Waaaaaay back in college, I spent some time on queueing theory (you know, Poissan distributions and all that). The most surprising part for me was that a random distribution of arrivals pretty much ensures that you will have clusters that are very busy, and times when you are totally idle. Once you work on the math a bit, you understand why, but our commonplace notion is that "random" should be "smooth".

Incidentally, this also explains why it's so hard to determine whether environmental factors are causing health issues. You can't just look at a cluster of cancer cases (for example) and surmise that there is something causing it, since a random distribution will give you clusters. So you have to do some fairly sophisticated mathematics to determine whether the cluster is due to random chance or whether there is something else going on.

If the average person understood this - and they could with some very simple experiments - it would help science understanding immeasurably. Humans are programmed to extract patterns from data, and it's not surprising that we see patterns that are really just random chance.

So, once again, I've digressed a bit, but I assure you that this really does have something to do with floating point arithmetic. The point of the journey is not to arrive...

I was talking about clustering, which brings us to the topic of newsgroup questions. It's not uncommon to not get a specific question for 6 months, and then get the same question 3 times in a week. The question for this week is "I'm doing something mathematical, and the answers are wrong."

The problem usually has to do with the fact that the person asking the question doesn't understand that floating point is an imprecise representation. I got this drummed into me long ago in my numerical analysis class, where I learned (and promptly forgot) all about poorly conditioned matrices and the like.

Back, once again, to the topic.

The canonical discussion of FP arithmetic (for this audience, at least) is a 1991 paper by David Goldberg titled "What Every Computer Scientist Should Know About Floating-Point Arithmetic"

Even if you know a fair bit about FP math, there's a lot of good stuff there.