Here is my latest news story for Nature.
Mathematical laws make industrial growth and productivity predictable
Predicting the future of technology has often seemed a fool’s game: no one forgets IBM founder Thomas J. Watson’s (possibly apocryphal) prediction that the world would need five computers. But a team of researchers in the USA now says that technological progress really is predictable, and backs up the claim with evidence from 62 different technologies.
It’s not a new claim. But a group of researchers at the Santa Fe Institute in New Mexico and the Massachusetts Institute of Technology in Cambridge, Massachusetts have put to the test several hypothetical mathematical laws describing how the costs of technologies evolve. They find that one proposed as early as 1936 supplies the best fit to the data .
That proposal was made by aeronautical engineer Theodore Wright, who pointed out that the cost of airplanes decreased as the total number of planes manufactured (the cumulative production) increased . Specifically, this cost was proportional to the inverse of the cumulative production raised to some power. This has since been put forward as a more general law governing costs of technological products, and is often explained on the basis that, the more we make, the better and more efficient we get at making.
But it’s not the only contender. Much more famous than Wright’s law is the relationship proposed in 1965 by Gordon Moore, cofounder of the microelectronics company Intel. He pointed out that the computer power was increasing exponentially over time  – which means, in effect, that the cost per transistor was falling exponentially.
So who is right: Wright or Moore? Perhaps neither, for several other hypothetical relationships between scale and cost of production have been suggested – that, for example, costs fall purely due to economies of scale. All of these ‘laws’ predict that costs tend to fall over time, but at slightly different rates.
“The predictive ability of these hypotheses hadn't been tested against a large dataset before,” says Trancik. She and her colleagues tested six of them by collecting data on 62 technologies, ranging from chemicals production to energy technologies (such as photovoltaic cells) and information technologies, spanning periods of between 10 and 39 years. “Assembling a large enough data set was a big challenge”, says Trancik.
The researchers evaluated the performance of each ‘law’ with hindcasts: using earlier data to make predictions about later costs, and then seeing how these compared with the actual figures. They used statistical methods to figure out which law produced the smallest predictive errors.
And the winner was… Well, in fact there wasn’t a huge difference between any of the laws. The best was Wright’s law, but Moore’s law was close behind, at least for a relatively modest time horizon of a few decades. In fact, their predictions were so similar that the researchers suspected the two laws might be related.
This seems quite likely. In 1979 political scientist Devendra Sahal pointed out that if cumulative production of an item grows exponentially, then Wright’s law and Moore’s law are equivalent . The new data confirm that production does show such growth for a wide range of products. “You wouldn’t necessarily expect that”, says Trancik.
That Moore’s law applies at all to so many different industries is a surprise, since computing has often been regarded as a special case. “It’s a much more general thing”, says coauthor Doyne Farmer, currently at the University of Oxford.
Economist William Nordhaus of Yale University warns that these laws will only work for technologies that survive – which is not itself easy to predict. “History is written only about the victors”, he says. “Those technologies that didn’t make it in the market don't make it into the data set. This is one reason why it is so difficult to forecast which of many nascent energy technologies will survive.”
The future of some technologies will depend crucially on governmental policies, not just conventional market forces. For example, in climate-change technologies, in which Nordhaus specializes, he says that the evolution will depend on the future pricing policies of carbon emissions. “Some technologies, such as carbon capture and storage, won’t even get off the ground with a zero carbon price”, he says.
Estimating the potential costs of climate-change mitigation technologies is one of the prime applications the researchers envisage for their findings. A key question is whether costs will fall just as a matter of time, as Moore’s law implies, or whether stimulating growth by public policies (such as subsidies or taxes) that boost production might accelerate the fall, as Wright’s law implies.
The results seem to imply the latter, which is good news. “We have more control over these things than we might think”, says Farmer.
1. Nagy, B., Farmer, J. D., Bui, Q. M. & Trancik, J. E. PLoS ONE 8, e52669 (2013). [doi:10.1371/journal.pone.0052669]
2. Wright, T. P. J. Aeronaut. Sci. 10, 302-328 (1936).
3. Moore, G. E. Electr. Mag. 38 (1965).
4. Sahal, D. AIIE Trans. 11, 23-29 (1979).