Mesofacts: slowly changing facts

I have an article in this Sunday's Ideas section of the Boston Globe entitled Hard to find: Why it's increasingly difficult to make discoveries - and other insights from the science of science. It discusses a scientific paper of mine published recently in Scientometrics, which is the journal of the "science of science". The journal article entitled Quantifying the Ease of Scientific Discovery (also freely available on the arXiv), discusses how to think mathematically about how scientific discovery becomes more difficult over time.

Examining three different scientific areas of discovery - the number of mammalian species known, the number of minor planets (asteroids) known, and the number of chemical elements known - I found that their "ease of discovery", as quantified by using size, all have the same mathematical shape. For example, I calculated the average diameter of asteroids discovered each year, and this decreases according to a clear function (for those interested, it's an exponential decay).

Of course, the increased difficulty of discovery within a single discipline should not lead to a state of despondency, where we assume everything than can be discovered already has been. Instead this type of quantitative research can help us to understand the social and technological processes that underlie scientific discovery.

Both the Globe piece and the scientific article were a lot of fun to write, since I got to discuss scientometrics and patterns in science over hundreds of years of discovery. In addition, all the data sources I used are freely available, so you should feel free to play with the data sources.

Here's a figure from the paper, if you're interested (A shows the average size of discovered minor planets, B shows the average size of discovered mammal species, and C shows the average inverse size of discovered chemical elements):