Sunday, May 31, 2020

Experience curves, large populations, and the long run

If our civilization avoids catastrophe, will we generally be able to advance technology to close to physical limits, match or exceed observed biological abilities, and colonize the universe? Or will we be stuck in a permanent technological plateau before that, reaching a state where resources are insufficient to make the breakthroughs to acquire resources and continue progress? Experience curves, which forecast cost improvements in technology as a function of cumulative production, are a popular tool for technological forecasting and perform relatively well compared to other statistical approaches, although they inevitably have significant and increasing error as one extrapolates further. If we consider the maximum energy resources and population of the Earth, combined with the potential lifetime of human civilization (absent existential catastrophe), experience curves extrapolate to immense technological improvements (constrained by physical limits), more than sufficient to colonize the rest of the solar system, which in turn yields a billionfold increase in potential scale to fund interstellar colonization. Such extrapolation would suggest matching or exceeding biological capacities we currently lack, such as the computational efficiency of brain tissue, or the rapid energy payback of algae as solar energy and manufacturing devices.


Heroic extrapolations of experience curves as data for forecasting

As discussed in the previous postexperience curve models forecast technological progress with a learning rate, i.e. a constant percentage cost improvement per doubling of cumulative production, i.e. Wright's law. Nagy et al (2013) used a database of 62 technologies to to see which extrapolation rules best predicted subsequent technological improvement, and found that Wright's law came out ahead (although not hugely, these measures are all correlated, e.g. when production grows exponentially with time, Wright's Law matches exponential improvement with time) of constant proportional improvement with time, economies of scale with instantaneous production levels, time and experience, experience and scale, and lagged Wright's law.

Such learning rates are not constant, have bidirectional causation (tech improvements increase sales) and change with unevenness in the technological landscape (e.g. as physical limits are approached, or a bottleneck with worse scaling properties comes to dominate production), but they are a good baseline to start with for extrapolating future technological growth, supplemented with data on physical limits and scaling, often backed by data over several or in some cases many orders of magnitude (e.g. transistors).

Nagy et al show the mean logarithmic error for Wright's law hindcasting for each of their datasets:




And growth of error for the varied extrapolation rules:





Any forecasts drawn from these rules will have very large error bars, but they can serve as one source of evidence

Learning rates and self-sustaining growth

Nagy et al's datasets, in the supplement of their paper, show a variety of learning rates:




For information technologies, a doubling of production was associated with close to a halving of unit costs. That enabled the incredible growth of Moore's Law, with many orders of magnitude increase in transistor counts but slower (albeit still rapid) growth in total dollars of transistor sales. Bloom et al (2020) find that over the period they study Moore's law involved 35% annual growth in transistor density (with similar relationships for unit costs), while the number of researchers used increased at a rate of 7%, low enough to be paid from increasing revenues and continue rapid progress until slowing in recent years.

For energy technologies a doubling yielded substantially less than a halving of costs, so $ of revenue had to grow much more to pay for each doubling of production. Rapid growth in solar photovoltaic sales (possible because of the low solar share of world energy use) have driven impressive progress, albeit still far short of Moore's Law, but in the long run market growth for an individual technology is capped by the growth of the overall economy and the passage of time. The vast majority of technologies, such as manufacturing of non-IT goods and agriculture, lie in this category.

On the other hand, a technology where costs fell by more than half with each doubling of production could undergo superexponential growth on a fixed annual budget, as each doubling would take less time than the previous one without budgetary growth.

Historically, the overall world economy grew at an accelerating rate as advances in a variety of technologies combined to increase sustainable populations and output: metalworking for agricultural tools, better crops, techniques such as crop rotation, etc. Each technology fell short of being able to sustain exponential growth on its own, but collectively they increased the sustainable and actual population (via Malthusian dynamics), driving up demand, so that the combination of cost falls and demand growth would make each doubling of output faster than the previous on average. In the last century human population has fallen short of technology's capacity to support it, but when we project over long periods of time we should expect industrial output to rise to closer to technological limits, either by selection as cultural practices with high reproduction grow, or by fast-growing automation replacing human labor.

In the meantime, the fact that current technology could support much more than the current population lets us be more confident about room for future growth.


Absent collapse, terrestial production can scale up enormously in time, energy and population

In discussions of longtermism and to establish large potential future populations, scholars sometimes set aside the possibility of space setttlement, avoiding debates about its technical feasibility or associations with science fiction in favor of the philosophical and especially robust empirical points. They note things like the typical lifespan of a mammalian species on the order of a million years, longer for broader categories, and the hundreds of millions of years of habitability remaining for the Earth (without major intervention).

Because our civilization's production has been scaling up so rapidly, total production throughout all of history is only a few years to decades of current production, depending on how fast the particular technology is growing (e.g. for GPU and AI ASIC transistors, as a result of 30%+ growth rates, only a few years worth of today's production have ever occurred, while cumulative world product is much of a century of current world product because of growth rates of a few percent) :




So a million years of ongoing civilization at current production levels would see several hundred thousands times the AI chip production and more than ten thousand times economic output,  without accounting for further growth and technological improvement.

That compares favorably to the thousandfold increase in terrestrial civilization's energy consumption (and a population increase greater or smaller depending on energy use per capita) that intense terrestrial solar power exploitation could enable. However, temporal extension suffers relative to spatial extension in that it misses out on economies of scale at a given time, and impatient investors reduce investment in temporally extended projects as the later returns are heavily discounted (although this might change if long-run focused investors or governments gain power in the long-run, as one might expect). Likewise, if the international order does not become stable, eventual war with future weapons of mass destruction could cause loss of technological knowledge, although data preservation provides a strong bulwark against technological loss for survivors, and institutions may stabilize peace over time.

Combining increased instantaneous scale on Earth, other catch-up growth, long possible lifetimes for technological civilization, quite large cumulative increases in productions are possible from scaling up spending with the broader economy:



Scale growth10% learning rate20% learning rate40% learning rate
1.00E+032.86E+009.24E+001.63E+02
1.00E+071.16E+011.79E+021.44E+05
1.00E+103.31E+011.66E+032.34E+07

For the technologies with faster learning rates (e.g. IT, DNA sequencing), the cumulative production gains would be greatly augmented by cost falls increasing spending, with moderate augmentations for the lower learning rate technologies. Baumol effects would likely reduce demand and cumulative production (e.g. manufacturing as a share of output has fallen with economic growth, in favor of sectors with lower productivity growth) for some goods.

Long-run terrestrial resources look vastly greater than required to colonize the solar system

The massive scaling opportunities on Earth could accordingly improve IT/robotics, solar power, space launch capacity, and manufacturing, technologies used in expanding beyond terrestrial resources.

The recent decline in improvements in general-purpose computer price-performance, regression to the broader mean for IT (which has been exceptionally fast), and physical limits to feature shrinkage suggest lowering projections of learning rates there. But there clearly remains room for large gains by comparison to physical limits and the existence proofs of animal brains, and learning rates remain strong compared to most technologies. Small ants can have brains making up more than 10% of body mass, ant queens can produce many thousands of eggs per day, and their feed conversion efficiency is fairly high. If one imagines industrial production of brain tissue, breeding/engineering for brain mass and fast growth, biological brain tissue could be produced for a few dollars per kilogram, about the size of a human brain) If one takes a low estimate of human brain computational power of 100 teraflops, running on ~20 watts,  that is far superior to existing chips. E.g. an A100 GPU delivers a few hundred teraflops of tensor core instructions but costs $10-20,000 and uses 400 watts, 20x as much as the brain. If we take a higher estimate of human brain equivalent at 10 petaflops, the comparison would come off 100x worse for the brain.

Software improvements also have substantial learning rates, illustrated by faster than Moore's Law progress in neural network efficiency during a period of rapid scaleup of resources for ML research, and neural network models (among other programs) exhibit predictable scaling of performance across many orders of magnitude of increased compute expenditure in training and execution, indicating substantial learning rates. Combining these factors, extrapolating out learning curves would suggest superhuman performance across many AI tasks, likely including robotics for space industry, well before exhausting long-run terrestrial resources.

Biological solar autotroph systems can manage energy payback times of hours to days, vs months to years for current commercial solar panels. Growing solar to max out terrestrial solar resources even for a limited time suggests approaching the biological range there, with further improvements over time if civilization lasts. Lighter and more efficient solar cells improve the economics of space solar power, and reduced manufacturing/operation costs combined with rising land prices from exhaustive exploitation of the terrestrial solar resource would drastically improve the tradeoffs of building space industry: instead of space solar power competing against the best desert solar on Earth, it would be the only way to acquire much more solar irradiation.

For space launch capacity, SpaceX launch capacity is close to $1,000 per kg and falling (already having brought down prices substantially). From an ICES paper:



 Energy costs of rocket launch are a fraction of 1% of that, and could decline further if renewables drive a general decrease in energy prices. 100x improvements from scale would thus be close to what one might get from a robust reusable vehicles (a common comparison is that airplanes and spacecraft are not very different in cost of production, but the latter are thrown away after one use, or refurbished at a cost per flight that is a substantial share of manufacturing cost). Extrapolating experience curves would suggest attaining such gains with heavy exploitation of the Earth relatively quickly, faster if the space industry grows as a share of the global economy (the lack of immediate payoffs in space beyond satellites raises questions about that, but ongoing government funding provides a case for thinking the share of output spent in space would grow rather than shrink).

Incremental improvements in the efficiency of manufacturing, and especially flexible manufacturing such as 3-D printing, flexible robotics, or bioreactors (which can have organisms/DNA sequences swapped) would likewise reduce the costs of moving to space.

Where profitable space colonization was wildly infeasible in the 70s, with several to many orders of magnitude improvement in all the relevant technologies and eventual full exploitation of terrestrial resources, one would expect it to become profitable. Billionfold changes to cost-effectiveness can make many formerly impractical schemes practical.

The luminosity of the sun is 3.846E26 W,  vs 1.740E17 W for the share intercepted by the Earth, a difference of ~2 billionfold, and colonizing the solar system would allow for a longer lifetime for civilization than discussed above. Moving that much further along the relevant experience curves seems plenty to use nuclear power and other advanced technologies to reach other stars in the galaxy (for another factor of ~100 billion), and potentially other galaxies (although long travel times and the expansion of the universe mean the ability to share knowledge decreases to 0 with sufficient distance) for  a factor of billions.

Extrapolating technological progress and experience curves in almost every field across those additional ~30 orders of magnitude runs into physical limits (most often this happens at the terrestrial scale or perhaps solar system scale).

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