The first two examples are for finding more of a type of thing we already know to exist (astronomical objects, elementary particles). The third example is less obviously so. So, your priors are different.
That aside, I suppose there is no difference. The only thing that I’d consider is the opportunity cost.
Thank you for your reply. I agree with it. However, how would one estimate these prior probabilities at all and decide whether it is rational or not to try X? It should depend on its cost (basically the time spent since you have all the equipment according to the set up of the problem) and on the gain (for example, if X in (1) is just one more asteroid, gain is not large, if it is asteroid that might collide with Earth gain is larger). Most difficult, how to do it in the third case? How much time X would require to be rational to try? 5 seconds? 5 years? Where this estimate can come from?
The first two examples are for finding more of a type of thing we already know to exist (astronomical objects, elementary particles). The third example is less obviously so. So, your priors are different.
That aside, I suppose there is no difference. The only thing that I’d consider is the opportunity cost.
Thank you for your reply. I agree with it. However, how would one estimate these prior probabilities at all and decide whether it is rational or not to try X? It should depend on its cost (basically the time spent since you have all the equipment according to the set up of the problem) and on the gain (for example, if X in (1) is just one more asteroid, gain is not large, if it is asteroid that might collide with Earth gain is larger). Most difficult, how to do it in the third case? How much time X would require to be rational to try? 5 seconds? 5 years? Where this estimate can come from?
No easy answers to these questions. Welcome to LessWrong where we try to figure it out. I’d recommend reading the Sequences if you haven’t already.
Thank you!