Friday, September 25, 2015

Very Unique

Some people object to using a modifier like "very" or "a little" with the adjective "unique". They say that "unique" means "one of a kind", and that is a strict binary.

Well, they're wrong. "Unique" is not a strict binary. As with most other things, it's a continuum, and things can be more or less unique.

For example, consider the Wright brothers. They built bicycles. At first, their bicycles we made using the same designs as any other bicycle. It would be safe to say they weren't unique. But the Wright brothers were inventive fellows, and they came up with ways to improve the design of their bicycles. At that point, their bicycles were unique. There were no other bicycles like them. Then they built an even more unique machine. A machine that did something no previous machine had done. The bicycles were unique, but they were still bicycles. The airplane was a whole new thing.

Another example. Consider two books. One is full of old tropes and tired clich├ęs. Utterly predictable, but not plagiarized. It's not unique in that it mimics other books, but it is unique in that it consists of a sequence of words that had never been written before. The other book is more original. It's unique in that no other book has a similar plot, but it's not unique in that it still consists of words printed on paper. The latter book is more unique than the first.

There are many ways something can be one of kind, and the more ways that apply, the more unique a thing is.

Friday, September 18, 2015

The Sun of God

Do you believe in the sun? Do you think that the sun exists?

I certainly do. I've never doubted the sun's existence, even when it was out of sight. And I don't think anyone else has either. Certainly, I've never heard of anyone who claimed that the sun doesn't exist. Even solipsists, I'd be willing to bet, would admit that they perceive the sun, even if they deny that their perceptions are indicative of reality.

People even agree on details about the sun, even when those details change, and vary from place to place. Someone in China will say the sun is up at the same time someone in America will say the sun is down, but both will agree that the other is correct for their location.

Why are people in such unanimous agreement about the sun? Is a supernatural entity using telepathy to mind-control us? No, the reason we agree about it, is because we can see it. The evidence for its existence is right there, clear as day.

Some people say that the evidence for god is clear and obvious, but it's clearly not as obvious as the evidence for the sun. If it were, there wouldn't be such disparate religions. Christians, Muslims, Hindus, Buddhists... People can't even agree on whether god exists, let alone specific details about him.

Some people say that god wants us to believe in him. But surely an omnipotent would be capable of performing a feat that an inanimate object has managed. If god wants us to believe in him, he must not want it very much.

Thursday, June 4, 2015


Note: This post contains spoilers of Avengers 2: Age of Ultron.

I liked Avengers 2: Age of Ultron, but as tends to happen with Marvel villains, Ultron's motivation is unclear. Why does he interpret his mission of "peace in our time" as "kill everyone"? Why does he hate Tony Stark so much? I have two ideas about this.

The first idea is that Tony didn't actually create Ultron. He simply downloaded the consciousness of the mind stone into a computer. As evidence of this, when Ultron is first activated, one of the first things he asks Jarvis is "Where is your body?", and upon learning that he's a machine, says "This feels weird. This feels wrong.".

Under this interpretation, the reason he hates Tony so much is because Tony is the one who put him into a machine. He hates Tony more than Bruce Banner, because it was Tony's idea. As for the mission, he never cared about peace. He just said that to confuse and make fun of the Avengers.

The second idea is that Tony did actually create Ultron, and Ultron was performing his mission. He saw that humans are a divisive and warlike species. He realized that we would never accept an externally imposed order. But that we might unite to fight a common enemy. And that plan worked, at least as far as getting the Maximoffs to put aside their differences with the rest of the Avengers.

In this case Ultron hating Tony was the lie. Ultron figured that Tony, having created him, would be less willing to fight him. So he made sure Tony would think he he hated him, so Tony would hate him back.

Monday, May 11, 2015

Redefining Marriage

Conservatives like to complain that allowing same-sex couples to get married is redefining marriage. The most common response to this is to argue that redefining marriage isn't necessarily bad, and to point out the many times marriage has been redefined in the past. However, I think the argument can be refuted on another level: Gay marriage is not a redefinition of marriage.

Or rather, the redefinition of marriage which logically leads to gay marriage already happened, and it happened a while ago. The change happened gradually, over a long time. There wasn't a single landmark court case I can point to like Loving v. Virginia.

A long time ago, a woman was considered to be basically the property of her husband. Even after that was the case, a woman was still supposed to be subservient to her husband. He had authority over her.

But over time that changed. Eventually, a marriage was no longer a relationship between owner and property, or between superior and inferior. It became a relationship between equal and equal. And once that happened, there was no longer a masculine role and a feminine role, and thus no need for a man and a woman. Just two people.

Tuesday, December 9, 2014

Quis custodiet ipsos custodes?

There have been a lot of stories recently about police abuses of power. Undoubtedly, these stories are not representative. The vast majority of police-civilian interactions do not end with death or violence. Most cops are good cops.

But that doesn't matter, when the whole system is bad.

When a police officer can kill someone with no provocation, on camera, and get away with it, it doesn't matter that there are more good cops than bad cops, because the good cops are part of a system that does nothing to stop the bad cops.

And it's not just the major abuses like that. I've heard (not being a cop, I don't know for sure) that police officers will usually not give other officers tickets for traffic violations. Of course, that's a very minor thing, but it's indicative of the problem. Police officers are held to a lower standard of conduct than civilians.

"With great power comes great responsibility." Unless you're a cop.

Monday, November 24, 2014

Binary Addition

Before, I talked about how to use binary to represent a number using only two values. But what if you want to actually do something with those numbers? How do you add numbers using Boolean operations?

Well, let's start with a simple case: adding two one-bit numbers. We'll call them X and Y, and since they each only have one binary digit they can only have the values 0 or 1. So here are the cases we need to account for: 0+0=0, 0+1=1, 1+0=1, 1+1=10.

Notice the answer for that final case has two digits. A Boolean function can only return one value, so how can get that? By having two functions, one for each digit.

So, the function for the rightmost digit has to satisfy this truth table:
What Boolean operation does that look like? XOR.

The function for the next digit will have to satisfy this truth table:
That's the same as the AND operation.

I'm using the subscripts here to indicate which digit in the overall number. So our two bit answer Z has the individual bits Z1Z0, where Z1 = X AND Y, and Z0 = X XOR Y;

So, that's how you can add two one-bit numbers. But what if you want to add bigger numbers? Well, the way you add the second bits together is pretty much the same as the first bits, with one major difference: You need to account for the bit that got carried from the sum of the first bits. If that carry bit was 0, then the result of the next bit will be same as the first. But if it's one, then the result is increased by one. So, 0+0+1=1, 0+1+1=10, 1+0+1=10, 1+1+1=11.
So, now we have these two truth tables:
So, Z1 = X1 XOR Y1 XOR C and Z2 = (X1 AND Y1) OR (X1 AND C) OR (Y1 AND C). C, the carry bit, comes from the second bit of the result of the sum of the first two bits, that is C = X0 AND Y0.

Each subsequent bit works just like the second, with the second bit of the previous result being carried over. Generally, and Zn = (Xn AND Yn) OR (Xn AND Cn-1) OR (Yn AND Cn-1), and Cn = Xn XOR Yn XOR Cn-1.

Here's another challenge for you: How do you do subtraction in a similar manner?

Sunday, November 2, 2014

Utilitarianism, Capitalism and Utility Monsters

A common criticism of utilitarianism is the idea of a utility monster. Suppose you had some extra ice cream, and you decided to give it away, so as to maximize utility. You only have enough to give to one person, and there are only two people available for you to give it to: Alice and Bob. If Alice likes ice cream, and Bob does not, then obviously you should give your ice cream to Alice. Giving it to Bob wouldn't increase his utility. What if Bob did like ice cream, but Alice like it more? Then, you should still give your ice cream to Alice, because that maximizes utility. What if Alice likes everything more than Bob does? Then you should take Bob's stuff and give it to Alice, because that will maximize total utility.

On a separate note, utilitarianism and capitalism go really well together.

Utilitarianism says you should try to maximize utility. When you buy something, you do so because it will make you happier, or help you achieve your goals, in other words, increase your utility. And you're trying to get best deal, you don't want to pay any more money than you have to. So money works as a not too bad proxy for utility. Which is good, because it's hard enough to get people to agree what utility is, let alone measure it in any meaningful way.

Before, I talked about the spherical cows of economics, that is, the conditions under which the free market is maximally efficient. One of those spherical cows in economic equality. A rich person can outbid a poor person, not because they value what they're buying more, but simply because they have more money to spend.

But if money is a proxy for utility, then maybe the rich person really does value it more. Maybe the rich person, in fact, has a greater capacity to value things at all. In other words, maybe rich people are utility monsters.