Friday, January 16, 2009

Probability Schmobability?

Never let it be said that probabilities don't matter. Sally Clark, a British woman whose two sons suffered cot death (a.k.a. SIDS), was arrested under suspicion of murder. Her prosecution included testimony from Roy Meadow, a pediatrician who claimed that the probability that both sons died of natural causes was less than 1 in 72 million. He got that figure by squaring the 1 in 8500 likelihood of cot death in affluent families.

He irresponsibly ignored the requirement that events be independent for his calculations to yield meaningful results.

Furthermore, his results imply that there was only a 13 billionth of a percent chance that Mrs. Clark was not a murderer, apparently assuming that it was improbable even for the first son to die. With probability, it's extremely important that the "clock" be started exactly with the surprising event, never including previous "related" events. If the Pick 3 numbers for one day are 1-9-6, that's not surprising. If they're also 1-9-6 the next day, it is surprising. So if the odds are 1-in-1000 for winning, the probability telling us how surprising our "coincidence" is would be closer to 1-in-1000 (the odds of getting 1-9-6 the second day) rather than 1-in-1 million (the odds of getting 1-9-6-1-9-6) since it wasn't surprising in the least until the second 1 popped out. In the same way, nothing was surprising in Sally Clark's case until the second son died, so even without considering the other error she would only have a 1-in-8500 surprise value.

There may have been other evidence involved, but it's horrifying that someone so careless with evidence would be involved in a murder trial.

She served more than three years in prison before she was released on further evidence.

Moral Relativism - Part 2

Every idea, whether or not it's accurate, is based on other ideas, itself, some mixture of the two, or nothing. Relativism has a lot to do with ideas and implications, so I'll say a little on that subject before I get back to why it's important.

Because ideas are only anchored to each other, all ideas are ultimately "floating in space" in a sense, and the entire corpus of human knowledge is not "well supported" as a whole. Put another way, the "infallible" process of logical deduction (applying what we know) is worthless without the "fallible" process of logical induction (predicting what's "probably" true).

There are, however, ideas well worth believing. Bertrand Russell says, "the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it". This is the trick to all of our ideas: our basic, fundamental assumptions are so simple or necessary that it's not worth considering the alternatives. For instance, many of our ideas are based on reliable sensory experiences. If our sensory experiences are so misleading that there's no way to follow them to the "real truth", then the "real truth" will be irrelevant until that changes. It doesn't matter if everything is a dream unless and until we wake up or find a good reason to question it all. So there is a legitimate basis to many ideas, just not one that's supported by evidence, technically speaking.

Now back to relativism. It's my contention that you can't get from a moral statement to a non-moral statement. The implications of a moral statement ("X is good") are also moral statements ("we should do X", "there's not enough X"...). The nearest thing to non-moral conclusions would be explicit responses ("I will do X"). These responses also depend on other moral statements ("I do things that are good"), and they have a decidedly non-universal sense to them. Moral statements can also be related to God in significant ways ("God wants me to do X"), but that only extends the "moral statement bubble" as opposed to penetrating it, because they're still a type of moral statement and lead to more of the same ("God says to do good", "God is good", I will do what God says to do").

My belief is not that God-based morality is empty or flawed, or even that it's necessarily on equal footing with moral relativism, but that relativism is no more self-defeating or contradictory than moral universalism. Neither system minimizes the personal responsibility to make decisions, act on one's convictions, or seek the truth, although relativism leaves a few extra unknowns as far as how to go about it.

Moral Relativism - Part 1

Ethics and values and morals, oh my! It's time to throw caution to the wind and discuss relativism. Before I do, though, I'll need to invoke my muse and put all my energy into doing this just right. The internet is full of discussions about relativism, and as far as I can make out, it's all either horse poo or extremely boring. I'm going to try my best to keep this and any further posts manageable and well-organized. Here goes...

What difference does it make being a relativist? Does a relativist believe that whatever makes you feel good is "right"? If you see a relativist on the street, how will you know? Think hard about those questions, and don't jump to the easy answers right away, because they're the focal point of the idea of moral relativism.

I make the claim that relativism itself makes very few direct prescriptions, and only provides a few vague implications. It's a mental model for understanding "moral propositions", or statements involving words like "good", "bad", "righteous", "evil", "right", "wrong", "should", and "ought". Yes, it's all just about words, and that can be frustrating, but words make up such a big part of our lives that sometimes they deserve a second look.

Consider the statement "exercise is good". How do you respond to such a statement? You might get up and go for a walk, eat a piece of cheesecake out of defiance, or make an excuse for not exercising. If you have no response whatsoever, and immediately forget the statement, what purpose does it serve? It might still make someone else feel good to say it, or fill a gap in conversation. If, on the other hand, nobody has any response to a statement, in what sense does it still have value? Probably not in much of a practical sense. I take the position that a statement only has practical value if it affects some feeling or behavior, either immediately or down the road.

That in no way berates moral claims themselves or makes people stupid for holding moral beliefs. There is usually a very strong response to moral statements. However, it makes our relationship with such statements a little more explicit. That's not the essence of relativism, but it's a foundation for further argument, and if we can come to agreement on this point then it'll help keep the rest of the discussion sane.

Tuesday, January 6, 2009

An Allegory of Colors

There's a city where everyone loves yellow. It's the color of happiness and excitement, so all the people there paint things bright yellow and wear yellow clothes all year. But Bob really likes the color blue. It's not that he dislikes yellow, but to Bob, a little splash of blue looks nice alongside the yellow.

When Bob was a little boy, his preschool class drew crayon pictures. He drew a big yellow sun. Then he used black crayon to draw his house, and filled it in bright yellow. With a green crayon he filled in his front lawn, and then he asked his teacher for a blue crayon to draw the creek that ran nearby.

"What do you want the blue crayon for?" asked his teacher.
He explained, "I need it to draw the water."
The teacher blinked and then told him, "Blue is a sad color. That's why we call it 'feeling blue' when someone's sad. Water's actually clear, so why don't you just draw the edges of the water with black?"
He said "okay" and went back to his desk, but he couldn't understand what was wrong with the blue crayon. He didn't think it was a sad color, or any particular kind of color even. It was just blue.

A few years later, for Bob's birthday, his friend gave him a blue shirt with "Bob" written on the front. He really liked it and rushed upstairs to change into it. Then he noticed that his friends seemed distracted and a little uncomfortable whenever he talked to them. He thought, maybe they don't like my shirt, but he sort of liked standing out, and he didn't mind too much if a couple of people thought he was weird. After they all went home, he went on a walk, and an old lady yelled across the street at him, "Is that some kind of protest?"
"What?" he called back.
"Your shirt is blue. Are you trying to annoy everyone?"
"It's just a color. What's it to you?"
She scowled. "Everyone else likes yellow. You're probably just trying to get attention..."
He did like some of the attention he had gotten, especially since it was his birthday, but he was pretty sure that wasn't the only reason he liked wearing the shirt.

After that day, whenever he noticed his blue shirt in the closet, he always thought of the old lady, so he didn't feel like wearing it anymore. Eventually it was just taking up space in his closet and his mind, so he threw it away.

One day, when Bob was all grown up, he needed to paint his fence. His house was already solid yellow, so he went to the store and bought the last can of pastel blue paint for the fence. After a long afternoon of painting, he finally had the last fencepost covered. He stood back to admire it, and then went inside for the night. When he woke up the next morning, he looked out of his window, and his fence was yellow again! He asked his next-door neighbor about it later, and the neighbor said, "Don't you like it? We noticed you couldn't find yellow paint for your fence, so the whole neighborhood pitched in to surprise you."
Bob felt a little silly. "Well, I kind of liked it better when it was blue..."
"Buddy, the whole town loves yellow, and you're the only one who likes blue. You'd better learn to like things yellow or you'll never be happy around here."
He relented. "Yeah, I guess you're right. It does look pretty good yellow."

And he meant it...sort of. But sometimes when he was thinking hard about something, he would suddenly remember his fence wasn't blue anymore, and then he remembered he was trying to like yellow, and soon his head was spinning with conflicting emotions and he would forget what he had been thinking about.

One rainy day, Bob was thinking about the blue shirt he had when he was younger, and he realized something. When other people made things yellow, they weren't trying to do anything in particular. They were just doing what came naturally, it was easy, and Bob wanted them to be happy, too. On the other hand, whenever Bob thought something should be blue, it was always a big event. It wasn't just that yellow was popular, it was mostly that people expected things to be yellow. When he wanted something blue, he always had to have a reason for it, and people would assume that he wanted to be irritating.

Sometimes, when he felt like things should be different, he did like to irritate people a little, because it seemed like it would help change things somehow. He discovered, though, that when he irritated people, they tried even harder to find things that could be yellow, if not to spite Bob then to lift their spirits. Like quicksand, he could do nothing and things would gradually get worse, or he could try to do something and the situation would decline even faster.

The more he realized that his perspective didn't matter, the more it frustrated him every time he noticed yellow going up somewhere. It hadn't always been a big deal. Like he had said, it's just a color. He tried to learn not to care, but he felt frustrated with himself for ever having cared, and soon it wasn't just about the colors anymore. Now he was always frustrated, and nobody could understand why Bob always got so worked up over colors.