sweet designer German board game, like Dominion.  These  examples are taken from points in my life. Your mileage may vary. The examples demonstrate that, very often, external factors in your life play a huge role in how happy you are. I believe it is possible to influence those external factors, but influencing them Isn’t as simple as just saying “I choose the happy path.”

A more predictive model of happiness must therefore take into account external factors as well as personal choices.   After giving this idea a lot of  thought, I came up with a model, based upon the concept of ‘Experience-Space.’  Experience-Space is the set of all possible experiences that an individual could have. Points in Experience-Space are points in both time-space and sensation-space.  In other words, a single point in experience space describes the exact feelings you feel at a given time.   To make things as easy to understand as possible, we will say that the only sensation one can experience is happiness, and that, at any given instant in life, one can make one of three choices. Why three? When there is only one sensation, Experience-Space becomes two dimensional: time is one dimension, and the experience you have is the other dimension. We can represent life with an image. Your experience of life is a path traced by a pixel through that that image from left to right.  At each step in time, the pixel can either go straight forward, diagonally up, or diagonally down.  We will label these choices straight, up, and down.

Look at this example:

In this example, the person is currently happy. They have a choice to make: in the next time tick, they will be happy if they choose straight or down, unhappy if they choose up.  This is a very simple model, but it proves surprisingly powerful in generating useful predictions about how we can make ourselves happier.

Suppose you know everything about the universe, and your goal is to be as happy as you possibly can.  You start out at some initial point in experience-space, and your goal is to maximize the sum of the happiness of the experiences you have over the course of your entire life.  (Is that a reasonable goal? A question for another blog post!). Suppose that experience space looks like this:

If this is your universe, wherever you start out, your most logical move is to always choose to go down (when possible) and then go straight along the bottom edge of the graph, when (if) you ever reach it.  That’s easy enough. Let’s consider a more complicated model of the world:

In this model, most experiences are either slightly positive or slightly neutral. There are quite a few “great” experiences, and a small number of “terrible” experiences. These big experiences are so big that they affect you for some time after you experience them.   How would you navigate this graph, in order to maximize your happiness? The problem begins to look like an artificial intelligence.  I’m not going to go into artificial intelligence algorithms such as A* search (as much as I’d like to.) Instead, I’m going to draw to draw some conclusions from this model.

In the real world, we don’t know the entire universe ahead of time: we only know the choices that we have made, and their ramifications. In other words, our graphs look like this:

That’s not a lot to go on. It would be hard to take that information and build a model of the world and use it to predict where to go next.  While walking like this, you’d probably notice that some areas were nicer than others, and that the really nice areas and really bad areas tended to clump together, but you’d still have a hard time determining which areas to go towards. Suppose there are 50 people in the universe, and you all share information about the choices you have made and the results those choices have brought you. Then, your picture of the universe looks like this:

This picture is much more complete than the picture you were able to generate by yourself.  By using information you glean from asking others about the choices they make, you can make yourself happier.

Conclusion: Talk to as many people as you can, and learn about their experiences.  Doing this talking will allow you to gain a much more accurate model of the world as a whole, in order to determine what will make you happy. Ask people about their history, and specifically about choices they have made that made them happy or unhappy.

I hope to write more on this subject in the future. Stay tuned!

7 years ago today, a group of Islamic hijackers killed 2,999 Americans.  Many questions arise, and I plan to explore one today: “Why do people do bad things?”  I will present two different analytical models which are commonly used to answer this question, and explain how they apply to the 9/11 attacks.

First off, I will note that ‘good’ and ‘bad’ are purely subjective terms.  Every person has his own perspective of what ‘good’ and ‘bad’ mean.  Every logical person, however, can use analytical models to determine what do to in response to people doing things they personally find bad.  It is my belief that most people reading this blog share similar ideas of what kinds of actions are ‘bad’ – killing people, for example, is generally viewed as a bad thing.

The first model I shall present is the simplest model. I call this the ‘atomic model of bad things.’ It works as follows:

Atomic Model of Bad Things

• Some people are inherently good, and some people are inherently bad
• Good people tend to do good things, and bad people tend to do bad things.

That’s it. Very simple.  What does this model imply? If the atomic model is accurate, it means that in order to stop bad things from happening, we have to prevent bad people from doing them by incapacitating them somehow.

The most effective way to incapacitate someone is to kill them. Therefore, the most effective strategy to be pursued, if the atomic model is accurate, is to identify bad people and kill them.  Does this present a problem? Only if you think killing bad people is a bad thing.  If killing bad people is a bad thing, then you still have other options for incapacitating bad people. You could put them in jail, indefinitely.  That would prevent them from doing most bad things.  What if you think putting people in jail indefinitely is a bad thing to do? I’m not really certain.  Ultimately, if you want to stop bad people from doing bad things, the atomic model says you have to do something to prevent bad people from acting as they are inclined to do.

An objection arises:  what if the bad people think we are bad? This is very likely to happen, but it doesn’t change the most effective strategy for responding to bad events. It simply implies that the people we’re trying to kill also have it in their most logical interest to try to kill us.

This atomic model is quite violent; it advocates a lot of killing. Is there another way from this endless cycle of violence and death?

Yes. I call it the ‘relativistic model.’ It is more complex than the atomic model.

Relativistic Model of Bad Thigns

• People are a product of their environments; no person is inherently ‘good’ or ‘bad’
• Someone who does bad things does so as a result of some external stimulus, usually a bad thing that has happened to them

What does this model imply? If we wish to stop people from doing bad things, we have to prevent bad things from happening to people. Note that the optimal strategy under the relativistic model is the exact opposite of the optimal strategy under the atomic model: if the relativistic mode is accurate, than anyone following the atomic model is making the situation in the world worse; they are causing more bad things to happen, and therefore they are influencing more people to do bad things.

Which model do I prefer? Both. I think they both have their applications; which model is more accurate simply depends upon the circumstances.

Example

I once saw a news program about an illegal immigrant on trial for murder.  The immigrant had been apprehend for speeding previously, and was released back into the general population. One host of the show,  (We will call him the atomist for reasons that shall become clear) was outraged, and said that this immigrant should have been deported upon being arrested for speeding. He was arguing in favor of legislation that would deport all illegal immigrants charged with any crime.  The other host of the show, the relativist, was arguing against the legislation.

Let’s look at the situation from both mens’ perspectives.  To the atomist, breaking the law and coming into this country illegally is something that only a bad person would do. By entering the country illegally, the immigrant has shown himself to be a bad person. Upon his being apprehended for speeding, he should have been deported in order to prevent him from doing something bad. The fact that he committed murder was practically to be expected – he is a bad person, after all. Therefore, the fact that he wasn’t sent back across the border represents a glaring problem with our legal system.

To the relativist, anyone in the situation of the immigrant would probably have tried to cross the border illegally. Who doesn’t want to give themselves a better life by migrating to the land of opportunity? How were the police to know he would commit murder after being apprehended for speeding? Any law that would treat all illegal immigrants as potential murderers is draconian, and because it does bad things to many people, would probably create more problems than it would solve.

In this case, I agree with the relativist. I don’t think that breaking into the country illegally makes someone a bad person,  because many people break into the country illegally, and not all of them are murderers.

Back to 9 / 11

The relativistic model for 9/11 is that we were attacked because of our expansive foreign policy, and because we favor Israel over Palestine. If we would change our attitude towards the middle east, be more even-handed in our dealings with Israel and Palestine, and stop interfering with foreign governments, the relativists argue, we would prevent future attacks.  The atomic model says there is a jihad by some of the Islamic people in the world against the west, and that the only way to prevent future attacks is to find and kill jihadists wherever they are.

Note that, once again, the atomic and relativistic models are completely at odds with each other. If we base our strategy on the atomic model, then the relativistic model predicts that we’ll simply inflame tensions in the middle east, creating more terrorists and making our problems worse. If we follow the relativistic model, the atomic model says nothing good will be trying to ‘make nice’ with the very people who are out to kill us, and that our weakness will only embolden them.

Which model is accurate? They are both accurate. Which model’s strategies make the most sense to follow? They both do.  We should stop supporting middle eastern governments that oppress their people, but at the same time we should take take military action against states that support terrorism.  Unfortunately, most people in America subscribe to only one of the models, while completely rejecting the other.    Conservatives in America tend to be atomists, while liberals in America, and pretty much the rest of the world tend to be relativists.  Here’s hoping more people will see the light in the other model, and start advocating a mixed policy, one that is gracious and kind to the majority of people in the world, but merciless towards those who harbor ill will in their hearts.

Imagine you go to a carnival for fun. You buy a fried Twinkie, see the world’s largest living pig, and perhaps ride the whirl-and-puke. You then head over to the midway with the intent of playing some silly games for entertainment. This carnival, however, is different – along with usual staples like the ‘milk bottle ring toss’ and themed shooting galleries, there’s a coin flipping game. You are given a penny, and you get to flip this penny 1000 times. The number of heads you get is recorded, and whoever gets the most heads is awarded a monetary prize. There is no monetary cost to play the game, but you do have to sit there and flip the coin 1000 times. A question arises: How large would the prize have to be in order to convince you to play the game?

Let’s say you can flip the coin once every second. That’s a pretty generous estimate, but I’m a generous guy so we’ll go with it. At that rate, it takes around 17 minutes of sitting there flipping a coin to play the game. Flipping a coin for 17 minutes would get pretty boring. Is it worth it, though, for a shot at, say, $10,000? The odds of you winning are 1 divided by the number of people who play the game. This is where it’s important to mention that the fair is really, really big – let’s say around 200 million people big. Suppose only half of those people decide to play the game. Your expected value, then, for this game is $10,000 / 100,000,000 which is $0.00001. Even if the prize were an astronomical $100,000,000, you’d still only expect to earn one dollar, for 17 minutes of boredom flipping that coin. A rational person would conclude that it makes no sense to play the game. The thing is, most people are irrational and a large number will still play the game even after you explain the math to them. If you doubt me, look at the number of people who buy lottery tickets. My game has a positive expected value – lottery tickets have a negative expected value and people still buy them. Unless you really enjoy flipping coins, it just doesn’t make sense to play the coin flipping game.

What does this have to do with voting? We can easily look at voting systems as large, multi-player games. The payout if you win (your vote chooses the guy who gets elected) is very high. However, the probability that your vote will be the deciding vote is vanishingly small. There is no monetary cost to voting, but it does take time. Going to the polling place and voting takes probably 15 minutes, and you could spend hours each week educating yourself on the issues. Unless you really enjoy doing these things, it just doesn’t make any sense to spend your time attempting to influence an event, when the probability of your actually having an effect is so small that it might as well be zero.

A common rebuttal to this argument is ‘what if everybody thought this way?’ If everybody was rational and decided voting didn’t make sense, it would suddenly become rational to vote, because one vote would decide the election. The same logic works for the coin flipping game, however – if everybody realized how stupid it was to play the game, nobody would play it, and then any one guy who decided to play would win. The fact that a decision makes sense in an alternate reality where everybody behaves perfectly rationally doesn’t in any way mean it makes sense in our reality. The ‘what if everybody thought this way argument’ is like arguing ‘well, if we lived on the moon it would make sense to play basketball with 30 foot high hoops. ‘ Yes, but we don’t live on the moon, so it doesn’t make any sense.

Do you owe it to society to educate yourself and vote? Even people who are very educated about world affairs disagree with each other on the best course of action. The Pew Center for People and the Press does a typology survey every few years, breaking the electorate down into different groups based upon common values and shared attributes. In the 2004 survey, the two groups that followed world affairs most closely were the Enterprisers, who were Bush’s staunchest supporters, followed by the Liberals, who aligned themselves with Kerry. More education most likely isn’t going to change your mind – it’s just going to give you more reasons to believe that you’re right and that your political opponents are idiots.

What about convincing other people to vote? By taking a stand and convincing others around you to vote your way, surely you’re making a difference, right? Unfortunately, the answer is still ‘no’ unless you’re very persuasive. A statewide election decided by 10,000 votes is still considered very close. Unless you can convince 10,000 of your friends to change your mind and vote your way, you really aren’t making a difference.

What does all of this mean? It means that our political decisions are made by people who are irrational – they don’t understand the math governing the logic of making decisions in massively multi-player games. This means that pure democracies, where everything is decided by a majority vote, are probably the worst form of democratic government possible. How can we do better? The electoral college is a start, because it increases the probability that you will be able to influence an election. Increased federalism is another huge step in the right direction – instead of choosing a president who is essentially a king in a giant winner-take-all election, choosing a president who has a limited set of powers prescribed by a constitution interpreted strictly literally lessens the blow of having a bunch of irrational people make decisions.

A final improvement could be gleaned from implementing a recursive system of representatives. Suppose every 1000 people chose a single representative among them. Each 1000 of those representatives would choose a meta-representative, who represents 1,000,000 people. We could have each 100 of those meta-representatives choose a single meta-meta-representative, and so on. Due to the exponential nature of the math in this system, the government would only need 3 or 4 layers. Each of the different layers would be charged with different levels of power, with most of the power at the bottom levels of the system, where it makes the most sense for individual voters to participate. When only 1000 people are voting, your vote matters much more and suddenly it becomes much more rational to vote and to try to convince others to vote your way. Will this ever happen? Probably not. Still, a guy can dream, can’t he?

I don’t know as much as I ought to about the Greco-Persian wars, but the tiny nugget of understanding I have is as follows: The Greeks were a collection of squabbling city states all controlled independently. They spent most of their time farming and discussing philosophy; when they weren’t doing that, they were fighting each other. Persia was a rapidly growing empire controlled by one king and his appointed cronies, financed by treasure taken from conquered nations. The Persians, first under Darius, and then Xerxes, were trying to expand their empire by adding Greece. The Greeks didn’t realy care for this idea.

Xerxes, the Persian emperor, doesn’t really want to fight a long protracted battle to control the Greeks. He’d much rather have them submit to him like the rest of the peoples he’s had his army conquer. He sends out a bunch of messengers to Greeks, telling them they should surrender to him. “I’ll treat you well,” he says, “Just pay taxes to me and do whatever I say, and we’ll be good.” The Greeks, not really famous for their hospitality, respond by throwing the Persian messengers down a well.

Everything started to go pretty poorly for the greeks around this time; a variety of bad omens were observed. It was decided that maybe they shouldn’t have thrown those Persians down the well after all. The greeks figured they should offer some of their own men to make up for the Persians they killed. A call goes out for patriotic young men to sacrifice themselves for their country, and two guys step forward – Sperthias and Bulis. These aren’t just random joes; they’re from well off families. Think of two frat boys at Duke.

Sperthias and Bulis make their way to the persian capital. Everybody in Persia knows what these guys are doing, and they’re respected for it. A Persian Official, Hydarnes, gives them a place to stay. He’s impressed by their conviction and courage. He tries to convince them to join the Persians. “You guys are brave,” he says. “Xerxes knows how to reward brave guys. If you join him, you could be in charge of Greece.”

Their response to Hydarnes gives me shivers each time I read it:

“Hydames, you have not equally weighed each side in your advice to us. For you have tried the one which you advise, the other has remained untried by you. You know what it means to be a slave, but you have never yet tried freedom, to know whether it is sweet or not. For if you had tried it, you would have advised us to fight for it, not merely with spears, but also with axes.”

Can you imagine anyone with that attitude now? Recently, Iran (modern Persia) captured a bunch of British Marines. Instead of fighting to their deaths, the Marines simply acquiesed to the Iranians and went willingly as prisoners. They posed for a bunch of propoganda pictures, and were eventually released.  Watching the whole episdoe disgusted. me I have nothing but contempt for those who would let themselves be used in such a way, for ‘men’ who value their wretched lives over all else. That seems to make me a minority.

Sperthias and Bulis argued that Hydarnes counciled against fighting for freedom because he didn’t understand what freedom was like. We live in a world freedom is the only thing many people have known, and for that reason, they don’t really value it. Like the Persian satrap Hydarnes, they argue against fighting for freedom. Not because they don’t know what it’s like to be free, but because they don’t know what it’s like to be a slave. They’d rather be alive than free. I think that’s a damn shame.

In my experienece, most people have little to no understanding of capitalism. They think it encourages greed, and they are completely wrong in that belief. Unfortunately, it’s not just critics of capitalism that think this – I’ve met many defenders of capitalism who have the attitude that greed is good. Greedy people are assholes, and if the world were rid of them, it’d be a lovely place. I think it’s absurd to even debate that. Unfortunately, many defenders of free markets try to do just that. They don’t really understand why the thing they’re defending is worth defending; they just know that the alternative is worse. The fact that many defenders of capitalism try to defend greed probably causes many intelligent, well meaning people to become socialists. This reaction, is, of course, based upon a logical fallacy – a poor argument in support of an idea says nothing about whether the idea itself is poor. The principles underlying free-market capitalism aren’t based upon the idea that greedy people are good, they’re based upon the idea that greedy people are greedy.

Consider a simple story. I frequently start political or philsophical discussions over meals, I suppose because I enjoy harangueing people with my ideas, and I usually eat in some sort of group if I can. Suppose we are eating at a fast food restaurant, and we have finished our meal. Most fast food places provide garabge cans, and bins for used trays. When customers finish eating, they usually take their trays, empty them in the trash, and stack them in the bins. Some people just leave their trash at the table. In any case, the restaurant will pay people to clean up the restaurant, to make sure it looks nice. A nice restaurant is more enjoyable for everybody than a dirty restaurant. The owners of restaurant pay people to clean it up because they want to entice customers into their restaurant. They are motivated by greed. Their greed, coupled with the mechanism of capitalism, ensures that there will be somebody to clean up the mess and that it will get cleaned up.

The people who leave their food on the table are also greedy. Are they making the world better through their greed? No, not at all. They’re leaving their crap for other people to clean up. Does capitalism encourage this? No. It’s not designed to, either. The reason I think capitalism is a great idea is that it ensures that people who are greedy – the restaurant owners – will still be encouraged to do things that benefit others – like cleaning up the mess left by other lazy people. My support for capitalism certainly doesn’t mean I think that greed is a good thing, or that the world would be better if there were more greedy people in it. It just means that I recognize the reality of the world, that it is full of people who are greedy, and that greed is an extremely reliable motive.

There’s a lot more to my support of capitalism – particularly, because of the freedom in a capitalist system. Even if planned economies were more efficient and lead to better standards of living, I wouldn’t want to live in one, because I value my freedom above all else. Fortunately for me, and my fellow capitalists, planned economies are lousy, and despite the warnings of leftist academics in the past, the planned economies around the world have stagnated and collapsed, unable to deliver upon promises made, while the more free markets have grown and prospered.