In the last post I mentioned the tendency people have to look for causes. It's innate; there's nothing to be done. We're conditioned by the world of our senses: a leaf falls in front of us, so we look up to find the tree. And this works fine, most of the time, for the macroscopic objects that we can see, touch, hear and smell.
It stops working so well on the microscopic scale. (And it goes completely to pieces on the really submicroscopic scale, when the colors of quantum mechanics start to seep through into the picture, but that's another story.) When we don't have direct sensory experience of the steps in a process, our intuition can be crippled. You can learn your way around the problems, but that has to be a conscious effort - the rules that we've all been practicing since birth won't be enough.
And this is where a lot of really bad ideas are born. Take the idea of a "cancer cluster." If we see a pile of large rocks with no others around, we assume that something moved them there. If we see a group of similar plants, we assume that they've grown there together from seeds or roots. But what is there to say when there's a group of cancer victims in a given area?
The temptation is overwhelming to say "something put them there." But it doesn't have to be so. People who haven't thought much about statistics don't usually have a good feel for what "random" means. It doesn't mean "even scattered in no particular pattern." It means "no particular pattern, and let the chips fall where they may." Looked at locally, a large random distribution isn't even at all - it's lumpy and patchy. Show a dozen untrained eyes a large scatterplot of random numbers and they'll never guess that there's no design behind it. Surely that bunch down there means something? And that swath that cuts over this way! Imposing patterns is what we do.
Discriminating between these accidental groups and any that might have a cause is fiendishly difficult. Generally, the only proof is statistical - you end up saying that you can't reject the null hypothesis, that this group is not larger than you would expect by chance. So in the absence of any hypothetical cause, there's no reason to assume that it's anything other than noise. Does that convince anyone? No one that really needs the convincing.
Statistics are all that'll save you, though, because the alternative is just noise and advocacy: trying to settle arguments by who's louder and more convinced that they're right. People who understand the math get upset when they argue with people who don't, because they can't make themselves understood. Their best evidence is in a language that the other side can't speak. Likewise, the advocates get terribly frustrated with the statistics-mongers, because they seem to be in the business of denying what's right in front of their eyes.
And that's why scientists and engineers are so happy to talk with other scientists and engineers. It's not that there aren't arguments - oh yeah, plenty of 'em - but there's at least a chance that you can convince people with data. Outside of those fields, I've come increasingly to think, the chances of doing that are often minimal.