Saturday, October 20, 2018

Financial returns of interstellar colonization for the sedentary

Summary: In thinking about the likelihood of interstellar colonization by our civilization, or possible alien civilizations, one question is motivation: how strong are the incentives to do so? If moderately fast self-replicating probes can build infrastructure in a new solar system and send back information or material goods requiring extensive experimentation or computation to produce, then even at current market interest rates a colonization mission could deliver extremely high return on investment. For patient long-lived decision-makers with strong property rights or stability, returns could be overwhelming.

In the short run, human colonization of other planets and asteroids is very expensive with few benefits. Advanced closed ecosystems, self-replicating robots building solar cells, and autarky-enabling manufacturing and AI technologies could first be used more profitably on Earth. For protection against existential risk, isolated bases in Antarctica or under the sea would be cheaper and more effective than space colonies for some time to come. But in the long run as our civilization's energy production approaches terrestrial limits of solar radiation and other resources, the relative desirability of making use of extraterrestrial and ultimately extrasolar resources should increase.

The long-run plausibility of colonization is of some interest in thinking about the future prospects of our civilization (e.g. the scale of what we could lose to an existential risk), and accounting for the so-called Fermi Paradox , the absence of signs of alien intelligence. Among the plethora of explanations offered, is the view that no civilization would undertake interstellar colonization because the distances involved prevent sufficient payoffs for the civilization sending out colonization vehicles. This explanation is not very plausible as a major factor, since it depends on extreme convergence across civilizations (an issue with many 'what aliens want' accounts, see Sandberg, Drexler, and Ord's 'Dissolving the Fermi Paradox' for some helpful analysis about the level of paradox in infrequent intelligence), but it seems worthwhile to examine the basic issues to assess it, at least to the degree of one post.

Back-of-the-envelope calculations suggest that for a civilization with advanced space, robotics, and manufacturing technologies sending out one or a handful of probes to colonize the universe would pay off at current market interest rates.

Colonization probes could harvest many orders of magnitude more resources than they require, and send back valuable information goods
Suppose that interest rates were very low, civilization was ultra-stable with strong property rights, the population was composed of patient immortals, and that trustworthy robotic probes could be designed to self-replicate in a new star system, producing solar panels, computers, and interstellar communication or transportation systems. In this case the return on investment of interstellar colonization could clearly be extremely favorable for stay-at-homes.

Armstrong and Sandberg discuss many aspects of colonization costs for various launch speeds:

Each year 5.5×10^24 J of solar energy reach the surface of the Earth, and 1.2×10^34 J in total are emitted by the Sun. Stellar life-times for Sun-like stars are measured in the billions of years, adding another 9-10 orders of magnitude. A probe used self-replicating robots to construct space-based solar satellites in a Dyson swarm could eventually harvest 10,000,000,000,000,000,000,000,000 times the energy used in its trip or more at a destination star. It could also use that energy to send out further probes to harvest other stars at no direct cost to the Solar System.

The energy and computational resources in the new star system could be used to conduct scientific and technological research, sending results and blueprints home. Extrasolar Hollywood could send back new entertainments discovered searching through the combinatorial explosion of possibilities. Any information goods that can be pursued in parallel could be produced in this way, and the Solar System would save on energy, so long as it would otherwise have expended even a trivial share of its resources on developing such information goods.

With the initial probe sending out further probes in von Neumann fashion the total resources dedicated to producing information goods would go up by a factor of billions as the galaxy was colonized, and perhaps some additional orders of magnitude as other galaxies are reached (although the most distant would be unable to send communications back to the expansion of the universe).

Interest rates and journey times
Patient immortals with perfect stable property rights may not have an issue with waiting decades or centuries for their return on investment to start to be delivered, and billions of years to be fully enjoyed, but those are strong assumptions.

Discounting future payouts with a constant exponential discount/interest rate of a few percent per annum renders far future returns negligible (although such a constant rate may be a poor reflection of our preferences). At current market interest rates the delay before a colonization mission reaches its destination, builds infrastructure, and begins transmitting information goods back could matter quite a lot. Here are the discount factors for returns after various periods (in years) for some different discount rates:


With 1 year of solar radiation reaching Earth's surface at 6 orders of magnitude greater than energy costs of a mission, and close to 10 additional orders of magnitude for a Dyson swarm to harvest, a mission that could proceed at 10% of lightspeed and reach a destination in decades (with a delay of years for messages returning home) could comfortably pay for its energy costs with current discount rates. At 1% of lightspeed or less, low discount rates or fast construction would be important. Probes set at a high fraction of c could reach a destination in less than a decade and pay off easily.

Future interest rates and property rights
By the time advanced space and robotics technologies are available to conduct interstellar missions, interest rates might be much higher or much lower than today. For instance a robotic economy on Earth or the Solar System with vast untapped mineral and energy resources could grow exponentially, with a doubling time of capital equipment measured in months (or perhaps faster, weeks or days, rates that we can see in biological systems' growth given abundant resources). Rapid technological innovation could similarly drive up growth and interest rates enormously. However, limits to Solar System resources, and economic activity given those resources (see, e.g. Hanson)  would relax this pressure (and be reached quickly by such an economy).

With slower economic growth at home, interest rates would be set more by the time horizons of investors. Indefinite life extension (medicine for humans, and lasting computer programs), mind modification technologies that allow individuals to adjust their levels of patience, and selection for long-run investors over time could make it easier for extremely patient investors to enter the market and outgrow short-horizon investors. However, even the most patient investor must still discount for the chance that their investments will be expropriated. If investors face an annual wealth tax of
2%, of the value of their investments, then they will have to discount at least at that rate.

Similarly, if occasional wars and revolutions expropriate or destroy investors and investments, that could again cause substantial discounting (and they might become much more frequent if the subjective speed of thought of powerful beings increased  by multiple orders of magnitude). For long-run discount rates, this effect would be limited though, so long as investors had some significant credence in eventual development of a stable regime (before the NPV of investments declined to negligible levels), as discussed by climate economist Martin Weitzman.

The earlier analysis about interest rates and travels times also assumed that investors could capture the benefits of the information goods sent back from their mission, i.e. that property rights could be maintained over great distances and times, perhaps by extraordinarily stable artificial intelligence. If colonists do not provide any special favor to those who sent out a colonizing mission, simply acting as a new trading partner for the Solar System, then the creation of the colony is a public good, and there would be collective action problems in creating it (although it would still be quite beneficial for a large government to do, and wealthy entities might fund travel in order to participate as colonists).

Material goods and passengers could also be transported, inefficiently or slowly
Information goods are valuable, but stay-at-homes may also want physical resources, which could be used to extend their lives and increase the local standard of living in ways that information alone could not.

The high energy costs and time delays of interstellar transportation would make the return of physical goods and resources somewhat wasteful, but this could still easily be of great benefit to the stay-at-homes and justify sending out a mission.

High-speed transportation systems might deliver a payload with usable energy content of 50%, 10%, 1%, 0.1% or less of the energy required to send them, depending on speed and cargo. Extremely value-dense cargo could include data storage media (if that winds up cheaper than electromagnetic signals at the relevant margin), rare or expensive-to-synthesize elements and particles (e.g. antimatter) or individuals (if wealth and political power distributions continue to have fat tailed distributions, one would expect some individuals who could and would pay to travel and enjoy the resource abundance of new less populated worlds).

Patient homebodies could receive a much higher proportion of harvested resources delivered through slow, efficient transfer orbits, perhaps at 0.1% of lightspeed or less, permitting far greater computation and life in concentrated locales.

In the very long run of billions of years, the Sun's radiation will increase and then diminish, and other resources will be exhausted. Instead of transporting in new resources, minds could be (slowly) transported to other solar systems, allowing greatly extended existences and per capita wealth.

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