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 Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe
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Product Description
Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to discover one of the greatest problems in mathematics. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem, which was to find proof of the conjecture "all non-trivial zeros of the zeta function have real part one-half". That statement may be nonsense to anyone but a mathematician but Derbyshire walks the reader through the decades of reasoning that led to the Riemann Hypothesis in a way that makes it perfectly clear. Riemann never proved the statement and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step maths and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea and allows readers to explore the theory without insisting on page after page of formulae. In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, GH Hardy, Alan Turing, André Weil and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire and he makes the effort seem very worthwhile. --Therese Littleton, Amazon.com
Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe
Challenging, but worth it, 15 Sep 2008
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:
"Has anyone proved the Riemann Hypothesis?"
Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis.
Interesting, 19 Aug 2008
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though.
A popularisation the focuses on the actual mathematics, 05 Jan 2008
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.
This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.
No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical.
Do not buy any others, 12 Apr 2007
I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper.
Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.
This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.
This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.
I cannot do more than endorse the other reviewers' praise for this classic-to-be.
A fabulous read, 19 Jan 2005
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it!
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone. ...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way. A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business. Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain. A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe Challenging, but worth it, 15 Sep 2008
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:
"Has anyone proved the Riemann Hypothesis?"
Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis. Interesting, 19 Aug 2008
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though. A popularisation the focuses on the actual mathematics, 05 Jan 2008
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.
This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.
No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical. Do not buy any others, 12 Apr 2007
I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper.
Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.
This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.
This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.
I cannot do more than endorse the other reviewers' praise for this classic-to-be. A fabulous read, 19 Jan 2005
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it! not for the faint of heart..., 24 Oct 2002
Euclid begins by stating a few a definitions and logical rules. 'A line is a breathless length' and 'Things that are equal to the same thing are equal to each other'. The proofs that follow are simple and elegant. The second flowing from the first in a natural sequence. But this is no higgledy piggledy random wandering. In the first book the author leads the reader to Pythagoras theorem. Just as every statement Euclid makes is essential to the proof, every proof is essential to the book's goal. The clarity and beauty of this book is something to behold Heath's commentary is a very interesting complement. He provides alternative ancient and modern proofs as well as notes on the historical development of the mathematics. A word of warning - this book took me about six months to read. I was unable to follow the book without following the proofs with a compass, ruler etc. However, if you are prepared to put in the time the rewards are considerable.
One of the 10 great scientific books of the last 2000 years, 19 Jul 2001
This book is the foundation on which the mathematics is built. It is greatly enhanced by the translator's annotations. If you want to know what mathematics is all about, then you must have this book.
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Product Description
In his charming mathematical history, Euclid's Window Leonard Mlodinow asks "How do you know where you are?" This question and others about space and time grew out of simple observations of the environment by a select group of thinkers whose lives and brains Mlodinow dissects. Starting with Euclid geometry has flowed out over the centuries describing the universe and, Mlodinow argues, making modern civilization possible. This is not just a history of geometry--it's a timeline of reason and abstraction, with all the major players present: Euclid, Descartes, Gauss, Einstein and Witten, each represented by a mini-biography. Lots of examples pepper the narrative to help readers achieve their own "eureka!" And it's impossible not to be staggered at the mathematical feats of these geniuses, accomplished as many of them were in the absence of anything but observation and intense thought. Each story builds satisfactorily upon the last until at the end of this delightful book one has a sense of having climbed a peak of understanding. A working knowledge of basic geometry is helpful but not essential for enjoying Euclid's Window, and Mlodinow's chatty style lends itself remarkably well to explaining these deep and revolutionary concepts. --Adam Fisher
Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone. ...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way. A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business. Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain. A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe Challenging, but worth it, 15 Sep 2008
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:
"Has anyone proved the Riemann Hypothesis?"
Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis. Interesting, 19 Aug 2008
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though. A popularisation the focuses on the actual mathematics, 05 Jan 2008
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.
This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.
No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical. Do not buy any others, 12 Apr 2007
I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper.
Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.
This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.
This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.
I cannot do more than endorse the other reviewers' praise for this classic-to-be. A fabulous read, 19 Jan 2005
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it! not for the faint of heart..., 24 Oct 2002
Euclid begins by stating a few a definitions and logical rules. 'A line is a breathless length' and 'Things that are equal to the same thing are equal to each other'. The proofs that follow are simple and elegant. The second flowing from the first in a natural sequence. But this is no higgledy piggledy random wandering. In the first book the author leads the reader to Pythagoras theorem. Just as every statement Euclid makes is essential to the proof, every proof is essential to the book's goal. The clarity and beauty of this book is something to behold Heath's commentary is a very interesting complement. He provides alternative ancient and modern proofs as well as notes on the historical development of the mathematics. A word of warning - this book took me about six months to read. I was unable to follow the book without following the proofs with a compass, ruler etc. However, if you are prepared to put in the time the rewards are considerable.
One of the 10 great scientific books of the last 2000 years, 19 Jul 2001
This book is the foundation on which the mathematics is built. It is greatly enhanced by the translator's annotations. If you want to know what mathematics is all about, then you must have this book.
An illuminating read, 12 Nov 2008
This is the sort of book I wish had been around before I went to university as it sets out some of the concepts around geometry that impact theoretical physics in an acccessible way. I now realise that glib lines such as 'parallel lines meeting at infinity' are way more subtle than they seem and that I now have lots of questions that I have noone to ask on what it all actually means.
Good introduction, 21 Apr 2004
Structured along the lines of the "big man-style of history" (i.e. Euclid,Descrates, Gauss, Einstein and Edward Witten) this book takes us from theGreeks to Superstring (M-Theory) of the present. The explanations arevery clear and the historical elements are interesting and concise.
In a book of this size it can only be an introduction, of course, but itvery readable and contains mathematical details, where justified.
I would recommend The Elegant Universe by Brian Greene as an excellentcontinuation to the later chapters on Superstring and M-Theory.
Through Euclid's Window Clearly, 12 Mar 2003
Fantastic. This is definitely one of the best lay science books I've had the pleasure of reading, and I read alot of scientific books. Clear, witty, down-to-earth, and written with a real understanding of how to present complex ideas in everyday language. Read this, and you can't help but learn and enjoy. You'll emerge the other end feeling you've bettered yourself and had a really pleasant time doing it. You'll read things that you want to tell everyone you know, because Mlodinow makes them so interesting.
A funny, well written book about the history of geometry, 01 Apr 2002
This book describes the history of geometry as if it was the stuff of audacious adventurers and bold explorers. Very well written indeed for such a potentially boring subject. I even had trouble putting the book down... In the first three chapters the author explains the Greek origin of Euclidian geometry and its unchallenged use throughout the Dark Ages, the improvements made by Descartes in the 17th century and the struggles of 19th century German mathematicians to improve its fundamental flaws that resulted in non-Euclidian geometry. The last two chapters explain Einstein's theory of relativity as well as the unifying theory of strings and touch upon the role non-Euclidian geometry plays in them. The details of the characters involved and their motivations in developing geometry make this book fascinating. The humouristic style of writing and the often hilarious examples make this book really enjoyable to read as well. A recommendation for anyone interested in mathematics and/or history !
A funny, well written book about the history of geometry, 01 Apr 2002
This book describes the history of geometry as if it was the stuff of audacious adventurers and bold explorers. Very well written indeed for such a potentially boring subject. I even had trouble putting the book down... In the first three chapters the author explains the Greek origin of Euclidian geometry and its unchallenged use throughout the Dark Ages, the improvements made by Descartes in the 17th century and the struggles of 19th century German mathematicians to improve its fundamental flaws that resulted in non-Euclidian geometry. The last two chapters explain Einstein's theory of relativity as well as the unifying theory of strings and touch upon the role non-Euclidian geometry plays in them. The details of the characters involved and their motivations in developing geometry make this book fascinating. The humouristic style of writing and the often hilarious examples make this book really enjoyable to read as well. A recommendation for anyone interested in mathematics and/or history !
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone. ...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way. A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business. Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain. A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe Challenging, but worth it, 15 Sep 2008
The great German mathematician, David Hilbert was once asked what question would he ask if could come back in 500 years' time. His response was immidiate:
"Has anyone proved the Riemann Hypothesis?"
Reading this book, you'll understand why Hilbert didn't hesitate. This is by far the most 'mathematical' of the popular books on the RH, and if you are a mathematical numpty like me, you might be discouraged at first glance. Don't be!!! Derbyshire actually does a really good job of walking you through it. It's an extremely rewarding read. I particularly like the way he also wove in the politcal and social upheavals that were taking place in Germany and Europe in general at the time that Riemann was formulating his hypothesis. Interesting, 19 Aug 2008
I enjoyed the first half of the book - which provides a good background of the subject matter. Towards the latter half I grew weary of the author's style of writing and also found all the non-mathematical anecdotes annoying. I think the author's effort to dumb everything down ultimately destroys the point of the book. But this is a good starting point for a layperson who is interested in the Riemann hypothesis. I yearn for a more mathematical book, though. A popularisation the focuses on the actual mathematics, 05 Jan 2008
Most books of this kind don't bother to try to talk about the actual maths, so they waffle on about the mathematicians, which is something like watching interviews of rock stars when you want to be seeing them performing.
This book is an exception - it does its mightiest to actually explain the innards of the conjecture and goes some way towards achieving its aim.
No quibble - this is the best book on its subject that's available at the moment, unless you're going for something more technical. Do not buy any others, 12 Apr 2007
I have read this book and one of the other two popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.
It emphasises the centrality of Riemann's other parts of the paper apart from the famous Hypothesis and so helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous hypothesis: roughly that as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason is because of the techniques that Riemann invented in his paper.
Riemann's starting point was to generalise Euler's formula which relates the sum of a reciprocals of natural numbers: 1+1/2+1/3+1/4+... to the product of the inverses of the prime numbers. Derbyshire's explanation is far clearer than others and even I was able to understand it.
This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.
This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.
I cannot do more than endorse the other reviewers' praise for this classic-to-be. A fabulous read, 19 Jan 2005
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it! not for the faint of heart..., 24 Oct 2002
Euclid begins by stating a few a definitions and logical rules. 'A line is a breathless length' and 'Things that are equal to the same thing are equal to each other'. The proofs that follow are simple and elegant. The second flowing from the first in a natural sequence. But this is no higgledy piggledy random wandering. In the first book the author leads the reader to Pythagoras theorem. Just as every statement Euclid makes is essential to the proof, every proof is essential to the book's goal. The clarity and beauty of this book is something to behold Heath's commentary is a very interesting complement. He provides alternative ancient and modern proofs as well as notes on the historical development of the mathematics. A word of warning - this book took me about six months to read. I was unable to follow the book without following the proofs with a compass, ruler etc. However, if you are prepared to put in the time the rewards are considerable.
One of the 10 great scientific books of the last 2000 years, 19 Jul 2001
This book is the foundation on which the mathematics is built. It is greatly enhanced by the translator's annotations. If you want to know what mathematics is all about, then you must have this book.
An illuminating read, 12 Nov 2008
This is the sort of book I wish had been around before I went to university as it sets out some of the concepts around geometry that impact theoretical physics in an acccessible way. I now realise that glib lines such as 'parallel lines meeting at infinity' are way more subtle than they seem and that I now have lots of questions that I have noone to ask on what it all actually means.
Good introduction, 21 Apr 2004
Structured along the lines of the "big man-style of history" (i.e. Euclid,Descrates, Gauss, Einstein and Edward Witten) this book takes us from theGreeks to Superstring (M-Theory) of the present. The explanations arevery clear and the historical elements are interesting and concise.
In a book of this size it can only be an introduction, of course, but itvery readable and contains mathematical details, where justified.
I would recommend The Elegant Universe by Brian Greene as an excellentcontinuation to the later chapters on Superstring and M-Theory.
Through Euclid's Window Clearly, 12 Mar 2003
Fantastic. This is definitely one of the best lay science books I've had the pleasure of reading, and I read alot of scientific books. Clear, witty, down-to-earth, and written with a real understanding of how to present complex ideas in everyday language. Read this, and you can't help but learn and enjoy. You'll emerge the other end feeling you've bettered yourself and had a really pleasant time doing it. You'll read things that you want to tell everyone you know, because Mlodinow makes them so interesting.
A funny, well written book about the history of geometry, 01 Apr 2002
This book describes the history of geometry as if it was the stuff of audacious adventurers and bold explorers. Very well written indeed for such a potentially boring subject. I even had trouble putting the book down... In the first three chapters the author explains the Greek origin of Euclidian geometry and its unchallenged use throughout the Dark Ages, the improvements made by Descartes in the 17th century and the struggles of 19th century German mathematicians to improve its fundamental flaws that resulted in non-Euclidian geometry. The last two chapters explain Einstein's theory of relativity as well as the unifying theory of strings and touch upon the role non-Euclidian geometry plays in them. The details of the characters involved and their motivations in developing geometry make this book fascinating. The humouristic style of writing and the often hilarious examples make this book really enjoyable to read as well. A recommendation for anyone interested in mathematics and/or history !
A funny, well written book about the history of geometry, 01 Apr 2002
This book describes the history of geometry as if it was the stuff of audacious adventurers and bold explorers. Very well written indeed for such a potentially boring subject. I even had trouble putting the book down... In the first three chapters the author explains the Greek origin of Euclidian geometry and its unchallenged use throughout the Dark Ages, the improvements made by Descartes in the 17th century and the struggles of 19th century German mathematicians to improve its fundamental flaws that resulted in non-Euclidian geometry. The last two chapters explain Einstein's theory of relativity as well as the unifying theory of strings and touch upon the role non-Euclidian geometry plays in them. The details of the characters involved and their motivations in developing geometry make this book fascinating. The humouristic style of writing and the often hilarious examples make this book really enjoyable to read as well. A recommendation for anyone interested in mathematics and/or history !
Well done.., 22 Jul 1999
Bold has a gem of a book here. It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years. The title describes the book perfectly. These really are "Famous Problems from Geometry" and he does indeed explain how to solve them. The book has four major sections/chapters. He discusses in detail the three problems from antiquity (one section each): squaring a circle, doubling a cube, and trisecting an angle. Furthermore, he spends significant time with constructions of regular polygons (the fourth section) - which ones can be constructed and why. He also discusses which ones cannot be constructed and why. The reader will be expected to understand concepts from Modern Algebra, particularly the concept of a Field. While Bold does spend time explaining what a Field is, his definition is quick and is assumed to be more of a refresher for someone who has already learned about them. Bold also has a section on Complex Numbers where he derives one of the formulas used later in the book. Again - this section is assumed to be a refresher on Complex Numbers. High School Geometry or Algebra students would have significant trouble understanding his explanations and proofs. Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem being studied. The problems are good. As a third year college student majoring in mathematics, I found the explanations/solutions to be sometimes hard to follow. He assumes a great deal about the reader's level of proficiency in math and in geometry. As a result, he liberally skips steps in proofs that are assumed to be "obvious." If you're expecting simple proofs to these problems, you're not going to find them. If they were simple, they wouldn't have taken 2000 years to solve. But they are explained clearly here in terms that anyone with a college degree should be able to understand. Overall, a superb book. A must have for anyone interested in the famous problems from the history of Geometry.
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