Of course, you can also use the chain of negative-utility cases to make a direct argument for specks vs. torture.
Say you prefer 1 slap to N1 specks. Then you prefer 1 kick to N2 slaps, 1 bruise to N3 kicks, 1 broken arm to N4 bruises, and so on, up until the last step where you prefer years of torture to Nk of something.
It follows that the specks vs. torture point comes at N1 x N2 x N3 x …. x Nk. This is pretty much always going to be less than 3^^^3 -- if the steps were truly small, the factors are all going to be less than a trillion or so, and there’s probably going to be less than a trillion steps, and (1 trillion)^(1 trillion) is still insignificant compared to 3^^^3.
Of course, you can also use the chain of negative-utility cases to make a direct argument for specks vs. torture.
Say you prefer 1 slap to N1 specks. Then you prefer 1 kick to N2 slaps, 1 bruise to N3 kicks, 1 broken arm to N4 bruises, and so on, up until the last step where you prefer years of torture to Nk of something.
It follows that the specks vs. torture point comes at N1 x N2 x N3 x …. x Nk. This is pretty much always going to be less than 3^^^3 -- if the steps were truly small, the factors are all going to be less than a trillion or so, and there’s probably going to be less than a trillion steps, and (1 trillion)^(1 trillion) is still insignificant compared to 3^^^3.
Of course. Except that I think you mean trillion^trillion, not trillion*trillion.
Er. Right. Fixed. And it’s a testament to the magnitude of 3^^^3 that I need to change absolutely nothing else.