The real ubiquity is complexity itself
Let's begin with a counter-thesis, namely that the "ubiquity" found in simplistic computer models ("games") which are then related to real world systems such as earthquakes, sandpiles, the stock market, political and social history, etc., may be an artificiality and a whole lot less significant than Buchanan supposes.
The fact that the games are, as Buchanan reports, tinkered with so that they yield a "power law" similar to that found in natural phenomena reveals the artificiality. What this "power law" really amounts to is something like "the frequency of a big change is at least two times and maybe four times (or more) less than the frequency of a small change." The "power" in the "power law" is nothing more than an exponent, as in something-squared, or something-cubed, etc. It's simply a power of a number as a measure of difference. Now, if the differences fell exactly on two times or four times, etc., then perhaps there would be some great significance. But when something is 2.14 times less likely (as it is when the avalanche is doubled in the sandpile game [p. 45, p. 57]) or 1.19 times less likely (as it is for magnets pointing in the same direction in the Onsager and Kaufman experiment [p. 129]) then calling the differences an example of a "power law" at work seems a bit forced and, at any rate, trivial.
Incidentally, the word "history" as used in this book refers to a past that is different than now in a way that cannot be exhaustively unraveled. This idea comes from complexity theory and owes something to information theory. Buchanan attempts to apply it to a wide variety of phenomenon with varying degrees of success.
But what is really being asserted here is the mundane fact that a big change is less likely than a small change in a complex system near the edge of chaos. Such systems: forests, the geological earth, the stock market, the international political arena, etc., are seen as having "self-organized criticality," and it is this sort of complexity that they have in common, and this is what is significant, not some artificially derived "power law."
Another key idea in the book is that the immediate "cause" of a big event in such systems is no different (or so it seems to our discernment) than the cause of a small event. This is an idea from complexity theory, and an exciting one. What it means is that such systems are in principle impossible to predict. In the sandpile game, for example, we don't know when we drop the latest grain whether it will trigger a big avalanche or a small one or none at all. This is similar to the "butterfly effect" in complexity theory in which it is thought possible that the flap of a butterfly's wings in the Sahara Desert, for example, may affect the amount of rain that falls on Cuba.
Where I think Buchanan goes astray here is in making unwarranted connections between systems by using superficial and forced similarities. For example, one of the ideas from the study of earthquakes is that there is no typical size for an earthquake. In his desire to generalize Buchanan tries to find the same sort of phenomena in the interesting study Sidney Redner did on the fate of scientific research papers. Buchanan writes on page 200 that there was "no typical number of citations for a paper, and, by extension, no typical magnitude for the reshaping in the network of ideas that any paper ultimately entails." However on the previous page Buchanan has already reported that there was indeed "a typical size." That size was zero. Of the 783,339 papers published, 368,110 had no citations at all.
Buchanan also asserts on page 169 "...there is no size for a city in the United States or elsewhere, and no reason to see special historical or geographical situations behind the emergence of the very biggest." I agree there is no typical size for a city, but to ignore the effect of rivers, lakes and protected harbors as well as other factors such as nearby mineral and other resources in the growth of cities is silly. Chicago, for example, is a big city not by happenstance but because of its location on a great lake and because of its proximity to the middle of a great, growing country. Similar arguments can be made about other great cities in the US and around the world. The historical and geographical circumstances are special and they really are crucial.
Buchanan further extends the thesis to include social and political revolutions. This makes for lively reading and there is no doubt that there are similarities between the critical state of a nation before a revolution and that of a sandpile before an avalanche or a forest before a fire, but the stresses are of an entirely different sort. He sees the readjustments of governments as a way to prevent the maladjustments that lead to revolutions as similar to the small forest fires that forest managers start to prevent a large forest fire as similar. (p. 209) Whether these similarities are more than conceptional analogies is another matter. Buchanan himself notes, still on page 209, "None of this is meant to be fully convincing." And on page 230, when seeing similarities between the "behaviors of the mass of humanity" and the "wild fluctuations of the magnet poised between its...phases," Buchanan adds, "It goes without saying that nothing I have mentioned in the past few chapters proves this. The message is simply that this is a real possibility." I agree, and I think these statements really could apply to the entire book.
In conclusion, I disagree with the notion that the world is simpler than we think. I believe the opposite is manifestly true, and I found nothing in Buchanan's very interesting arguments to prove otherwise.
--Dennis Littrell, author of “The World Is Not as We Think It Is”