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Ubiquity: The Science of History . . . or Why the World Is Simpler Than We Think

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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.

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.

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.

Since other reviewers have described the book in some detail, I will not attempt to duplicate their efforts. (As to the reviewer who thinks that power laws with integral exponents are somehow more convincing than power laws with non-integral exponents, I can only suggest that Nature may not share his prejudices.) Buchanan writes with incredible clarity. I'm reading the book for the second time and am really appreciating the economy of prose. Buchanan is not selling snake oil, he judiciously weighs the evidence and points you to the literature if you want more. On the dust jacket Per Bak, a founding father and wonderfully clear writer on self-organizing criticality himself, says that he wishes that he had written the book. I know exactly what he means. I eagerly look forward to Buchanan's next book on the science of networks and highly recommend this one.

This is one of those books that will make you stop and think about almost everything you believe you know. Per Bak's 'How Nature Works', whose work is frequently cited in Ubiquity is the original on the topic. While it too is a good book and obviously came from directly from one of main researchers in the field, this book is much more accessible.

The power law and the idea that this basic tenet applies to everything from the distribution of the size of cites to the distribution of the intensity of earthquakes, is amazing almost to the point of being 'spooky'. But the data is there and difficult to dispute.

Buchanan has written a great book here; even Per Bak said "this is the book I wish I had written'.(see the back cover of Ubiquity)

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 <typical> 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 <take home> 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.

Firstly, it is important that I qualify my comments by stating that I read this book as a layperson. The book is very well written for those who don't have advanced degrees in theoretical physics, math, or adjoining fields. In, "Ubiquity", Mark Buchanan sets out to demonstrate that there is a, "natural structure of instability woven into the fabric of our world". The book then covers a wide range of human events, events where man and nature share influence, and where nature, in theory, acts alone. He presents the concept that that all of the mentioned tend to organize into critical states, and that at some unpredictable point they will pass their point of stability and become unstable. He uses events that range from the incident that touched off World War I, to forest fires, and traffic congestion to demonstrate the premise.

The fundamental problem that I had while reading the thesis was accepting that there are events that we have never been able to predict, and the statement that there will never be a method for prediction in the future. I have read enough science texts to know that, "never", is not only a very strong word, it is an absolute, and a very tenuous position to take. Scientists are constantly revising what is believed to be true, and everyone knows the traps that lie when stating absolutes. There are several categories of events that are measured and graphed in an effort to demonstrate commonality among seemingly diverse events. In certain given situations there does appear to be anecdotal evidence regarding, for example, how often a given war will occur based upon the previous conflict and its size.

The mathematical results that are graphed do in fact look similar, but I never have understood that proof of a theory could be an, "almost". Graphs and numbers may be similar, but how far apart can the numbers be to disqualify a theory stated in absolute terms, i.e. never?

Science and technology are forever finding ways to surmount barriers that were once thought to be absolutes, or hurtles that never could be overcome. And while predicting an earthquake certainly appears to be a fantastically difficult task, I don't understand how never can be applied to the problem. One does not have to go very far back in history to find statements by recognized experts that absolutely dismissed the idea of the mass utility of a computer. The idea that hundreds of millions of choices would be made by a machine that is portable and sits on your lap did not even qualify for science fiction.

The book is fascinating reading, and perhaps I have missed the mark. I still would suggest that anyone who is inquisitive read the book, as it is well worth the time invested.

It is a matter of degree. If I, with my degrees in Chinese Lit, were to hurl a hundred frozen potatoes at a wall, I would probably end up in a stait-jacket. If someone with degrees in Physics does that, it's research.

Mark Buchanan, however, does away with degrees. As the title of this book implies, all or nothing: Ubiquity is a sole authority. Only my knife cuts potatoes, no knife but mine can cut potatoes. While I agree that the existence of power laws is fascinating, I would not perhaps extend them as far as Buchanan does; I would be more interested in probing why distribution is so regular, rather than insisting that all phenomena must be explained by this, and only this, rule. A power law may signify that a country can be bled, or a forest burned, so far before you run out of fuel. This is more interesting than assuming that because the numbers resemble each other, the conditions necessarily illuminate each other. (As to the power law, please note the comments in Dennis Littrell's review of this book).

I got to the point where I dreaded having to read about yet another game that, amazingly enough, proves the power law (do any games disprove it?). Games seem to go to Buchanan's head, where they practically replace reality, which, needless to say, is far more complex. There are games and there are games, though. On page 126 (paperback version), Newton is praised for simplifying for ease of reasoning; then on page 142, economists are excoriated for simplifying for ease of reasoning. I never thought I would see the day that I stood up for economics, but isn't this a double standard? By the same token, after he so thoroughly debunked the efficient market hypothesis, I was surprised to read on page 188 that after war releases stress, 'each nation is brought back into rough balance with its true economic strength.' But as he says on the next page, 'None of this is meant to be fully convincing.' It's not.

Buchanan at times seems to forget that there is more to human history than wars and revolution, and that great people can change the course of history; where would we be today if George Washington Carver had not saved southern agriculture? Buchanan's total belief in the ubiquity of his games leads him to say something as ridiculous as "the mark of the great scientist lies not so much in having profound ideas that revolutionize science, but in taking ideas ... and making that potential real"(p183). ...limits our reviews to 1,000 words, so I will leave it this sentence for you to explode .

Even if we discount the role anybody but scientists and soldiers play in history, there should be some difference between incipient wars. Consider World War II, in which Germany and Japan geared for widespread conquest, planning meticulously years in advance. The German army would not have rolled through the center of Europe so irresistibly if the Hitler Youth had not trained the young so well; Japanese school children were primed to attack China before the Marco Polo Bridge Incident. Then compare this to the American Revolution, a beef far across the oceans between some (not all) ill-prepared colonists and a Great Britain preoccupied with India. Is it any surprise that WWII spread far and wide, while the American Revolution was fought locally?

I think the author has intriguing ideas, but he has overextended them. Nonetheless, Buchanan's doctrines have a familiar ring. Buddhism long has taught that any event is the result of an infinite number of causes, and the cause of an infinite number of results. The ideas in this book are well worth pondering, but with a grain of salt. One grain. Now, if you have a whole pile of grains of salt, one more might avalanche....

Mark Buchanan writes well and I found this easy to read in spite of the sometimes complex subject matter. I have some background in science and have always been curious about current events. If you are as interested as me about science you will enjoy this book very much. I found the discussion of statistical(Poisson)distributions most fascinating and it lead me to do some further study on the subject. I recommend this book and I don't understand how one reviewer found it boring. It is an exceptional look at science and history and even economics from a prospective you should find interesting.

This is not one of my favourite reads. In some ways I found it a labour as it went over the same material again and again, albeit in very diverse areas. I understand the power law that Mr Buchanan describes and its implications, but it seems to be such an after-the-event view that can have little material impact on modern endeavours. It proves futility. It is as if what is ubiquitous is our necessary failure to achieve. But I'm sure we do do better than that.

On the other hand there was one revelation in this book that truly fascinated me. I have always been interested in the dinosaurs and their extinction. Books like 'The Dinosaur Heresies' by Bakker and 'Hot-Blooded Dinosaurs' by Desmond developed a genuine need-to-know-more. But the matter of extinction is so challenging. There are strong suggestions that an impact of an asteroid caused such havoc that the dinosaurs became extinct - all of them, the small ones, the large ones, the carnivores, the herbivores, the pterosaurs (flying dinosaurs) and the plesiosaurs (sea-going dinosaurs). And yet, for all that, other animals - notably mammals - did survive. What allowed them through the window of extinction? In my reading I have encountered this debate many times and most writers do have a preference for one theory or another. But even those who do support the impact theory do not have evidence of an impact associated with each of the great periods of extinction that have occured through time. So, the thesis of 'Ubiquity' does provide an alternative - that sometimes the effect of even a small change will cause monumental alterations to the world according to the ubiquitous power law. What was the small change that extinguished the dinosaur SPECIES but allowed others to survive, and in the absence of the dinosurs, thrive? It seems to me that knowing what this small change was would fundamentally advance our knowledge of what the dinosaurs really were.

The most powerful voice in the campaign for popularising the impact theory of dinosaur extinction is Alvarez who discovered the site of the impact that occured 65 million years ago just about the time the last dinosaur walked on the Earth. What Buchanan points out, that so few other writers do is this ....

'...the bulk of the long 1980 paper by Alvarez and his colleagues was 'confined to the geological and physical evidence for an impact, and the physical results of the impact. The discussion of the biological results of the impact occupies only half a page. (quoted from M. Benton) The reason is simple: no one really has much of a clue about what an impact would really do to life all over the planet.'

This is perhaps the strongest argument I have read against the impact causing the extinction of the dinsoaurs. Not that it couldn't have, but that the opinionated science community is so set on Alvarez' findings that they have taken the most tenuous suggestions from Alvarez' paper to support their theories.