Venu: You definitely can do that in Mathematics, but that’s because reasoning about Mathematics has some special properties that most reasoning about the real world does not.
Math is black and white If you find a proof for something, it’s true. Until you do, you can’t really call your hunch math. However, in the real world, it’s very easy to find arguments for things that are false.
Math has monotonicity What this means is, that if you use Lemma A and Lemma B to prove Theorem Z, then whether or not Lemma C is true has nothing to do with whether your proof of Z still stands. The real world isn’t like this, in that you can’t arbitrarily pick a subset of the things you know to reason from. If A, B, C and Z were causally related events in the world, ignoring C would be cherry-picking your evidence.
The upshot is, if you try to backward chain from a conclusion in our non-monotone probabilistic world, you’re quite likely to find a nice sounding but possibly flawed argument starting from cherry-picked premises. In fact, if your conclusion is wrong, you pretty much have to, unless your argument generator is so awesome that it fails to come up with arguments when you try to find one for a wrong conclusion. Sadly, we know from experience that the human argument generator isn’t that awesome.
The first thing I thought when I read this question was that the dust specks were obviously preferable. Then I remembered that my intuition likes to round 3^^^3 down to something around twenty. Obviously, the dust specks are preferable to the torture for any number at all that I have any sort of intuitive grasp over.
But I found an argument that pretty much convinced me that the torture was the correct answer.
Suppose that instead of making this choice once, you will be faced with the same choice 10^17 times for the next fifty years (This number was chosen so that it was more than a million per second.) If you have a problem imagining the ability to make more than a million choices per second, imagine that you have a dial in front of you which goes from zero to a 10^17. If you set the dial to n, then 10^17-n people will get tortured starting now for the next fifty years, and n dust specks will fly into the eyes of each of 3^^^3 people during the next fifty years.
The dial starts at zero. For each unit that you turn the dial up, you are saving one person from being tortured by putting a dust speck in the eyes of each of the 3^^^3 people, the exact choice presented.
So, if you thought the correct answer was the dust specks, you’d turn the dial from zero to one right? And then you’d turn it from one to two, right?
But, if you turned the dial all the way up to 10^17, you’d effectively be rubbing the corneas of the 3^^^3 people with sandpaper for fifty years (of course, their corneas would wear through, and their eyes would come apart under that sort of abrasion. It would probably take less than a million dust specks per second to do that, but let’s be conservative and make them smaller dust specks.) Even if you don’t count the pain involved, they’d be blind forever. How many people would you blind in order to save one person from being tortured for fifty years? You probably wouldn’t blind everyone on earth to save that one person from being tortured, and yet, there are (3^^^3)/(10^17) >> 7*10^9 people being blinded for each person you
have saved from torture.
So if your answer was the dust specks, you’d either end up turning the knob all the way up to 10^17, or you’d have to stop somewhere, because there’s no escaping that in this scenario, there’s a real dial in front of you, and you have to turn it to some n between 0 and a 10^17.
If you left the dial on, say, 10^10, I’d ask “Tell me, what is so special about the difference between hitting someone with 10^10 dust specs versus hitting them with 10^10+1, that wasn’t special about the difference between hitting them with zero versus one?” If anything, the more dust specks there are, the less of a difference one more would make.
There are easily 10^17 continuous gradations between no inconvenience and having ones eyes turned to pulp, and I don’t really see what would make any of them terribly different from each other. Yet n=0 is obviously preferable to n=10^17, and so, each individual increment of n must be bad.