Meeting the Dragon in Your Garage.
Suppose you observe the following dialogue:
A: If we do X we observe Y.
B: We tried X and we did not observe Y.
A: Apparently, you did not do X correctly.
B: Apparently, there is no Y. The reports of Y are just mistakes in the experiment.
There are many people joining both positions. Zero hypotheses, or hypothesis of no Y, of course, is simpler than hypothesis of Y that can be observed via X. No theory predicts Y, neither the existence of Y invalidates current theories.
Now, you are another explorer, and you already have all the necessary equipment to do X (and you can ask people supporting A how to do X correctly). Would you try to do it to observe Y?
Consider the following cases:
1) Y is a new astronomical object. X is the equipment (a telescope) to observe it, and where to look. Assume photography is not invented yet.
2) Y is a new generation of elementary particles. X is the design of the experiment.
3) Y is God. X is a specific way to pray if you want to understand if God exists or not (i.e., not a prayer of healing, intercessory prayer etc).
If your answer is different for these three examples, what is the difference?
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!
I don’t think that whether it worth investigating further depends on how well that area is figured out.
I woudl give that if I am interested in an area I would probably be interested in both X->Y and not(X->Y). But random facts are not enough for me to spend thaaat much effort ot figure them out. LIke if a random person makes a claim on a street corner I would not build a million dollar machine to test that out or apply for a grant to build one. I would need to have an independent reason to care or have it be beneficiary of general curiosity.
I am also more likely to spend effort in areas that I find “important” or “interesting”. There is the fact that if there is a detailed description how a experiment is carried out I mostly take peoples word that they did it or suspect that their error is close to the level of description they are providing. But I don’t actually personally verify any significant amount of things. I don’t naturally measure zeroes and you kinda need to motivate me to unnaturally do so with money or theorycrafting.