Thursday, June 29, 2017

Something You Believe Is Wrong

No one is omniscient. No one knows everything. That means everyone believes something that is wrong (at least everyone who's not in a state of radical doubt). That includes me and you.

There is something I believe that is wrong. There is something you believe that is wrong. The problem is false beliefs feel just the same as true beliefs. Even something you know is true, might still be false.

And the only way to improve the situation, is to be willing to change your mind. Keep that in mind when you interact with someone who disagrees with you. They're probably not evil. They might not be stupid. They may not even be wrong. They have reasons for believing what they believe, just like you do. They might not be good reasons, but you can't determine that until you know what they are.

Note that I'm not saying you should blindly accept what someone who disagrees with you says. But nor should you blindly reject them either. You should be willing to listen to their arguments, and honestly evaluate them. Even for things you're absolutely sure are true, because those are the things you're least likely to question on your own.

So, always be willing to keep an open mind. Someone who disagrees with you might know something you don't.

Monday, May 30, 2016

Socially Subjective Facts

Philosophical realism is the idea that there is an objective reality that exists independently of our beliefs. I think philosophical realism is obviously true, and it always surprises me to find out there are people who don't (which includes nearly 20% of professional philosophers).

However, there is a sense in which non-realism actually makes sense.

For example, money. There is almost nothing useful you can do with a dollar bill. What few things you can do with it (like burning it for heat) can be better achieved with other, more readily available materials (like wood). The only reason money is valuable, is because people believe it's valuable. We're willing to trade useful items for money, because we know everyone else is also willing to trade useful items for money, not because the money itself is useful.

Many things in society are like that. The leader of a organization is the person whose orders are followed, and people follow the orders of the person they believe is the leader of the organization. Laws are what police and judges enforce, and police and judges enforce what they believe the laws are. Art is whatever people believe art is.

I'd go so far as to say that most people's experiences are shaped more by these socially subjective facts, than by physically objective facts. Maybe that has something to do with some people's rejection of even physical realism.

Wednesday, January 27, 2016

Binary Subtraction and Two's Complement

A while ago, I talked about how to use Boolean algebra to add two binary numbers. Now I'm going to show you how you can do subtraction in a similar way.

To start with, I'm going to ignore negative numbers. I'll get to those later, but for now, for simplicity's sake, I'm going to assume the first number will always be larger than the second, so the answer will always be positive.

Let's start again with 1-bit numbers. 1-1=0, 1-0=1, 0-0=0, so we have this truth table:


The question mark is to denote a value that can be either 1 or 0. We don't care about that particular value, because it would be negative. Because of that value, there are two functions that satisfy this truth table: X XOR Y, and X AND ¬Y.

Extending this to multiple digits is similar to extending addition to multiple bits, but instead of sometimes needing to carry, we'll sometimes need to borrow. The difference between carrying and borrowing is that instead of adding one to the next digit to the left, you subtract one from the next digit to the left, and you borrow in cases where the result would be less than 0, instead of greater than 1.


BN-1 indicates whether a borrow was required for the digit to the right of the current one, and BN indicates whether the current digit requires a borrow. For the rightmost digit, BN-1 is 0.

So, Z = X XOR Y XOR BN-1, and BN = (¬X AND Y) OR (¬X AND BN-1) OR (Y AND BN-1)

Now, what about negative numbers? For that matter, how do we even represent negative numbers? Computers only have 1 and 0, there's no -.

Well, there are a number of ways you could do that. You could for example designate one bit to be a sign bit, where one value indicates positive, and the other negative. Normally, the sign bit is the leftmost digit, and normally 0 indicates positive. So, 0101 would be 5, while 1101 would be -5.

This particular method has the disadvantage of wasting a number, because 000 and 100 represent 0 and -0, which are equal. It also requires different algorithms for adding and subtracting negative numbers.

Wouldn't it be nice if there were a representation of negative numbers that allowed the use of the same algorithms for both positive and negative numbers? Well, there is one, it's called two's complement.

It's not very intuitive, but it's very convenient for doing these bitwise functions. Like the method I just described, the leftmost digit is a sign bit, and 0 represents positive. But instead of the rest of the bits being the same as the positive representation, you flip all the bits, and then add 1.

0101 would still be 5. To get the bits for -5, first start by replacing every 1 with a 0, and every 0 with a 1, so we get 1010. Then add 1, so we get 1011. If the rightmost digit is 1, it carries the way you would expect, so -3 ⇒ 0100 ⇒ 1011 ⇒ 1100.

Notice what happens when you try to represent -0 like before. 0000 ⇒ 1111 ⇒ 0000. So, there's only one possible representation of 0. 1000 would represent -8. In general, with N bits, the highest number you can represent is 2N-1-1, and the lowest is -2N-1

When you use two's complement, you can use exactly the same algorithm I described above to subtract with both positive and negative numbers. You can also add using the same algorithm I described in my previous post.

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.