Laws upon which forecasts can be based

Moore's law (the number of transistors per circuit doubles every two years) is well known but why it is true remains something of a mystery. In the absence of a better explanation, there are those that propose that it is true because we expect it to be true and it becomes a self-fulfilling reality.

I am intrigued by unknown or not commonly recognized laws that govern outcomes. Moore’s law is not just for computers by Philip Ball reports on the research results from a team from MIT and the Santa Fe Institute.

In a study published in PLoS ONE, they compared several mathematical laws that purport to describe how the costs of technologies evolve, and found that the most accurate was one proposed as early as 1936.

That proposal was made by aeronautical engineer Theodore Wright, who pointed out that the cost of aeroplanes fell as the number of planes manufactured rose. Specifically, he said that the cost was proportional to the inverse of the number of planes manufactured raised to some power. This theory has since been put forward as a more general law that governs the 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 much more famous than Wright’s law is a relationship proposed in 1965 by Gordon Moore, co-founder of the microelectronics company Intel. He observed that computer power per dollar was increasing exponentially over time — which means, in effect, that the cost per transistor was falling exponentially.

Several other relationships between scale and cost of production have been suggested: for example, that costs fall purely because of economies of scale. All these ‘laws’ predict that costs will fall over time, but each suggests a slightly different rate.

“These hypotheses haven’t really been tested against data before,” says MIT's Jessika Trancik. She and her collaborators collected data for 62 technologies, ranging from chemicals production to energy devices (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 six such ‘laws’ using hindcasts — use of earlier data to predict later costs — and then looked at how these compared with the actual figures.

In fact, the laws didn't differ much at all. The most accurate was Wright’s law, but Moore’s law was close behind, at least for a relatively modest time horizon of a few decades. The predictions were so similar for these two laws, in fact, that the researchers suspected they might be related.