It’s worth pointing out that if time just advances forever, so that your current time is just “T seconds after the starting point”, then it is simultaneously true that:
time is infinite
every instant has a finite past (and an infinite future)
The second point in particular means that even though time is infinite, you still can’t wait an infinite amount of time and then do something. I think that’s what MichaelStJules was getting at.
Your mixed strategy has its own paradox, though – suppose you decide that one strategy is better than another if it “eventually” does more total good – that is, there’s a point in time after which “total amount of good done so far” exceeds that of the other strategy for the rest of eternity. You have to do something like this because it doesn’t usually make sense to ask which strategy achieved the most good “after infinite time” because infinite time never elapses.
Anyway, suppose you have that metric of “eventual winner”. Then your strategy can always be improved by reducing the fraction you donate, because the exponential growth of the investment will eventually outpace the linear reduction in donations. But as soon as you reduce the fraction to zero, you no longer get any gains at all. So you have the odd situation where no fraction is optimal – for any strategy, there is always a better one.
In a context of infinite possible outcomes and infinite possible choice pathways, this actually isn’t that surprising. You might as well be surprised that there’s no largest number. And perhaps that applies just as well to the original philanthropist’s paradox – if you permit yourself an infinite time horizon to invest over, it’s just not surprising that there’s no optimal moment to “cash in”.
As soon as you start actually encoding your beliefs that the time horizon is in fact not infinite, I’m willing to bet you start getting some concrete moments to start paying your fund out, and some reasonable justifications for why those moments were better than any other. To the extent that the conclusion “you should wait until near the end of civilization to donate” is still a counterintuitive one, I claim it’s just because of our (correct) intuition that investing is not always better than donating right now, even in the long run. That’s the argument that Ben Todd and Sanjay made.
It’s worth pointing out that if time just advances forever, so that your current time is just “T seconds after the starting point”, then it is simultaneously true that:
time is infinite
every instant has a finite past (and an infinite future)
The second point in particular means that even though time is infinite, you still can’t wait an infinite amount of time and then do something. I think that’s what MichaelStJules was getting at.
Your mixed strategy has its own paradox, though – suppose you decide that one strategy is better than another if it “eventually” does more total good – that is, there’s a point in time after which “total amount of good done so far” exceeds that of the other strategy for the rest of eternity. You have to do something like this because it doesn’t usually make sense to ask which strategy achieved the most good “after infinite time” because infinite time never elapses.
Anyway, suppose you have that metric of “eventual winner”. Then your strategy can always be improved by reducing the fraction you donate, because the exponential growth of the investment will eventually outpace the linear reduction in donations. But as soon as you reduce the fraction to zero, you no longer get any gains at all. So you have the odd situation where no fraction is optimal – for any strategy, there is always a better one.
In a context of infinite possible outcomes and infinite possible choice pathways, this actually isn’t that surprising. You might as well be surprised that there’s no largest number. And perhaps that applies just as well to the original philanthropist’s paradox – if you permit yourself an infinite time horizon to invest over, it’s just not surprising that there’s no optimal moment to “cash in”.
As soon as you start actually encoding your beliefs that the time horizon is in fact not infinite, I’m willing to bet you start getting some concrete moments to start paying your fund out, and some reasonable justifications for why those moments were better than any other. To the extent that the conclusion “you should wait until near the end of civilization to donate” is still a counterintuitive one, I claim it’s just because of our (correct) intuition that investing is not always better than donating right now, even in the long run. That’s the argument that Ben Todd and Sanjay made.