Some years ago, I was asked to review a paper for a mathematics journal. I agreed. The paper concerned geometry, in particular geometric constructions. For those of you who don't remember those, that subfield of geometry concerns the variety of things you can do with an unlabeled straightedge and compass. (The Wikipedia article is OK, probably more useful for the links it provides.) I don't know if this is even taught any more; if you learned it, you may remember finding the midpoint of a given line segment. This was a fairly important branch of math at one time, and still generates some interest from so-called mathematical cranks, people who believe they can do the impossible, or have "discovered" a simple way to do something hard.
[By the way, this is a major flaw in the Tom Friedman idea that we'll discover the next big thing in energy by providing incentives to garage projects. Someone will have to sift through all the energy crank-submitted ideas, and we'll be paying tax money to folks who are doing the equivalent of squaring the circle; in other words, impossible things.]
At any rate, this paper used then-nascent geometry software to slap circles and arcs and lines all over a plane, then calculate various angles that were produced. Then the author back-engineered this to create a "method" for constructing a, for example, 89.23° angle. He ended up with quite a few of these in which one could perform 36 steps to get this angle (or other angles close to significant ones like 60°, 45°, or 30°).
I don't know if I've made clear what was happening here, but, in essence, this author was putting large numbers of points on a plane, then using the software to take those points in sets of three and finding the angles that were formed. He then looked through the numbers that were generated and found those that were pseudo-significant.
If this had been an article for a mathematical Rube Goldberg competition, in which we go through a whole lot of steps to accomplish something useless, perhaps a light-hearted look at the world of geometric construction, it might have been good for a quick feature. But it was useless; there is no use for an 89.23° angle, and one is bound to find such things if enough points are generated (if you have 500 points, there will be more than 20,000,000 angles among these points - you'll find pretty much any measure you want).
If this article had been written in such a light-hearted way, or if it had been clearly intended for the April issue, or if it was being used to make a point about the lack of significance of results that come out of mass quantities of data (not to pick on Chris Anderson again), any one of those reasons might have made it acceptable.
But none of those was true. Instead, the article was written so as to make it clear that the author seriously believed his results were important, that he had in effect invented a new branch of mathematics, one in which cherry-picking almost-significant results somehow had the potential to revolutionize the field. Keep in mind he was showing nothing generally new; there was no theory behind any of this, nothing which said, "hey, want a 15° angle, here's how you might find one." It was mathematical crankery of the first degree.
The term "black swan" (meaning an event that is completely unpredictable, but has giant effects) has rapidly become almost ubiquitous, especially in light of the "unforeseeable" meltdown in the housing market, the financial market, the consumer market, and so on. The term comes (most recently) from Nassim Nicholas Taleb's bestseller, The Black Swan: The Impact of the Highly Improbable (2007).
Taleb, a successful Wall Street trader, uses the black swan as a metaphor to spin a theory (I'm sorry, he doesn't like theories, call it a conjecture) of, well, almost anything. Until people from the West went to Australia, they thought a black swan was impossible; their existence then became an exemplar of what some might call a paradigm shift, something that changes one's framework for reality. Taleb believes the black swan metaphor is central to our existence, that large-impact, unpredictable events have an effect that cannot be foreseen but that swamps any of the things that we believe important. 9/11 was a black swan in that we didn't see it coming, but it changed everything. As a result, our models of reality are useless, because a black swan will eventually happen.
And we're off for 300 pages of trips to Extremistan and Mediocristan, the saga of Yevgenia Nikolayevna Krasnova, severe criticism of Gauss and pretty much everyone else. If you plow through this work, you'll find out why everything you know is wrong, why every expert in almost every field is incorrect, why forecasts are useless, why economics is a waste of time. And a great deal of what Taleb writes is dead on the mark; much of this book is quite accurate in talking about the limitations of our knowledge.
So why did The Black Swan remind me so much of the story I recounted above? Because the tone of this book and that article are exactly the same. Taleb earnestly believes two things: 1) his "black swan" idea is new and revolutionary and significant; and 2) he is pretty much the smartest guy in the world for having discerned it.
This book carries an almost religious devotion to the temple of Taleb, the sense that we are fortunate that he has spent years poring over old tomes and selecting reality out of all the nonsense that has gone before, and been willing to share it with us. Oh, he didn't come up with this all on his own; he has his mentors, his Montaigne, his Popper, and, especially, his Mandlebrot. But it is Taleb who will rock the world, oh yes he will.
And what does this theory come down to? Essentially, the real world is too complex to be boiled down to the simplistic models that so often are used to describe it. We teach probability through casino games, then assume that the world fits those same rules - and it cannot. We can't take everything into account, so we try to create narratives that we can handle, but those narratives are incapable of modeling reality. Linear extrapolations are inherently unrealistic. And, then, always lurking in the background, is the BLACK SWAN - even if our model was perfect, in will fly the swan to upset everything.
It's difficult for me to know what to say about this. If you've read this blog for any length of time, you know that it is based on this very kind of thinking (and I claim no singularity in that, unlike Taleb). I've had any number of posts as to why economics is not a science, something that Taleb elevates to divine revelation (though he certainly seems to have a special irritation with the Nobel Prize). I've written about how the assumptions of future employment that will "naturally" result from spending on energy are based on nothing.
Again, I cite myself not to put me on the "special insight" platform on which Taleb puts himself, but because I know my arguments the best. There are others who offer counterintuitive ideas, who understand the limitations of conventional thinking, but most of us are not quite as irksome as Taleb about it (at least, I hope not).
I guess my overall impression of this book is that it contains some good ideas, but badly needed a strong-handed editor. The self-indulgence of Taleb's writing does nothing to enhance his points. There is, maybe, a 130-page book here, one without the self-aggrandizement and the pointless autobiographical side trips. (It is also the kind of book that fills me with despair that so many people find it significant, because the limits of knowledge should not be so revelatory; that there are people in high positions who are learning something from this is profoundly depressing.)
An editor might also have ironed out some of the things that are wrong or poorly-explained. How does Taleb's Extremistan produce Black Swans - it would seem that cause and effect are reversed here? The computer, the Internet, and the laser were certainly not unplanned or unexpected, though some of the effects of each were unforeseen - such is the way of all significant inventions. Microsoft's market share domination of Apple is not the result of luck, at least not to the extent that Taleb implies.
The most disappointing aspect of The Black Swan is the set of conclusions, because they are non-conclusions. Taleb says that, instead of using imperfect models to predict the future, which is impossible, we should move to empiricism. What he means, of course, is intuition - we should try things and see what works instead of reasoning from principles. This only applies to some fields, however, but we can't really know which fields are which. If this sounds incoherent, it is (Taleb apparently had some problems with a medical diagnosis, which is unfortunate, but it's a big leap to the idea that we should go with intuition). Empiricism always sounds great until we realize that there are many more NOTs in the universe, many more blind alleys than through streets.
I don't want to take the flyleaf as an important input, but it does state that, "He offers surprisingly simple tricks for dealing with black swans and benefiting from them." Taleb does nothing of the sort. He offers an investment strategy (invest 85% of your money in perfectly safe instruments, put the other 15% into wildly risky inifinite-upside Black Swan things) that is completely unhelpful (it might be possible if you're playing with a whole lot of OPM - Other People's Money - as he presumably was).
What Taleb is doing here is trying to overturn the basis on which people do things, wanting us to cast aside all those inaccurate models based on logic. But there's nothing here to replace that thinking, we're just supposed to wander around, experiencing life, and, I guess, hoping for the best.
It comes down to something simple but unstated: Taleb's success itself is a Black Swan, the result of chance. He was lucky to hit it big enough on investments to finance his self-styled epistemological research, then lucky enough again to find someone to publish a book with no editing and have it become a best-seller. He proves his own theory, which is useful, but it's unlikely any reader will learn anything that will help their own lives.
[By the way, this is a major flaw in the Tom Friedman idea that we'll discover the next big thing in energy by providing incentives to garage projects. Someone will have to sift through all the energy crank-submitted ideas, and we'll be paying tax money to folks who are doing the equivalent of squaring the circle; in other words, impossible things.]
At any rate, this paper used then-nascent geometry software to slap circles and arcs and lines all over a plane, then calculate various angles that were produced. Then the author back-engineered this to create a "method" for constructing a, for example, 89.23° angle. He ended up with quite a few of these in which one could perform 36 steps to get this angle (or other angles close to significant ones like 60°, 45°, or 30°).
I don't know if I've made clear what was happening here, but, in essence, this author was putting large numbers of points on a plane, then using the software to take those points in sets of three and finding the angles that were formed. He then looked through the numbers that were generated and found those that were pseudo-significant.
If this had been an article for a mathematical Rube Goldberg competition, in which we go through a whole lot of steps to accomplish something useless, perhaps a light-hearted look at the world of geometric construction, it might have been good for a quick feature. But it was useless; there is no use for an 89.23° angle, and one is bound to find such things if enough points are generated (if you have 500 points, there will be more than 20,000,000 angles among these points - you'll find pretty much any measure you want).
If this article had been written in such a light-hearted way, or if it had been clearly intended for the April issue, or if it was being used to make a point about the lack of significance of results that come out of mass quantities of data (not to pick on Chris Anderson again), any one of those reasons might have made it acceptable.
But none of those was true. Instead, the article was written so as to make it clear that the author seriously believed his results were important, that he had in effect invented a new branch of mathematics, one in which cherry-picking almost-significant results somehow had the potential to revolutionize the field. Keep in mind he was showing nothing generally new; there was no theory behind any of this, nothing which said, "hey, want a 15° angle, here's how you might find one." It was mathematical crankery of the first degree.
The term "black swan" (meaning an event that is completely unpredictable, but has giant effects) has rapidly become almost ubiquitous, especially in light of the "unforeseeable" meltdown in the housing market, the financial market, the consumer market, and so on. The term comes (most recently) from Nassim Nicholas Taleb's bestseller, The Black Swan: The Impact of the Highly Improbable (2007).
Taleb, a successful Wall Street trader, uses the black swan as a metaphor to spin a theory (I'm sorry, he doesn't like theories, call it a conjecture) of, well, almost anything. Until people from the West went to Australia, they thought a black swan was impossible; their existence then became an exemplar of what some might call a paradigm shift, something that changes one's framework for reality. Taleb believes the black swan metaphor is central to our existence, that large-impact, unpredictable events have an effect that cannot be foreseen but that swamps any of the things that we believe important. 9/11 was a black swan in that we didn't see it coming, but it changed everything. As a result, our models of reality are useless, because a black swan will eventually happen.
And we're off for 300 pages of trips to Extremistan and Mediocristan, the saga of Yevgenia Nikolayevna Krasnova, severe criticism of Gauss and pretty much everyone else. If you plow through this work, you'll find out why everything you know is wrong, why every expert in almost every field is incorrect, why forecasts are useless, why economics is a waste of time. And a great deal of what Taleb writes is dead on the mark; much of this book is quite accurate in talking about the limitations of our knowledge.
So why did The Black Swan remind me so much of the story I recounted above? Because the tone of this book and that article are exactly the same. Taleb earnestly believes two things: 1) his "black swan" idea is new and revolutionary and significant; and 2) he is pretty much the smartest guy in the world for having discerned it.
This book carries an almost religious devotion to the temple of Taleb, the sense that we are fortunate that he has spent years poring over old tomes and selecting reality out of all the nonsense that has gone before, and been willing to share it with us. Oh, he didn't come up with this all on his own; he has his mentors, his Montaigne, his Popper, and, especially, his Mandlebrot. But it is Taleb who will rock the world, oh yes he will.
And what does this theory come down to? Essentially, the real world is too complex to be boiled down to the simplistic models that so often are used to describe it. We teach probability through casino games, then assume that the world fits those same rules - and it cannot. We can't take everything into account, so we try to create narratives that we can handle, but those narratives are incapable of modeling reality. Linear extrapolations are inherently unrealistic. And, then, always lurking in the background, is the BLACK SWAN - even if our model was perfect, in will fly the swan to upset everything.
It's difficult for me to know what to say about this. If you've read this blog for any length of time, you know that it is based on this very kind of thinking (and I claim no singularity in that, unlike Taleb). I've had any number of posts as to why economics is not a science, something that Taleb elevates to divine revelation (though he certainly seems to have a special irritation with the Nobel Prize). I've written about how the assumptions of future employment that will "naturally" result from spending on energy are based on nothing.
Again, I cite myself not to put me on the "special insight" platform on which Taleb puts himself, but because I know my arguments the best. There are others who offer counterintuitive ideas, who understand the limitations of conventional thinking, but most of us are not quite as irksome as Taleb about it (at least, I hope not).
I guess my overall impression of this book is that it contains some good ideas, but badly needed a strong-handed editor. The self-indulgence of Taleb's writing does nothing to enhance his points. There is, maybe, a 130-page book here, one without the self-aggrandizement and the pointless autobiographical side trips. (It is also the kind of book that fills me with despair that so many people find it significant, because the limits of knowledge should not be so revelatory; that there are people in high positions who are learning something from this is profoundly depressing.)
An editor might also have ironed out some of the things that are wrong or poorly-explained. How does Taleb's Extremistan produce Black Swans - it would seem that cause and effect are reversed here? The computer, the Internet, and the laser were certainly not unplanned or unexpected, though some of the effects of each were unforeseen - such is the way of all significant inventions. Microsoft's market share domination of Apple is not the result of luck, at least not to the extent that Taleb implies.
The most disappointing aspect of The Black Swan is the set of conclusions, because they are non-conclusions. Taleb says that, instead of using imperfect models to predict the future, which is impossible, we should move to empiricism. What he means, of course, is intuition - we should try things and see what works instead of reasoning from principles. This only applies to some fields, however, but we can't really know which fields are which. If this sounds incoherent, it is (Taleb apparently had some problems with a medical diagnosis, which is unfortunate, but it's a big leap to the idea that we should go with intuition). Empiricism always sounds great until we realize that there are many more NOTs in the universe, many more blind alleys than through streets.
I don't want to take the flyleaf as an important input, but it does state that, "He offers surprisingly simple tricks for dealing with black swans and benefiting from them." Taleb does nothing of the sort. He offers an investment strategy (invest 85% of your money in perfectly safe instruments, put the other 15% into wildly risky inifinite-upside Black Swan things) that is completely unhelpful (it might be possible if you're playing with a whole lot of OPM - Other People's Money - as he presumably was).
What Taleb is doing here is trying to overturn the basis on which people do things, wanting us to cast aside all those inaccurate models based on logic. But there's nothing here to replace that thinking, we're just supposed to wander around, experiencing life, and, I guess, hoping for the best.
It comes down to something simple but unstated: Taleb's success itself is a Black Swan, the result of chance. He was lucky to hit it big enough on investments to finance his self-styled epistemological research, then lucky enough again to find someone to publish a book with no editing and have it become a best-seller. He proves his own theory, which is useful, but it's unlikely any reader will learn anything that will help their own lives.
1 comment:
I've just started reading this book, so I haven;t found all the deficiencies you've mentioned yet. Still, my first impression of what Taleb was writing about without his saying so was in fact the very thing you mentioned (and thus my dispair that you've beaten me to writing the review!!): The Black Swan (concept) is another way of looking at paradigm shift.
It seemed like such an obvious connection, and yet Taleb didn't mention it, nor Kuhn, nor Schwartz & Ogilvy; I wondered if he really didn't know and just thought he came up with it all on his own, or if he was being tricky.
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