Parable of the Multiplier Hole

Imagine that we discovered a “hole in space”, through which we could see an alternate Earth, filled with people recognizably like us, though different in many ways.  Those people could also see us.

While no objects could move from their side of the hole to ours, small items (but not humans) could move from our side to theirs.  Furthermore, the hole had the amazing property of multiplying everything we sent through by a factor F of a million!  That is, if you tossed a gold coin through the hole, a million identical coins would come out the hole on the other side.

How tempted would you be to toss useful items, like food, through the hole?   Remember, the cost to you, relative to the benefit to them, is 1/F, only one part in a million.  When considering the following variations, and their various combinations, consider not only F = a million, but also ponder what fraction F would make you indifferent to tossing or not:

  1. Your gift goes to a random person on the other side.
  2. Your gift goes to a government on the other side, which controls the hole.
  3. You can specify to whom your gift will go, using some simple descriptors like “poor”, “smart” etc.
  4. We could also do other things to help them, such as by studying a problem of theirs and sending them a report with suggested solutions.  But these other actions don’t get multiplied by F; a million copies of the report doesn’t help more than one copy.
  5. The hole isn’t very reliable, and only one time in a thousand do items you toss through the hole actually get to the people on the other side.  But when the hole does work 1000*F items come out the other side.
  6. You have very good theoretical reasons to think that most likely there are people much like us on the other side of the hole, but you can’t actually see through the hole (though they can see us).

The point of this parable is that interest rates would also greatly leverage any gift you gave the distant future folks.  For example, in 1785 a French author wrote a satire about Ben Franlkin, the most famous American to Europeans.  While Franlkin was famous for his Poor Richard’s Almanac, the satire mocked American optimism by having “Fortunate Richard” leave money in his will to be invested for 500 years before being given to charity.

Franklin responded by leaving £1000 each to Philadelphia and Boston in his will to be invested for 200 years.   He died in 1790,  and by 1990 the funds had grown to 2.3, 5M$, giving factors of  35, 76 inflation-adjusted gains, for annual returns of 1.8, 2.2%.  Why has Franklin’s example inspired no copy-cats?  Does no one care to help distant future folks through the multiplier hole of compound interest?

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  • Challenge

    I’ve discussed this with my girlfriend and parents, suggesting that I’ll try to leave $20,000-$50,000 in a fund with instructions for conservative, risk-averse management for the next 1,000 years. I’ve told them about Franklin’s donation.

    My parents think I’m crazy. My girlfriend points out that charity now could potentially pay off better over 1000 years than a conservative investment – which is a good point.

    • Jess Riedel

      In only a century or two, the most poverty on earth will almost certainly be eradicated. We live now in a very special time where there are many people who can be cheaply helped.

      200 years ago, it was logistically nearly impossible to help people on the other side of the world. 200 years from now, few people will be in dire need of help. Now is the time to give.

      • The belief that poverty will be eradicated in a century or two gives you reason not to postpone your donation 100-200 years. It doesn’t give you reason to donate now.

    • Challenge,

      Whilst I agree with Robin’s arguments, I think he ought to have mentioned that mitigating existential risk is a very plausible candidate for a strictly better alternative than cash donations to the future.

    • Carl Shulman

      Barring radically new physics, we’ll eventually hit the limits to growth. Reducing existential risk beats accelerating growth, and the key window to effectively do that is probably before space colonization and posthuman entities.

  • Future generations are less needy (so says the experience of the last few centuries). You’d expect this fact to exert a downward pressure on risk-free returns, but other factors overpower it

  • drscroogemcduck

    distant future people are likely to be much better off than us so our marginal piece of bread is worth more than a distant future marginal piece of bread.

  • If we care about consumption equality, as some claim to do in politics, we should disinvest in the future, in order to redistribute from the rich future to ourselves. Yes this is total-utility-reducing, but political advocates of redistribution already are willing to sacrifice efficiency to increase equality.

  • epv

    In the case of a bidirectional send, mono-directional view, with a large multiplyer: First action obscure their view. Second action the largest thermonuclear warhead you can find. People are jerks, might as well beat them to the punch.

  • Timothy

    Is the alternate Earth sufficiently similar to ours that it also has access to a second hole in space, through which it can send objects to a third Earth, to be multiplied at rate F? If so, should our sending objects to Earth2 be conditional upon them resending some portion to Earth3? How high a portion should be required for any given F? What if F is different for the two holes in space?

    Per 5), should Earth2 be contractually required to send objects to Earth3 after failed attempts to send from Earth1, or only successful attempts? If the number received by Earth2 is 0*F, 1*F or 2*F, should they then send objects to Earth3 in all instances (maximum benefit to Earth3), only after 1*F or 2*F (eg. proportionally) or only after 2*F (when return exceed expectations).

    Or, in Franklin’s example, if the trusts perform badly one year, should they be topped up, stay the same, or pay out some of their earlier earnings? (Assuming positive correlation between returns and the state of the economy.) Or, to approximate this, how risky should their investments be?

    How conservatively were Franklin’s funds invested? 1.8 and 2.2% would be approximately inflation-adjusted risk free returns, and much lower than returns to risky assets. Did Franklin (or Boston and Philadelphia) have more trust in the US (or their own) governments than optimism regarding American business? If the aim is to create a distant future utopia, would not encouraging higher-risk businesses, high returns and high variance in returns all increase the chances of this?

    On the other hand, Franklin might have supposed that, over 200 years, there was a non-negligible chance of one or more revolutions in which all government debt is repudiated, while even Revolutions (American, if not French) respect private property. Conversely, over long timeframes the rate of return to private property will show strong mean reversion (and possible overshoot) even if business conditions or government policy are consistently favourable or consistently unfavourable. He was showing his optimism in the survival of the young American Republic.

  • Les Cargill

    Is the hole smart enough to detect and prevent bad things from being sent? What if you threw an unpinned hand grenade through it?

    • Reminds me of the joke:

      After a very bad divorce, a man finds an old stereotypical lamp, rubs it, and sees a genie come out, who offers the standard three wishes.

      “But there’s a catch,” the genie says: “Anything I give to you, I must give twice as much to your ex-wife.”

      So the man thinks and says, “Okay, I want a billion dollars.”

      The genie replies, “Very well, but I’m also giving your ex-wife 2 billion dollars.”

      Then the man says, “I want to be the most powerful person in the country.”

      The genie replies, “Very well, but I will make your ex-wife twice as powerful.”

      Finally, the man says, “And for my last wish: I want you to beat me half to death.”

  • I suspect we would throw our waste down this hole.

    • gwern

      In enough quantities, waste ceases to be waste and becomes an asset.

      A little bit of feces is nasty and a health hazard. A lot and you can go into business. (Look at the Roman urine tax for an example.)

  • Isn’t that what I do when I contribute to educational institutions? (And most states still have rules against perpetual trusts?)

  • So one pretty basic answer seem to be

    The prevailing interest rate must form a lower bound on the rate of return (almost) everyone is willing to accept to transfer marginal resources to themselves in the future.

    Other people are typically less important to us than ourselves. Thus prevailing interest rates should not be enough to encourage us to give to them.

    Exceptions might be:
    1) exceptionally altruistic people
    2) those who anticipate very high returns in the far future
    3) those who wish to signal something special about themselves

  • In every scenario but #6, I would certainly toss useful things into the hole in exchange for useful information, but I assume the point of the hole is charity, not profit.

    In scenarios #1 & 2, I’d probably have to do some research to find out who would benefit more: random/government people through the hole, or people here on Earth for whom “pennies a day” can make a huge difference.

    In scenario #3 I would throw my entire charity budget down the hole, since any F>1 would result in higher utility than charity here on Earth.

    Scenarios #4 & 5 wouldn’t really change anything.

    Even with good theoretical reasons, I probably wouldn’t trust the hole in scenario #6 without some solid proof as to how well it works.

    Regarding the actual point of this post, compound interest for the future, I think one can help the future a lot more by helping the impoverished in the present. Plus, I don’t know how useful money will be in the future; what if 500 years from now the world is a paradise by our standards?

    • To what extent should charity be thought of as given purely with no hope of personal benefit, and to what extent should building a better world with real but hard-to-define gains for the giver be considered?

      If the latter, then giving to a one-way hole isn’t as good a choice as giving on earth.

      Giving to the future depends on how expansive your idea of your self is.

      A low probability bet would include the question of whether the hole will be one-way forever.

  • Philo

    Our additions to the stock of knowledge/understanding are our most important contribution to future people.

  • tim

    At a 3% annual interest rate and a 2% inflation rate, to make $2 million in 200 years I’d have to invest roughly $280 000 right now. I suspect that kind of money can do a lot more good right now than $2 million can in 200 years.

  • Tribsantos

    I think there is a problem with this parable. The situation whereby people send things down the hole is different in a very important aspect from the Franklin’s gift situation. We can only accept that such a gift is feasible if the size of the gift is too small to affect the interest rate. But if it is too small to affect the interest rate, it is too small to affect overall well-being.
    If everybody started doing the same, what would happen is that the savings rate would go up. What Solow demonstraded is that even though one can achieve a higher steady state by increasing savings rate, there is a point where of maximum comsumption – that is, even if my GDP is larger, I don’t consume more because I spend so much of it reinvesting.
    So if we assume we are already on the optimum level of saving, the effect, if the amount of the gift large, is negative, if it is small, the effect is only of redistribution. I don’t how it would be practical to try to make redistributive policy for the future.

  • Rich Rostrom

    “by 1990 the funds had grown to 2.3, 5M$, giving factors of 35, 76 inflation-adjusted gains, for annual returns of 1.8, 2.2%. ”

    This doesn’t make sense. Why are there two values for each number, separated by a comma?

  • Tribsantos, my gift helps the people who get my gift by a large amount, and if there isn’t a market failure I’m not hurting anyone else. So what is the market failure that makes my gift hurt other folks?

    Karl, so we shouldn’t give because the fact that we haven’t given shows we don’t want to give?

    Philo, why can’t you do both?

    tim, you “suspect”, that’s your argument?

    Bill, no it isn’t.

    • So I think I am saying a bit more than that.

      We have a multiplier hole for later versions of ourselves. We have a multiplier hole for our children via bequests. We have a multiplier hole for specific charities when we give gifts that will be invested. All of those holes are utilized.

      There is no reason the to think the multiplier hole for random strangers in the distant future is any more effective. Why should we expect people to give to it.

      Afterall, we don’t regularly throw money at random strangers in the present.

      Now, perhaps a more altruistic people would but I don’t see how the hole changes things.

    • Tribsantos

      The failure is in the rationality of the person that assumes the obligation to honor the interest rate. You hypotheses is based on the assumption that F*(your gift) so far in the future is a lot better than spending it now. If you didn’t think so, there would be no point in renouncing comsumption for such a distant person.
      Let’s assume that people live forever. So I lend you X dollars today, to collect in a thousand years. If it is obvious that the value I will get after interest rates is many times better than the value of spending it today, I have to be tricking you.

  • Doug S.

    Suppose I take $1000 and put it in the bank for 200 years and it grows into $2 million.

    Now suppose that I only let that $1000 sit in the bank for one year. At the end of that year, I take the $1000, plus interest, and spend it. The recipients of that $1000 plus interest immediately put the money back in the bank, and then spend again after a year passes. This process repeats every year for 200 years, at which point there is $2 million in the bank.

    So there ends up being $2 million in the bank regardless of whether the money gets spent or not along the way. What’s the point of setting up a 200 year trust, again?

    • Force concentration, if you think the administrators are going to be competent.

    • You don’t at all know that people who get paid when you spend will invest all of that spending. It usually doesn’t happen.

      • Doug S.

        If they don’t invest it, then don’t they give it to someone else by spending it? Not that much money sits around as cash in people’s mattresses these days, but I’ll admit that it may very well end up in a checking account that gets little or no interest. And money sitting around in a checking account gets turned into bank loans anyway. As far as I can tell, letting money sit in bank accounts for 200 years doesn’t increase the growth of the overall economy. Compound interest only produces money, not wealth.

  • If we can see them, you could use the hole to “hire” the other universe to perform intellectual work for you at low cost.

    However, I am not clear on *how* we can see them if no objects can move from their side of the hole to ours. Photons are surely material objects, no?

    Anyway, assuming that photons *can* make it through – there is a clear incentive to outsource information-processing tasks to the hole.

  • Great thought experiment, but I think there’s a good case that the future will be better served if you spend the money now on existential risk reduction during this brief period of a few hundred years in which we have the ability to send intelligent life extinct.

  • I would toss computers through and ask them to do calculations for me.

  • Charles

    Money isn’t magic. There is no multiplier hole in the Franklin example. It may have been ultimately good for Philadelphia and Boston, but that says little for whether it was ultimately good as a whole (whereas in the multiplier hole it clearly could be).

    Veblen covers this better than I could hope to in The Use of Loan Credit in Modern Business:

    • Doug S.

      Indeed. Wouldn’t throwing *cash* through our magic multiplier hole just cause inflation on the other side?

  • If you give to charities where your gift, after being utilized, doesn’t gain compound interest in utility, you’re not giving to an effective charity.

    Many charities, like most varieties of feed-the-hungry charities, have compounded negative interest, in that the momentary utility of saving some lives quickly begins compounding negative utility as there are now more mouths to feed in an area that was already beyond its sustainable capacity to begin with. But you can think of charities that do have compounded utility. Research or educational ones, for instance.

    • It seems mostly wishful thinking to think that research or education spending compounds at the market interest rates over long periods.

  • Jess, Grobstein, Peter, etc. I’ve posted before on why there is a good chance there will be poor in a few centuries. You don’t need a high chance to justify donations.

    • Jess Riedel

      I think we agree that donations are justified. The question is whether larger utility can be bought by donating to efficient charities today (e.g. the Schistosomiasis Control Initiative) or by saving money to be donated in the future. Given

      (a) the highly speculative nature of your post-em-transition future (which is what I’m assuming you’re talking about when you say “in a few centuries”),

      (b) the amount of compounding that will happen in a few centuries, minus inflation, (as I’ve stated before, I don’t find your prediction of future growth rates compelling)

      (c) the likelihood that the our intentions will be respected by those entrusted with the funds, and

      (d) the cost/feasibility of helping others in the future

      it doesn’t seem at all obvious to me that saving for the future yields higher expected utility than giving today. I’d welcome arguments that would convince me otherwise.

      Two tangential points: (1) The em scenario which leads to many poor ems in the future won’t motivate people who don’t assign moral value to running computer programs. (2) The value of existential risk reduction seems to trump direct charitable giving, either now or to the future.

    • In the Malthusian em situation you propose donations don’t necessarily increase per capita incomes unless they are conditional on the recipients abstaining from reproduction (which may be a harm to a total utilitarian anyway!).

    • I’ve argued for limits to growth independent of ems.

      • Jess Riedel

        Yes, but that’s the far far future, not “a few centuries”. Not only is exponential economic growth unlikely for the same reasons that exponential population growth cannot continue, but the likelihood that I can help anyone I would want to help given the extreme environment seems vanishingly small. At this point, the argument really seems like Pascal’s wager.

  • Jeremiah Dyke

    I haven’t shifted through all the posts let us consider that with such asymmetrical benefits as 1/F would lead many of us to donate to the point of cluttering the other world. Could it be said that the parallel earth would receive too many clothes, etc. So much that the relative benefits of receiving these goods would long surpass the relative costs of the sender. And if they started sending them back to use to free up space it may start an intergalactic reverse trade war…a charity war 

  • jsalvatier

    I think that Robin and some others are getting somewhat tripped up by monetary economics. I think it would be useful for Robin to try to reformulate his argument in a strictly barter economy.

    The reason is this: if an estate saves money, it demands money if it spends money it demands less money. So if an estate had a large amount of cash (relative to the economy as a whole) and then decided to spend it one day, it would cause a large drop in total money demand. One of two things can happen: if the central bank does nothing you get a large rise in the price level which reduces the activities of everyone; if the central bank offsets the change in money demand, by reducing the money supply. This later action reduces the economic activities of everyone else (not the estate).

    Simply saving cash does not move real resources into the future. In order to move resources into the future you need a non-financial phenomena that does it. Perhaps Robin has one in mind, but he hasn’t made it clear.

    It’s useful to think of money as giving you control over a fraction of economic activity at a particular time, not giving you control over an *amount* of economic activity.

    • jsalvatier


      The most obvious real mechanism someone could have in mind is that production is mostly capital constrained as opposed to technology constrained. If we have not run into significant declining marginal productivity of capital then saving more real resources now gives the future a lot more productivity. However, it seems fairly clear to me that we are mostly technology constrained, so I don’t think saving now gives the future a lot more productivity.

  • cournot

    You may also be using the wrong deflators. If you use standard CPI or other price indices, it does seem to be a lot of money. But if you think about it in terms of relative wealth you get a different figure [and standard price adjustments aren’t great for looking far back in the past]. I think a pound was about 5 dollars. So if we assume that 1000 pounds = 5000 nominal dollars and we use the Econ History’s price deflators
    we find that this comes to over $2M if we use the unskilled wage and about $5M if we use nominal GDP. As a relative share of GDP, this figure would have been an enormous $380M or so. The latter is not an irrelevant calculation.

    Given how wealthy someone had to be (relative to the poor in the 18th century) to fork over a thousand pounds in Franklin’s time, he might have done more good with it then than you could do with 2 to 5 million bucks today.

    • Doug S.

      Some interesting trivia: At his richest, John D. Rockefeller had more money than the annual budget of the U.S. federal government.

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