Conversation With a Slow Student
Student: Hi Prof. I've got a problem. I decided to do a little probability experiment—you know, coin flipping—and check some of the stuff you taught us. But it didn't work.
Professor: Well I'm glad to hear that you're interested. What did you do?
Student: I flipped this coin 1,000 times. You remember, you taught us that the probability to flip heads is one half. I figured that meant that if I flip 1,000 times I ought to get 500 heads. But it didn't work. I got 513. What's wrong?
Professor: Yeah, but you forgot about the margin of error. If you flip a certain number of times then the margin of error is about the square root of the number of flips. For 1,000 flips the margin of error is about 30. So you were within the margin of error.
Student: Ah, now I get if. Every time I flip 1,000 times I will always get something between 970 and 1,030 heads. Every single time! Wow, now that's a fact I can count on.
Professor: No, no! What it means is that you will probably get between 970 and 1,030.
Student: You mean I could get 200 heads? Or 850 heads? Or even all heads?
Professor: Probably not.
Student: Maybe the problem is that I didn't make enough flips. Should I go home and try it 1,000,000 times? Will it work better?
Student: Aw come on Prof. Tell me something I can trust. You keep telling me what probably means by giving me more probablies. Tell me what probability means without using the word probably.
Professor: Hmmm. Well how about this: It means I would be surprised if the answer were outside the margin of error.
Student: My god! You mean all that stuff you taught us about statistical mechanics and quantum mechanics and mathematical probability: all it means is that you'd personally be surprised if it didn't work?
Professor: Well, uh...
If I were to flip a coin a million times I'd be damn sure I wasn't going to get all heads. I'm not a betting man but I'd be so sure that I'd bet my life or my soul. I'd even go the whole way and bet a year's salary. I'm absolutely certain the laws of large numbers—probability theory—will work and protect me. All of science is based on it. But, I can't prove it and I don't really know why it works. That may be the reason why Einstein said, "God doesn't play dice." It probably is.