Sunday, April 14, 2013

Possibility Versus Probability

"I don't believe in ghosts."

"Why not?"

"I don't think they exist, that's all. It's very unlikely."

"You can't know that for sure! What if you're wrong? Science can't explain everything."

"That's true. Science can't explain everything. Doesn't mean the answer only lies in supernatural explanations. Or that I should accept the existence of ghosts as supernatural beings that were once living people. There could totally be other explanations."

"But you admit it's possible ghosts exist?"

"Sure. The possibility always exists. No problem with that. But I don't think it's very probable that they do."

"Huh? What do you mean?"

"It's possible that ghosts exist. It's not very probable that they exist."

"What's the difference?"

"It's possible that ghosts exist - maybe they do and maybe they don't. But that by itself doesn't mean anything. There can be all sorts of explanations apart from ghosts. What really matters is how probable the idea of ghosts is - meaning how likely is this explanation to be true compared to the other explanations."

"You're talking all fancy now. I don't understand you."

"Sorry. All I'm trying to say is being possible and being probable are two different things."

"Those are just words. You're trying to confuse me with fancy words."

"But words are what we use to symbolize what we mean. Yes, these are words, but these are words with specific meanings, and I mean those specific things by using these words. If you don't understand them, I can explain them, but just saying they are words and you don't understand them means you don't really care, and I'm wasting my time."

"Well alright, what do you mean then? Can you explain what you just said about possible and probable?"

"Let's take a simple example. Suppose I tell you we're going to visit these friends of mine, and they have a child who is five years old. I'm busy, so you have to go buy a toy for the child. Now, what kind of toy will you buy? For a boy, or for a girl?"

"I don't know. Is the kid a boy or a girl?"

"I haven't told you. You have to guess. What do you guess?"

"That's not fair. I don't know, I can't guess anything."

"Exactly. From your point of view, there are two possibilities - the kid can be a boy, or the kid can be a girl. But unless I give you more information, you can't tell which it is. What would you say about the probability? How likely is it that the kid is a boy, versus being a girl?"

"I don't know... could be either."

"Yes, again because you don't have more information. You've heard of probability, right? You're probably heard the language somewhere - 50 % chance of something, 10% chance of something, 90% chance, or 10 to 1 odds, or the like? Use whatever language feels comfortable to you. The idea is that because you don't have any other information, there's a 50% chance the kid is a boy, and 50% that it's a girl. Make sense?

"Yeah, sort of."

"But. Suppose I had phrased my sentence like this: We're going to visit these friends of mine. They have a child, and he is five years old. Now what can you say?"

"Well, the child is a boy!"

"Let's put it this way. They have a child, so there are still two possibilities - it's a boy or it's a girl. But my next sentence was he is five years old. That decides it, right? How likely is it that the child is a boy?"

"Ummm... 100%?"

"Yes. Of course, there is still a possibility that it's a girl, and that I made a mistake and said he is five years old, instead of saying she is five years old. But how likely is it that I made such a mistake? After all, I do have a good handle over the English language. Would you agree?"

"That you know English? Yes, you speak quite well. You wouldn't make a mistake like that."

"It is possible, certainly, but very unlikely. Since I'm unlikely to make such a mistake in speaking, it's more likely that the child is a boy. More likely means higher probability - now do you see what I mean? Possibility just tells you what options exist. Probability tells you which option is more likely than the others, and by virtue of being more likely, that option is a better one."

"But it's still just an option right? Other options might be less probable, as you call it, but they can still exist."

"Yes, they can. And sometimes it turns out that a less probable option is actually the correct one. But not usually. And in some cases, an option can be so unlikely that it's almost absurd. You can argue for example, that it's a possibility that the earth is flat, that sailors who sailed around the world, and astronauts who went into space somehow all managed to fool themselves, and the earth is really just flat, and that's certainly a possibility. But it's not very likely, is it? There is enough proof that the earth is round. The possibility that the earth is flat is not just extremely remote, it is patently absurd."

"And you think the same is true for ghosts?"

"Yes. You can explain supernatural phenomena using ghosts and things. But you can also use rational, natural explanations. Guess which set of explanations can be tested using theories and experiments? So yes, I'm not convinced that ghosts exist."