Superintelligence, pp. 122–3. 2014.

Consider a technologically mature civilization capable of building sophisticated von Neumann probes of the kind discussed in the text. If these can travel at 50% of the speed of light, they can reach some  stars before the cosmic expansion puts further acquisitions forever out of reach. At 99% of c, they could reach some  stars. These travel speeds are energetically attainable using a small fraction of the resources available in the solar system. The impossibility of faster-than-light travel, combined with the positive cosmological constant (which causes the rate of cosmic expansion to accelerate), implies that these are close to upper bounds on how much stuff our descendants acquire.

If we assume that 10% of stars have a planet that is—or could by means of terraforming be rendered—suitable for habitation by human-like creatures, and that it could then be home to a population of a billion individuals for a billion years (with a human life lasting a century), this suggests that around  human lives could be created in the future by an Earth-originating intelligent civilization.

There are, however, reasons to think this greatly underestimates the true number. By disassembling non-habitable planets and collecting matter from the interstellar medium, and using this material to construct Earth-like planets, or by increasing population densities, the number could be increased by at least a couple of orders of magnitude. And if instead of using the surfaces of solid planets, the future civilization built O'Neill cylinders, then many further orders of magnitude could be added, yielding a total of perhaps  human lives. (“O'Neill cylinders” refers to a space settlement design proposed in the mid-1970s by the American physicist Gerard K. O'Neill, in which inhabitants dwell on the inside of hollow cylinders whose rotation produces a gravity-substituting centrifugal force.)

Many more orders of magnitude of human-like beings could exist if we countenance digital implementations of minds—as we should. To calculate how many such digital minds could be created, we must estimate the computational power attainable by a technologically mature civilization. This is hard to do with any precision, but we can get a lower bound from technological designs that have been outlined in the literature. One such design builds on the idea of a Dyson sphere, a hypothetical system (described by the physicist Freeman Dyson in 1960) that would capture most of the energy output of a star by surrounding it with a system of solar-collecting structures. For a star like our Sun, this would generate  watts. How much computational power this would translate into depends on the efficiency of the computational circuitry and the nature of the computations to be performed. If we require irreversible computations, and assume a nanomechanical implementation of the “computronium” (which would allow us to push close to the Landauer limit of energy efficiency), a computer system driven by a Dyson sphere could generate some  operations per second.

Combining these estimates with our earlier estimate of the number of stars that could be colonized, we get a number of about  ops/s once the accessible parts of the universe have been colonized (assuming nanomechanical computronium). A typical star maintains its luminosity for some  s. Consequently, the number of computational operations that could be performed using our cosmic endowment is at least . The true number is probably much larger. We might get additional orders of magnitude, for example, if we make extensive use of reversible computation, if we perform the computations at colder temperatures (by waiting until the universe has cooled further), or if we make use of additional sources of energy (such as dark matter).

It might not be immediately obvious to some readers why the ability to perform  computational operations is a big deal. So it is useful to put it in context. We may, for example, compare this number with our earlier estimate (Box 3, in Chapter 2) that it may take about  ops to simulate all neuronal operations that have occurred in the history of life on Earth. Alternatively, let us suppose that the computers are used to run human whole brain emulations that live rich and happy lives while interacting with one another in virtual environments. A typical estimate of the computational requirements for running one emulation is  ops/s. To run an emulation for 100 subjective years would then require some  ops. This would mean that at least  human lives could be created in emulation even with quite conservative assumptions about the efficiency of computronium.

In other words, assuming that the observable universe is void of extraterrestrial civilizations, then what hangs in the balance is at least 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 human lives (though the true number is probably larger). If we represent all the happiness experienced during one entire such life with a single teardrop of joy, then the happiness of these souls could fill and refill the Earth’s oceans every second, and keep doing so for a hundred billion billion millennia. It is really important that we make sure these truly are tears of joy.