Economic growth and reversible computing

In my previous post on the debt, a commenter made the important point that there are limits to economic growth. USCD physicist Tom Murphy has some thoughtful posts on the topic (see here and here). If energy use scales with economic activity then there will be a limit to economic growth because at some point we will use so much energy that the earth will boil to use Murphy’s metaphor. Even if we become energy efficient, if the rate of increase in efficiency is slower than the rate of economic growth, then we will still end up boiling. While I agree that this is true given the current state of economic activity and for the near future, I do wish to point out that it is possible to have indefinite economic growth and not use any more energy. As pointed out by Rick Bookstaber (e.g. see here), we are limited in how much we can consume because we are finite creatures. Thus, as we become richer, much of our excess wealth goes not towards increase consumption but the quality of that consumption. For example, the energy expenditure of an expensive meal prepared by a celebrity chef is not more than that from the local diner. A college education today is much more expensive than it was forty years ago without a concomitant increase in energy use. In some sense, much of modern real economic growth is effective inflation. Mobile phones have not gotten cheaper over the past decade because manufacturers keep adding more features to justify the price. We basically pay more for augmented versions of the same thing. So while energy use will increase for the foreseeable future, especially as the developed world catches up, it may not increase as fast as current trends.

However, the main reason why economic growth could possibly continue without energy growth is that our lives are becoming more virtual. One could conceivably imagine a future world in which we spend almost all of our day in an online virtual environment. In such a case, beyond a certain baseline of fulfilling basic physical needs of nutrition and shelter, all economic activity could be digital. Currently computers are quite inefficient. All the large internet firms like Google, Amazon, and Facebook require huge energy intensive server farms. However, there is nothing in principle to suggest that computers need to use energy at all. In fact, all computation can be done reversibly. This means that it is possible to build a computer that creates no entropy and uses no energy. If we lived completely or partially in a virtual world housed on a reversible computer then economic activity could increase indefinitely without using more energy. However, there could still be limits to this growth because computing power could be limited by other things such as storage capacity and relativistic effects. At some point the computer may need to be so large that information cannot be moved fast enough to keep up or the density of bits could be so high that it creates a black hole.

5 thoughts on “Economic growth and reversible computing

  1. Well, that’s a rather big idea at the end there! But, not unheard of.

    QM Physicist Seth Lloyd has argued that a black hole would have to be the end point of physical computation. (

    Interestingly, some systems theorists, like futurist John Smart, hypothesize that the entire universe is a self-replicating information processing system which ultimately reproduces itself with a computational singularity that is, in physical terms, a literal black hole. James N. Gardner’s book Biocosm argues for a similar hypothesis. As does Tipler’s Omega Point theory (kind of).

    Of course, the Vikings believed that the Gods will fall at Ragnarok, and the Christians look forward to the second coming of Christ. And the Hopi Indians…etc etc. Perhaps these black hole theories are no more true. (Or no less.)

    interestingly, if Moore’s Law (broadly construed) continues indefinitely, we’ll be at black hole computational densities within hundreds, not millions,of years.



    1) i’m not sure reversible computing is an option for humans (though i’m also skeptical that actual quantum computing is feasible, apart from the fact that everything in nature can be viewed as a quantum computation).

    Humans are open systems (which is partly a reason why they want to compute, or find, solutions). Reversible computation assumes you can add states to an irreversible process to make it reversible, and theoretically i agree (though this does imply the assumption that naive physics interpretation is correct—-and i think would also rule out Prigogine’s ‘subdynamics’ view which is that actually naive physics interpretation is incorrect, and nature is intrinsically irreversible —via information loss in quantum measurement or coarse graining (“emergence”).

    however, to make the open system (human) be reversible, you might have to add all the states in the whole universe, to close it. But once you’ve done that (assuming you have the time, and the Comtian ability to get all the initial conditions of the universe) , you have the whole system (microcanonical ensemble of the universe) and so there is really nothing to compute, since you’ve done it.

    (Tipler’s physics of immortality’s discussion of Poincare recurrence and general relativity is a related set of ideas—which in his view i think would support the arguments in the post in a different way—-immortality is possible, in a ‘red queen’/Zeno sort of way—stay one step ahead and learn enough to forget what you have forgot.)

    2) i’m not sure the bookstaber argument that there is convergance to equality in a sense is all that relevant or true (just as i question whether an expensive meal is no more energy intensive than a cheap one). it depends on what you measure , and also how one measures ‘quality’. eg life expectancies may be converging among social classes, incomes, and world, but in other areas they may noty be, or even diverging. Similarily, while education in one sense costs the same today as in the past, though tuition rises, in fact while a ‘book’ or ‘pencil and paper’ may not differ much in price from the past, one might note a book on physics these days also has input from particle accelerators and space programs, for example.


  3. @Ishi 1) If you believe in the Church-Turing thesis (which I do) then computation is computation. You can always simulate any situation on any computer so it doesn’t matter if humans are open systems, it only matters if their economy is computable. 2) The only thing that matters is what the energy-GDP curve looks like. The Bookstaber argument is that it saturates. You may or may not believe that but empirically the developed world is using less energy per capita then say a decade ago. The developing world is using a lot of energy.


  4. i do pretty much agree with the church-turing thesis (though one can always consider s. shelah’s stuff on transfinite logic (search shelah in logic on arxiv)—i even met paul cohen on undecidability of the continuum hypothesis, as well as karl pribram who wrote stuff reminiscent of jack cowan on cognition. (stanford).

    i see my NY Review of books has a note on ‘human capitalism’ by brink lindsey—how economic growth has made us smarter and more unequal–next to an article on ‘is there a jewish gene’ by richard lewontin. compare that with bookstaber.

    i think it may matter if humans are open systems. as is pretty well known, general equilibrium theory of economics (arrow-debreu-hahn) is non-computable or at least NP-complete. (eg d. saari, sonnenchein).

    i dont believe even in time—i’m in the microcanonical ensemble.—no entropy increase here.

    i did go to the protest against the pipeline (keystone xl or something; bill mckibben sunday so thats my position.


  5. ps. the path integral paper was pretty good though i cant say i understand it—a different approach. i once saw marc kac (rip) give a talk; best one i ever seen—he had a book in the 50’s showing how classical mechanics/stochastic dynamics could be put into functional integral/path integral form. that also goes back to dirac and landau (a footnote in dirac’s qantum mechanics book which was used by feynman-wheeler to create an industry—eg kleinart—also known for quasicrystals).

    lester ingber (who has a website) among others also used path integrals for brain theory. ‘for completeness’. and there’s more in the system. ola


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