[This post was up a few weeks ago before getting taken down for complicated reasons. They have been sorted out and I'm trying again.]

Is scientific progress slowing down? I recently got a chance to attend a conference on this topic, centered around a paper by Bloom, Jones, Reenen & Webb (2018).

BJRW identify areas where technological progress is easy to measure – for example, the number of transistors on a chip. They measure the rate of progress over the past century or so, and the number of researchers in the field over the same period. For example, here's the transistor data:

This is the standard presentation of Moore's Law – the number of transistors you can fit on a chip doubles about every two years (eg grows by 35% per year). This is usually presented as an amazing example of modern science getting things right, and no wonder – it means you can go from a few thousand transistors per chip in 1971 to many million today, with the corresponding increase in computing power.

But BJRW have a pessimistic take. There are eighteen times more people involved in transistor-related research today than in 1971. So if in 1971 it took 1000 scientists to increase transistor density 35% per year, today it takes 18,000 scientists to do the same task. So apparently the average transistor scientist is eighteen times less productive today than fifty years ago. That should be surprising and scary.

But isn't it unfair to compare percent increase in transistors with absolute increase in transistor scientists? That is, a graph comparing absolute number of transistors per chip vs. absolute number of transistor scientists would show two similar exponential trends. Or a graph comparing percent change in transistors per year vs. percent change in number of transistor scientists per year would show two similar linear trends. Either way, there would be no problem and productivity would appear constant since 1971. Isn't that a better way to do things?

A lot of people asked paper author Michael Webb this at the conference, and his answer was no. He thinks that intuitively, each "discovery" should decrease transistor size by a certain amount. For example, if you discover a new material that allows transistors to be 5% smaller along one dimension, then you can fit 5% more transistors on your chip whether there were a hundred there before or a million. Since the relevant factor is discoveries per researcher, and each discovery is represented as a percent change in transistor size, it makes sense to compare percent change in transistor size with absolute number of researchers.

Anyway, most other measurable fields show the same pattern of constant progress in the face of exponentially increasing number of researchers. Here's BJRW's data on crop yield:

The solid and dashed lines are two different measures of crop-related research. Even though the crop-related research increases by a factor of 6-24x (depending on how it's measured), crop yields grow at a relatively constant 1% rate for soybeans, and apparently declining 3%ish percent rate for corn.

BJRW go on to prove the same is true for whatever other scientific fields they care to measure. Measuring scientific progress is inherently difficult, but their finding of constant or log-constant progress in most areas accords with Nintil's overview of the same topic, which gives us graphs like

…and dozens more like it. And even when we use data that are easy to measure and hard to fake, like number of chemical elements discovered, we get the same linearity: