Imagine you\'re in a tall building with a cat. The cat can survive a fall out of a low story window, but will die if thrown from a high floor. How can you figure out the lon
Doesn't this assume you're using "The Same Cat"?
You can approach it mathematically, but that's the nice thing about math... with the right assumptions, 0 can equal 1 (for large values of 0).
From a practical stand-point, you can get 'Similar Cats", but you can't get "The Same Cat".
You could try to determine the answer empirically, but I would think that there would be enough statistical differences that the answer would be statistically meaningless.
You could try to USE "The Same Cat", but that wouldn't work, as, after the first drop, it's no longer the same cat. (Similarly to, onecan never step into the same river twice)
Or, you could aggregate the health of the cat, sampling at extremely close intervals, and find the heights for which the cat is "mostly alive" (opposed to "mostly dead" from "The Princess Bride"). The cats will survive, on average (up to the last interval).
I think I've strayed from the original intent, but if you're going the empirical route, I vote for starting as high as possible and continuing to drop cats as the height decreases until they statistically survive. And then re-test on surviving cats to be sure.