Most Helpful Customer Reviews
29 of 31 people found the following review helpful:
5.0 out of 5 stars
The Physics of History, October 24, 2001
This review is from: Ubiquity: The Science of History . . . or Why the World Is Simpler Than We Think (Hardcover)
CERTAIN complex systems, under certain circumstances, have been discovered to behave in mathematically simple, similar ways. In 'critical states', there is no reason to look for specific causes of great events. The smallest force can have gigantic effects and sudden upheavals can strike seemingly out of nowhere. The approximate frequency of such upheavals can be predicted, but not when they will happen or what size they will be. Mark Buchanan's book reviews the current work on the subject to highlight a deep similarity between the upheavals that affect our lives in both physical and human systems. The book warmly communicates this novel way of thinking without compromising scientific integrity. This is made possible because the author is not only a science writer but also a physicist. Buchanan starts by discussing the principle of ubiquity which is that one should focus on the simplest mathematical game belonging to a same universal class. Details are not important in deciding the outcome because things in a critical state have no inherent typical scale in either time or space. The important issue which this book highlights is that in a critical state, something known as a `power law' comes into play to reveal a hidden order and simplicity behind complexity. A power law means that there is no such thing as a normal or typical event, and that there is no qualitative difference between the larger and smaller fluctuations. Buchanan illustrates this with the following example. If one takes a handful of rice (or sand) and drops the grains one by one on to a table top, a pile of rice is built soon. The pile will not grow taller for ever, though. Eventually the addition of one more grain will cause an avalanche. Such a grain is only special because it happened to fall in the right place at the right time. The addition of a single grain may have no effect, precipitate a small avalanche, or collapse the whole structure. One can predict the likely frequency of the avalanches, but not when they will happen or what size each will be. It may come as no surprise that big avalanches occur less frequently than small ones. What is surprising is that there is a power law: each time the size of an avalanche of rice grains is doubled, it becomes twice as rare. The book reveals that power laws have been discovered for events ranging from forest fires and earthquakes to mass extinctions and stock market crashes. This is the power law for forest fires: when the area covered by a fire is doubled, it becomes about 2.48 times as rare. If the size of an earthquake is doubled, these quakes become four times less frequent. The bigger the quake, the rarer it is. The distribution is scale invariant, that is, what triggers small and large quakes is precisely the same. A power law for the distribution of extinction sizes (that fits the fossil record well) happens to be identical to that for earthquakes: every time the size of an extinction (as measured by the number of families of species that become extinct) is doubled, it becomes four times as rare. Interestingly for economists, a power law has been discovered in the stock market. Price fluctuations in the Standard & Poor 500 stock index were found to become about sixteen times less likely each time the size is doubled. Not only that, but other human-influenced events come under the same 'natural' laws. Wars seem to strike with the same statistical pattern as do earthquakes or avalanches in the rice-pile game. What is more, the forest-fire game seems to capture the crucial elements of the way that conflicts spread. A war may begin in a manner similar to the ignition of a forest. Statistics over five centuries have uncovered a power law for wars. Every time the number of deaths is doubled, wars of that size become 2.62 times less common. Such a power law implies that when a war starts out no one knows how big it will become. There seem to be no special conditions to trigger a great conflict. Likewise revolutions are moments that got lucky... This view of history will make no one feel any safer or happier. After all, wars and revolutions could strike out of nowhere. But it is comforting that the tumultuous course of mankind need not be the outcome of human madness, but of simple mathematics. At the end of the book, one feels excitement about ubiquity. It seems that a profound breakthrough in our understanding of history is coming up. I experienced it. Join me. Read the book.
Help other customers find the most helpful reviews
Was this review helpful to you? Yes
No
5 of 5 people found the following review helpful:
5.0 out of 5 stars
Certainly plausible and explains a lot, August 19, 2002
This review is from: Ubiquity: The Science of History . . . or Why the World Is Simpler Than We Think (Hardcover)
Buchanan's book Ubiquity is a fascinating volume on self organizing criticality. It bears a striking resemblance to Per Bak's book How Nature Works, and Bak's research is cited a number of times throughout the text. As with the Bak work, Buchanan's covers a wide variety of subjects from wars to stock market fluctuations. Of particular interest to me was the discussion of evolution and the episodic character of mass extinctions, since I've read a number of books on the subject of the K-T boundary extinction. Like Bak, Buchanan points out that much that appears to have historical significance and specific causation, while it makes for good story telling, has little predictive value about it. He uses Bak's sandpile experiments to illustrate the futility of such efforts by creating a "Sandman's view" of catastrophe (pp. 179-180). He imagines a catastrophic sand slide from the point of view of a tiny survivor to whom events seem to have been "due" to negligence on the part of the individuals responsible for a steep area. From the point of view of the sandpile, though, the information required for such control would have to be staggeringly large and nearly perfect in order to have predicted the slide and its effects. Had some minute change to the pile been possible at the putative disaster site, a similar slide could have occurred elsewhere. Then the caretakers of the sandpile would have been blamed for causing a disaster rather than preventing one. One can see in this parable why politicians in the real world tend to seek their own ultimate good rather than that of their constituents or of the environment itself. The vagaries of prediction caused by the intertwining of particulars and the vastness of the data involved put such individuals in impossible positions. They are either guilty of not preventing or of causing various negative outcomes if they are unfortunate or praised for positive outcomes if fortunate. As the author points out in a quote of John Galbraith, "Politics is not the art of the possible. It consists in choosing between the disastrous and the unpalatable (p. 1)." The key point of the book seems to be that many systems are organized on the critical edge between instability and stability. Life itself may owe its very existence to that fact. Because of this poised-on-the-edge characteristic, small events may cascade in such a way as to produce major changes: a new value for stocks, a massive extinction that creates new opportunities for remaining species, a redistribution of power among nations, etc. Which outcomes occur and when, however, are not subject to predictive formulae, even though they may seem ideally suited to it. If even extreme events are the results of myriads of small, seemingly unimportant events-sort of the butterfly in Japan fluttering its wings concept-then there are no means by which catastrophic events can be predicted any more than smaller ones can be. According to the author, while there seems to be a mathematical frequency with which incidents of different magnitudes occur, there is no way of divining when a specific outcome of a given magnitude will actually occur, nor are the consequences should such an event be forestalled. This has implications for events meaningful to human beings: wars, the stock market peaks and valleys, even extinction events. For Buchanan, history itself may arise by virtue of natural resolutions of unstable systems of whatever kind. After reading the author's discussion of the Gutenberg-Richter power law and the scale invariance of some systems, it occurred to me that the end of the world scenario presented by Carl Sagan in his book Cosmos-and credited to an earlier researcher-may fall into this category. In that volume, a chart had been created that plotted murder (private war) to the total destruction of mankind against a time line, finding that total annihilation should occur a few years after the year 2000. (It was expected closer to mid 21st century, but the original author had not factored in the destructive power of nuclear war. Later individuals did and produced a chart that suggested armageddon would be around 2010). While the ultimate war may well occur, if Bak and Buchanan are correct, it might not be due to either predictable or controllable factors, and it will probably not occur on any clear cut timetable like that suggested in Cosmos. An amazingly interesting book full of concepts that, however theoretical, are certainly plausible and explain a lot about our world.
Help other customers find the most helpful reviews
Was this review helpful to you? Yes
No
7 of 8 people found the following review helpful:
4.0 out of 5 stars
Pareto is ubiquitous, December 1, 2002
This review is from: Ubiquity: The Science of History . . . or Why the World Is Simpler Than We Think (Hardcover)
In the book Ubiquity by Mark Buchanan, processes as diverse as forest fire size, stacking rice grains, market fluctuation, scientific paper citations, species extinction history, epidemiology, sizes of wars and earthquake severity are said to generate occasional catastrophic behavior following similar statistical behavior. Buchanan presents these arguments in a very readable style at a level that can be grasped by the layman. I found the physical descriptions of the processes fascinating. The phenomena is, indeed, ubiquitous. Repeatedly, we find that, if X measures severity and f is the frequency histogram of occurrence, then numerous processes containing a catastrophic component adhere to a linear log-log plot with negative slope. Although unsaid in the book, probably to allow access to a wider audience, the underlying probability density function of the ubiquitous process is a Pareto random variable with probability density function f(x)=(a/b)*(b/x)^(a+1) for x>b and zero otherwise. The enormously fat tails of this distribution allow the outlier-like catastrophic events described in the book. Taking the log of both sides of the density function gives log[f(x)] = -(a+1)*log(x) + constant which is a line of negative slope on a log-log plot. If U is a uniform random variable on (0,1), then X=b*U^(-1/a) is a Pareto RV. Using this, plots similar to the time series and log-log plots in Ubiquity can be straightforwardly simulated. Googling "Pareto distribution" gives a plurality of interesting web accounts, many mathematically deeper, of this remarkable phenomena made wonderfully accessible by Buchanan.
Help other customers find the most helpful reviews
Was this review helpful to you? Yes
No
|
|
Most Recent Customer Reviews
|
