Sqrt(a few billion + n) is approximately Sqrt(a few billion). Increasing functions with diminishing returns don’t approach Linearity at large values, their growth becomes really Small (way sub-linear, or nearly constant) at high values.
This may be an accurate description of what’s going on (if, say, our value for re-watching movies falls off slower than our value for saving multiple lives), but it does not at all strike me as an argument for treating lives as linear. In fact, it strikes me as an argument for treating life-saving as More sub-linear than movie-watching.
It’s not the overall growth rate of the function that becomes linear at high values; it’s the local behavior. We can approximate: sqrt(1000000), sqrt(1001000), sqrt(1002000), sqrt(1003000) by: 1000, 1000.5, 1001, 1001.5. This is linear behavior.
Uh… what?
Sqrt(a few billion + n) is approximately Sqrt(a few billion). Increasing functions with diminishing returns don’t approach Linearity at large values, their growth becomes really Small (way sub-linear, or nearly constant) at high values.
This may be an accurate description of what’s going on (if, say, our value for re-watching movies falls off slower than our value for saving multiple lives), but it does not at all strike me as an argument for treating lives as linear. In fact, it strikes me as an argument for treating life-saving as More sub-linear than movie-watching.
It’s not the overall growth rate of the function that becomes linear at high values; it’s the local behavior. We can approximate: sqrt(1000000), sqrt(1001000), sqrt(1002000), sqrt(1003000) by: 1000, 1000.5, 1001, 1001.5. This is linear behavior.