So after a lot of thought, and about 5 months spent reading articles on this site, I think I can see the big picture a little more clearly now. Imagine having a really large collection of grains of sand that are all suspended in the air in the shape of a flat disk. Imagine too, that it takes energy to move any single grain in collection upwards or downwards, but once a grain is moved, it stays put unless moved again.
Just conceptually let grains of sand represent people and grain movement upwards/downwards represent utility/disutility.
What Eliezer is arguing is that, assuming it takes the same amount of energy to move each individual grain of sand, then clearly it takes far less energy to move a single grain of sand very far downward than to move every grain of sand just slightly downward.
What I initially objected to, and what I was trying to intuit through in my first post, is that perhaps it is the case that the energy required to move a single grain of sand is not constant. Perhaps it increases with distance from the disk. I still hold to this objection.
Even if so, it is certainly a valid conclusion to draw that moving a single grain far enough downwards requires less energy than moving every grain slightly downwards. Increasing the number of grains of sand certainly affects this. And no matter what the growth factor may be on the nonlinear amount of energy required to move a single grain very far from its starting point, it is still finite. And you can add enough grains of sand so that the multiplicative factor of moving everything slightly downwards dwarfs the nonlinear growth factor.
Thus, given enough people (and I do stress, enough people), it may be morally worse to subject them all to having a single dust speck enter their eye for a brief moment than to subject a single individual to torture for 50 years.
Its just that our intuition says that for any scale our minds are even close to capable of reasoning about, exponential/super-exponential functions (even with a tiny starting value) greatly dwarf multiplicative scaling functions.
But this intuition cannot be accurate for scales larger than our minds are capable of reasoning about.
So after a lot of thought, and about 5 months spent reading articles on this site, I think I can see the big picture a little more clearly now. Imagine having a really large collection of grains of sand that are all suspended in the air in the shape of a flat disk. Imagine too, that it takes energy to move any single grain in collection upwards or downwards, but once a grain is moved, it stays put unless moved again.
Just conceptually let grains of sand represent people and grain movement upwards/downwards represent utility/disutility.
What Eliezer is arguing is that, assuming it takes the same amount of energy to move each individual grain of sand, then clearly it takes far less energy to move a single grain of sand very far downward than to move every grain of sand just slightly downward.
What I initially objected to, and what I was trying to intuit through in my first post, is that perhaps it is the case that the energy required to move a single grain of sand is not constant. Perhaps it increases with distance from the disk. I still hold to this objection.
Even if so, it is certainly a valid conclusion to draw that moving a single grain far enough downwards requires less energy than moving every grain slightly downwards. Increasing the number of grains of sand certainly affects this. And no matter what the growth factor may be on the nonlinear amount of energy required to move a single grain very far from its starting point, it is still finite. And you can add enough grains of sand so that the multiplicative factor of moving everything slightly downwards dwarfs the nonlinear growth factor.
Thus, given enough people (and I do stress, enough people), it may be morally worse to subject them all to having a single dust speck enter their eye for a brief moment than to subject a single individual to torture for 50 years.
Its just that our intuition says that for any scale our minds are even close to capable of reasoning about, exponential/super-exponential functions (even with a tiny starting value) greatly dwarf multiplicative scaling functions.
But this intuition cannot be accurate for scales larger than our minds are capable of reasoning about.
I understand now: “Shut up and multiply.”