## 3.1 Main Summary Graph

The first graph shows the expected number of articles in each topic each year. I’ll call the expected value the weighted sum, since the probabilities from the model are better thought of as weights. So for each topic-year pair, it looks at all the articles published that year, and sums the probability they are in that topic. The result is a point on this graph.

Now there is too much data there to take all of it in. And if your eyes can correlate the colors on key with colors on the graph, they are keener than mine. But still there are some things we can take away from the graph. And I want to stress that these things are really very resilient. I ran a lot of these models to find one that best reflects the trends in the journals, and all of the following features were stably true across the model runs.

First, the colors change over the course of the graph. The topics that are big deals in the early years are very different to the topics that are big deals in the later years.

Second, there are a lot more articles being published in recent years than in earlier years. This is in part because the universe of journals has grown, and in part because I focused on journals that are alive today. But it’s significant and a point that I’ll have cause to return to several times in this chapter.

Third, there is nothing like the dominance of ordinary language philosophy in the mid-century. If you cut down the number of topics to under thirty, then something like idealism becomes a single topic that is similarly large in the early years. (It basically collapses idealism and life and value from the main model of this book, and adds a bunch of pragmatism too.) And if you keep the number of topics under about fifty (or even sixty), then sometimes the model will put all of epistemology into a single topic, and its size in the 2000s is as big as ordinary language philosophy in the 1950s. But in this model—and in the vast majority of other models I looked at—ordinary language philosophy after the war is bigger than any other model at any time.

But the fourth result is the one that surprised me most of all, and one that I don’t really have a simple story about. There is a white triangle toward the bottom right corner of the graph, starting around 1960, peaking around 1980, and ending around 2000. This is again a very resilient result—almost all the model runs I did had something similar. Around 1980, the model sees all the topics being at least somewhat represented in the journals. But the farther from 1980 one gets, in either direction, the less likely it is to think that all the topics are there.

I’m going to come back to this much later in the book, because I think it’s fascinating. But apart from making this rise in the minimal values visible, this graph is otherwise something of a mess. Things are a bit clearer if we view the individual topics separately.

This is a bit clearer on the relative scale of the different topics over time. There are four notable shapes of graph here.

One is the graph with a high peak, but a rapid rise and fall either side of it. Some of these are predictable, like verification, or meaning and use. Others are more surprising, like promises and imperatives. I expected ordinary language to be like this, but it isn’t. The stylistic changes that were brought about didn’t totally stick - the graph does go down a little bit - but they don’t totally go away either.

A second is the graph with a sudden rise to a new equilibria. There are a few such topics in the model used in this book, such as explanations, population ethics and personal identity. Other models had a much larger number of these graphs, but once there are as many as ninety topics they start to get less common.

A third is the graph that just rises and rises as the years go along. That’s almost all of the last fifteen graphs here.

A fourth, which is almost nonexistent, is the graph that is such a mess that you need to fit a curve to it to see any trends. I’ll do some graphs with trendlines in a bit, but for now I want to note how little there is for them. Although the model wasn’t told about the age of different articles, and was just trying to classify them as best it could, it mostly came up with totals for each topic per year that were approximately continuous. That’s interesting, and tells us something about the way in which debates in journals really do seem to follow trends.

It is also somewhat useful to see the graph animated. This shows all the lines one at a time.