If you look back on history, you get the sense that scientific discoveries used to be easy.
Galileo rolled objects down slopes. Robert Hooke played with a spring to learn about elasticity; Isaac Newton poked around his own eye with a darning needle to understand color perception. It took creativity and knowledge to ask the right questions, but the experiments themselves could be almost trivial.
Today, it takes ever more money, more effort, and more people to find out new things. But until recently, no one actually tried to measure the increasing difficulty of discovery. It certainly seems to be getting harder, but how much harder? How fast does it change?
This type of research, studying the science of science, is in fact a field of science itself, and is known as scientometrics. From its early days of charting the number of yearly articles published in physics, scientometrics has broadened to yield all sorts of insights about how we generate knowledge. A study of the age at which scientists receive grants from the National Institutes of Health found that over the past decades, older scientists have become far more likely to receive grants than younger ones, suggesting that perhaps younger scientists are being given fewer chances to be innovative. In another study, researchers at Northwestern University found that high-impact research results are more likely to come from collaborative teams — often spanning multiple universities — rather than from a single scientist. In other words, the days of the lone hero scientist are vanishing, and you can measure it.
A scientometric approach to the question of quantifying how hard discovery gets over time found that difficulty increased along a curve of exponential decay.
What this means is that the ease of discovery doesn’t drop by the same amount every year — it declines by the same fraction each year.
For example, the discovered asteroids get 2.5 percent smaller each year. So while the ease of discovery drops off quickly, it can continue to “decay” a long time, becoming slightly harder without ever quite becoming impossible. Think about Zeno’s Paradox, where the runner keeps on getting halfway closer to the finish line of the race, and thus never quite makes it to the end.
The fact that discovery can become extremely hard does not mean that it stops, of course. But this study does tell us what kind of resources we may need to continue discovering things. To counter an exponential decay and maintain discovery at the current pace, you need to meet it with an effort that obeys an exponential increase.
You can’t just expend a bit more effort, sometimes you have to expend orders of magnitude more.
Adopted from The Boston Globe; Ideas, by Samuel Arbesman.