Hardly the most profound addendum, I know, but dummy numbers can be useful for illustrative purposes—for instance, to show how steeply probabilities decline as claims are conjoined.
For instance, suppose you have a certain level of gut feeling X that the papers saying LHC will not destroy the world have missed something, a gut feeling Y that, if something has been missed, the LHC would destroy the world, and a third gut feeling Z that the LHC will destroy the world when switched on. Since humans lack multiplication hardware, we can expect the probability Z ≠ X·Y (and probably Z > X·Y, which might help explain why a girl committed suicide over LHC fears). Should we trust Z directly instead of computing X·Y? I think not. It is better to pull numbers out of your butt and do the math, than pull the result of the math out of your butt directly.
Hardly the most profound addendum, I know, but dummy numbers can be useful for illustrative purposes—for instance, to show how steeply probabilities decline as claims are conjoined.
For instance, suppose you have a certain level of gut feeling X that the papers saying LHC will not destroy the world have missed something, a gut feeling Y that, if something has been missed, the LHC would destroy the world, and a third gut feeling Z that the LHC will destroy the world when switched on. Since humans lack multiplication hardware, we can expect the probability Z ≠ X·Y (and probably Z > X·Y, which might help explain why a girl committed suicide over LHC fears). Should we trust Z directly instead of computing X·Y? I think not. It is better to pull numbers out of your butt and do the math, than pull the result of the math out of your butt directly.