3.6 Weighted Sum of Pages

This is probably the second-best graph. Even the graph with ninety dots on it shows some trends.

A plot showing the importance of all topics over time on a single graph, as measured by weighted sum of pages. The underlying data is in Table B.5. It is mostly a mess of dots that doesn't show very much, but what information can be gleaned by looking is described in the text below.

Figure 3.11: All ninety topics—weighted sum of pages.

Interestingly, the growing length of articles takes away the bump that is visible in figure 3.1; now it seems like all topics get ten to fifteen weighted pages (at least) every year. The length increase is itself quite remarkable. Here’s the average article length over years.

The average number of pages in articles over time. It starts around 12, then rises unevenly to a peak of around 19 around 1910. It then falls almost linearly to around 9 in the mid-1960s. The it bounces, rising linearly at almost the same rate it fell. The new peak is around 20 at the end of the data in 2013, but it doesn't look like a peak; it looks like that's just where the data ends, and the trend would probably continue into the future.

Figure 3.12: Average article length.

And that same effect means that some of the big twenty-first-century topics are now outpacing ordinary language philosophy. I’ll come back to this article length increase in a bit, but first let’s see what this graph looks like with every topic having its own facet.

The same data as above, but with each topic shown as a separate facet.

Figure 3.13: The ninety topics—weighted sum of pages (faceted).

The acceleration in thelast fifteen topics is much more pronounced. And ordinary language doesn’t look like it has a rise and fall any more—it has a rise that it holds on to. Norms looks like it is about to eat everything, and maybe it is. This is even more vivid in the animated version of the graph.

It’s worth pausing for a minute about what’s driving this. As I showed above, page lengths increased substantially over the last few decades of the data set. That graph is fairly noisy at first, then a sharp dip takes us to a minimum in the early 1960s, and from then it is a steep rise. (One that is not, in my experience, abating anytime soon.) But an average covers up a lot of things. For instance, Noûs used to publish abstracts of APA presentations as research papers. These were often one page, and could really pull down averages. Here is a slightly more instructive way of looking at the data. The following graph shows various deciles of lengths over time. So the bottom line is the length such that 10 percent of articles are shorter than (or equal to) its length, the top line is the length such that 90 percent of articles are short than (or equal to) its lengths, and so on for the in between lines.

Another graph of article lengths over time. This shows the 10th, 30th, 50th, 70th and 90th percentile of page lengths in each year. All five graphs have the same shape, though they are much noisier than the previous graph. They all rise to an initial peak around 1910, then fall through the 1960s, then increase fairly rapidly through the end of the data period in 2013.

Figure 3.14: Distribution of article lengths.

Some of this could be explained by having a bunch of one-page notes, but not all of it. For much of the 1950s and 1960s, fewer than 10 percent of papers were over twenty pages. Now twenty pages is the median article length, in a universe of journals that includes Analysis. For that to be explained by having a bunch of very short articles, the olive line (at 30 percent) would have to be hugging the bottom of the graph, and clearly it isn’t.

Articles are getting much much longer.