When probabilities of some events become very low, it can be hard to calibrate your thinking and planning about them. The classic large-scale example is that of asteroid defense. The odds of an asteroid hitting the earth within our lifetimes are very low. On the other hand, the likelihood isn't zero, the negative consequences would be severe for millions if not billions of people, and we actually have the technical capability to do something about the problem with enough advanced warning. So, how much money should we as a species spend on asteroid defense? A bit closer to home, there are funding opportunities out there sometimes that are game-changing amounts of money, but getting the grant is something like a 0.5% chance, and the criteria are quite opaque. It's tough to get a good handle on how much time one should invest in the (relatively short) proposal....
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