Like a lot of Robin's stuff, he makes the assumption that everyone already knows about some argument that's mostly original to him, and then proceeds to deduce why they're not acting on that (nonexistent) knowledge. Personally, after reading his argument, I did become marginally more interested in doing something like what he describes. However, I'm not convinced that it's obviously the most altruistic way to use resources.
For one thing, it seems possible that making the world a better place now would actually yield greater returns in the long run.
Let's say I donate to AMF, saving 10 African children from dying. Those children grow up and do useful work, shifting the world economy a bit forward on its exponential growth curve (say, from t=10 to t=10.01). 12,000 years later, we're at t=12,010.01 instead of t=12.010--but since we're so far along the exponential growth curve at this point, that ends up making a much larger difference. The difference that your contribution makes will grow exponentially just like in Robin's plan:
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There are lots of people who are trying to maximize their individual return on investment (through buying stocks and stuff), so opportunities there are thoroughly picked over. By contrast, there are a relatively small number of dollars chasing Wikipedia-style projects that accelerate economic growth without delivering financial returns to their creators, so ROI should (theoretically) be much higher.
One problem with this plan is that although you'll have a larger impact on growing the world economy, it's not clear to what degree a wealthier world economy contributes to altruistic ends. If everyone becomes extremely uncharitable between now and the very far future, then you'd be relatively better off following Robin's plan.
Another problem: if we assume a constant background probability that your investment ends up being worthless (because humanity destroys itself, or because it gets stolen, or whatever), then this is exponential decay, which has the potential to cancel out exponential growth. Let's say your investment has a constant .99 probability of continuing to exist each year. In 100 years, the probability that your investment still exists is .36. After 12,000 years, the probability that your investment still exists is about .000000000000000000000000000000000000000000000000000004.
Another problem with Robin's plan: although your investment grows exponentially, it stays constant as a factor of the world economy. Let's say global GDP is $80 trillion and you put $1000 in to Robin's idea (000000001.25% of global GDP). Your investment grows at the same rate as the global economy, so a billion years later, your investment is still amounts to about 000000001.25% of global GDP. If the number of people alive with problems to solve has stayed roughly constant in that period, then it's unlikely your investment will do much good, since everyone should be ridiculously wealthy anyway (unless there's extreme global inequality).
So yeah, lots of potential problems with Robin's argument. Sorry if I'm repeating stuff that was already said in the comments here or there.
More points, some in favor of Robin:
The probability of losing your money each year is likely not independent. If you've managed to last the past 11,000 years, it's relatively more likely you'll last another 1,000.
Also, if the expected gain year-on-year is positive (for example, if our assets grow by a factor of 1.02 every year, and there's a .99 chance that they continue to exist, that means their expected year-on-year growth is a factor of 1.0098), then the argument could still work. But you start getting in to Pascal's Mugging territory there.
Another p...
Robin Hanson wrote, five years ago:
In the comments some people gave counterarguments. For those in a rush, the best ones are Toby Ord's. But I didn't bite any of the counterarguments to the extent that it would be necessary to counter the 10^100. I have some trouble conceiving of what would beat a consistent argument a googol fold.
Things that changed my behavior significantly over the last few years have not been many, but I think I'm facing one of them. Understanding biological immortality was one, it meant 150 000 non-deaths per day. Understanding the posthuman potential was another. Then came the 10^52 potential lives lost in case of X-risk, or if you are conservative and think only biological stuff can have moral lives on it, 10^31. You can argue about which movie you'll watch, which teacher would be best to have, who should you marry. But (if consequentialist) you can't argue your way out of 10^31 or 10^52. You won't find a counteracting force that exactly matches, or really reduces the value of future stuff by
3 000 000 634 803 867 000 000 000 000 000 000 777 000 000 000 999 fold
Which is way less than 10^52
You may find a fundamental and qualitative counterargument "actually I'd rather future people didn't exist", but you won't find a quantitative one. Thus I spend a lot of time on X-risk related things.
Back to Robin's argument: so unless someone gives me a good argument against investing some money in the far future (and discovering some vague techniques of how to do it that will make it at least one in a millionth possibility) I'll set aside a block of money X, a block of time Y, and will invest in future people 12 thousand years from now. If you don't think you can beat 10^100, join me.
And if you are not in a rush, read this also, for a bright reflection on similar issues.