The Mahalanobis Blog has an interesting comment on nonlinear relations (the blog is actually on a much different topic). His example is uses a straight line to describe a relationship, when the relationship is much more complicated. Rather than summarizing it, here is an excerpt:

“An analogous scientific consensus was the belief that nuclear testing caused millions of cancer deaths, popularized by scientific heavyweight Linus Pauling. High levels of radiation will certainly kill you, and lower levels will harm you. Linus Pauling calculated the damage at minuscule levels by extending that graph back in a straight line to zero. Zero radiation, obviously, causes no harm. At low levels not many would be harmed, but multiplying that low level by the population of the world, as Pauling did, allowed him to claim that continued nuclear testing would kill millions of children. So it should be stopped. Pauling organized a petition against nuclear testing signed by 11,000 scientists and presented to the United Nations, for which he won the Nobel Peace Prize (to add to his Nobel in chemistry). It was all science and logic. Naysayers were anti-scientific ideologues. But with poisons dosage is key, and highly nonlinear. The graph of radiation mortality does not go straight back to zero. It goes down to about 700 millirems a day, then heads back up again, like a hook. Low background levels of radiation seem to be good for you. The evidence that the “linear extrapolation to zero” is wrong, in that while bad for you in large doses, radiation does some good in small doses. It seems to keep the DNA repair mechanisms in good working order. The same principle is observed with alcohol, a potential poison: heavy drinking will kill you, but a glass of wine a day is good for you.

Theories that are really compelling are often wrong, because all theories are simplifications to a more complicated reality. So the fact that 90% of the population believe X causes Y and can be fixed by Z makes me highly skeptical. When in history has something complicated, true, and important, been so agreed upon prior to definitive evidence? It suggests the facts have little to do with it.”