Hard to Find: Discovery and the Science of Science

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.

2 Responses to “Hard to Find: Discovery and the Science of Science”

  1. Erik Nilsson July 20, 2010 at 4:56 pm Permalink

    This strikes me as a really silly idea. Science isn’t accomplished by asking the same question over and over again, but rather by asking more, new, and different questions.

    It’s getting harder and harder to find new mammal species. Really? Perhaps it’s because, thinking out loud here, there is a fixed number of mammal species, and they’ve nearly all been found? If you’re going to ask a silly question like that, at least pick something like lepidoptera or even all insects. Even then, it’s a silly question. This like saying we’re winning the battle against AIDS because the incidence of new cases is declining. That happens when a disease gets close to saturation in a population, so I a decline in new cases could be good or bad, depending on *why* the cases are declining. Same with the discovery rates you report. As I said, they’re the wrong questions anyway, but they aren’t even the right answers to the wrong questions, because it matters why you aren’t finding new mammal species, elements, or planetoids.

  2. Samuel Arbesman July 20, 2010 at 10:46 pm Permalink

    @Erik Thanks for your comment. As you note, science as a whole is much more than simply asking the same question. However, parts of science certainly do involve searching for more of the same category of discovery. And it happens to be that these very specific fields lend themselves to easily quantifying how discoveries become more difficult.

    Which is not to say that is the only way to do this. There are other ways, but in general, determining what consists of a discovery, and what it’s properties are, are rather hard questions. So I worked with the simplest version of the problem that could give some insight. Ultimately, measuring all of science and how it is done would be gratifying, but very hard, because science is exceedingly complex, involves putting ideas together to get new insights, and much more (as you noted).

    Regarding the number of species getting fewer: that is certainly correct. Is the rate at which they are being discovered declining though? That is not clear. And it seems to actually be increasing for asteroids, for example. It’s true that through guessing at the underlying distribution of the sizes of all mammals (or asteroids or elements), you could gain some insight into the reasons behind the exponential decay, but I ignored that as a first pass at trying to measure the ease of discovery only using the properties of the discoveries. Taking a distribution into account, as well as all the technological and social processes (which I mention in my paper), would be a very good next step.