Just recently, I spent a week in Bonito, Brazil, for the annual meeting of the bioGENESIS core project for DIVERSITAS. Over dinner, we strayed into rules, laws, paradoxes, and conjectures: which one we wanted to have and what it would be. Dan Faith decided that he wanted a Conjecture – and proceeded to suggest one. He proposed that any fairy tale or fable could be inverted so that its message would change in an interesting and informative way. Take, for example, the tortoise and the hare. Maybe the tortoise had heard the classic fable and so assumed he would win, thus losing owing to arrogance or inattentiveness. Or maybe the hare had heard it and so realized he would lose if he didn’t run steadily. Tortoise loses – hare wins – lesson changes: those who don’t pay attention to history are bound to repeat it. Having succeeded here, we tried a few other fairy tales and fables on the Conjecture and I have to confess it was a bit of a force to make it work. Time to give up on Faith's Conjecture.
A few days later, however, I got to thinking about it a bit more and realized that perhaps Faith’s Conjecture really was valid – but in a different context: ecology and evolution. I hereby restate Faith’s Conjecture as: any correlation from which a causal relationship might be inferred (the thing on the x axis influences the thing on the y axis) can be inverted (the things on the x and y are switched) to lead to a new causal inference. Here are some examples.
Some cool things I conjectured in Brazil.