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meririvilla's review against another edition
4.0
Me encanto bastante, me dio un insight a esta parte de las matematicas de la que no tenia ni idea y pues haber si escribo un resumen propio como debe de ser cuando este siendo menos vaga. Pero de momento, lo acabo de terminar, y de los mas simple statements me acuerdo de como simple systems can give rise to very complex behaviour, de cmoo chaos no quiere decir que algo no se pueda predecir, pero si que teniendo finitely accurate initial measurements, means errors grow exponentially when making predictions for the weather for example. Del descubrimiento del madelbrot set hasta la aplicacion de estas matematicas para construir una maquina para measure el quality del material para ser puesto into springs. Como todos los libros esto, rompe la concepcion de que el hacer matematicas es completamente irrelevante a la vida real. Cuando sin las matematicas, casi todo lo que tenemos simplemente no podria haberse developed.
Y aquí vienen los notes que he tardado un poqutín demasioda para sentarme y escribirlo o ejem más bien copiar los highlights del kindle y editarlo para acabar con un resumen que es un poquitin demasiado largo y estonces aca solo pongo lo q cabe y el resto esta guardado en el forder de books en el escritorio
Chaos occurs when a deterministic (that is, non-random) system behaves in an apparently random manner.
An inherent feature of mathematical equations in dynamics. The ability of even simple equations to generate motion so complex, so sensitive to measurement, that it appears random.
Slight change in the starting value: lose track completely of where it's going.
Out of chaos emerges pattern. Determinism for simple systems with few degrees of freedom, statistics for complicated systems with many degrees of freedom.
Poincaré founded the modern qualitative theory of dynamical systems. His greatest creation was topology – the general study of continuity. He called it analysis situs – the analysis of position.
Topology has been characterized as ‘rubber sheet geometry’. More properly, it is the mathematics of continuity. Continuity is the study of smooth, gradual changes, the science of the unbroken. Discontinuities are sudden, dramatic: places where a tiny change in cause produces an enormous change in effect.
In other words, instead of looking at all initial states, you can look at just Figure 24 If a point in phase space traces out a closed loop, then it will repeat the same motion periodically for ever. a few. Imagine a whole surface of initial states, and follow the evolution of each until (if it ever does) it comes back and hits the surface again (Figure 25). Can you find one state that returns exactly to where it started? If so, you've bagged a periodic solution.
Neptune, Pluto, and a grain of interstellar dust, the three -body problem
The piece of dust moves within the rotating mutual gravitational field of the two planets. It thinks of itself not as a member of a three-body system, but as a tiny ball rolling around on a rotating but fixed landscape. That's Hill's reduced model.
Chaotic motion obeys exactly the same laws as simple motion, it is just that even small internal variables and force must be accounted for precisely and individually
The nature of randomness and superpositions has meant it is physically impossible to know both velocity and position of particles. There must always be uncertainty.
in quantum mechanics uncertainty is physically manifested and probability waves are thought by some to have physical existence in our reality.
the arrows on nearby curves are fairly closely aligned. This means that the notional fluid, whose flow is represented by the lines, doesn't get torn apart: the motion is continuous.
First, on the left-hand side, there's a point towards which all nearby Figure 36 Phase portrait of a flow in the plane, showing (left to right) a sink, a saddle, a limit cycle, and a source. flow-lines spiral. This is known as a sink. It's rather like a plughole down which the fluid is gurgling, hence perhaps the name. Over on the right-hand side is a plughole in reverse, a point from which fluid spirals away. This is called a source. Think of fluid bubbling up from a spring. In between is a place where flow lines appear to cross. This is known as a saddle. Actually the lines don't cross; something more interesting happens, which I'll describe below. If two jets of a real fluid run into each other, you see saddles. Finally, surrounding the source on the right is a single closed loop. This is a limit cycle. It resembles an eddy, where fluid goes round and round. A whirlpool. In a few pages' time we'll see that, roughly speaking, flows in the plane possess (some or all of) these features, and typically nothing else. There can be several of each feature, but you won't find anything more complicated. I'll also explain why I use the word ‘typically’ here. But first, let's acquaint ourselves more closely with these four fundamental features of flows in the plane – differential equations with two degrees of freedom. Figure
Saddles (Figure 39) are more interesting. They're also the sort of thing that only a mathematician would think of – except that Mother Nature has an even more vivid imagination. In a sense, they're steady states that are stable in some directions and unstable in others.
The one shown is a stable limit cycle: nearby points move towards it. There is also an unstable limit cycle: nearby points move away.
limit cycles are really interesting. If you start on one (Figure 40), you go round and round and round forever, repeating the same motion over and over again. The motion is periodic. There are two basic kinds of limit cycle. The one shown is a stable limit cycle: nearby points move towards it. There is also an unstable limit cycle: nearby points move away.
quasiperiodicity. Here several different periodic motions, with independent frequencies, are combined together.
the criterion for the combination to be periodic is that the ratio of the periods should be a rational number – an exact fraction p/q where p and q are whole numbers.
structurally stable to mean a flow whose topology doesn't change if the equations describing it are altered by a small enough amount. This is a quite different idea from a stable state of a given equation.
So what does a general dynamical system do in the long run? It settles down to an attractor. An attractor is defined to be… whatever it settles down to!
‘Almost all’ numbers in the interval 0 to 1 have decimal expansions that are random. This was proved by an American mathematician called Gregory Chaitin, who studied the limitations of computability. It's believable if you say it right: a number chosen ‘at random’ will have random digits. So the deterministic dynamical system that we've constructed behaves in this random fashion, not just for a few weird initial points, but for almost all of them!
every continuous mapping of a line segment to itself must have at least one fixed point: a point that maps to itself.
Let me recap. If there's a line segment, such that every point starting on it eventually comes back to it, then there is at least one periodic solution passing through that segment.
to build a Cantor set you start with an interval of length 1, and remove its middle third (but leaving the end points of this middle third). This leaves two smaller intervals, one-third as long: remove their middle thirds too.
are now ready for an electrifying discovery. Not only does the wrap-ten-times mapping have the four curious properties noted – sensitivity to initial conditions, existence of random itineraries, common occurrence of random itineraries, and cake-mix periodicity/aperiodicity. So do the solenoid and its corresponding differential equation.
In 1950 the American ENIAC computer made the first successful calculations in weather prediction. By 1953 the Princeton MANIAC machine had made it clear that routine weather-prediction was entirely feasible.
Numerical weather-prediction is like a huge game of three-dimensional chess. Imagine a fine grid of points drawn on the surface of the Earth, at several heights to track the up–down motion of the atmosphere as well as north–south and east–west.
what are the rules of the game? The rules are the equations of motion of the atmosphere.
Thousands upon thousands of repetitive calculations based on explicit and deterministic rules.
the number of variables involved in the atomic model is far too large for a computer to handle. It can't track each individual atom of the atmosphere.
Institute of Technology in 1944, is cunning and surprising. The model is deliberately coarsened, to filter out the sound waves. You don't use the most accurate possible equations: you deliberately make them less accurate – to
the convection cells, going round and round in a periodic fashion. In a manner typical of classical applied mathematics, Saltzman guessed an approximate form of the solution, substituted it into his equations, ignored some awkward but small terms, and took a look at the result. Even his highly truncated equations were too hard to solve by a formula, so he put them on a computer. He noticed that the solution appeared to undergo irregular fluctuations: unsteady convection. But it didn't look at all periodic.
system of equations that has now become a classic: Here x, y, z are his three key variables, t is time, and d/dt is the rate of change. The constants 10 and 8/3 correspond to values chosen by Saltzman; the 28 represents the state of the system just after the onset of unsteady convection,
is paper shows the first 3,000 iterations of the value of the variable y (Figure 54). It wobbles periodically for the first 1,500 or so, but you can see the size of the wobble growing steadily. Lorenz knew from his linear stability analysis that this would happen: but what happened next? Madness. Violent oscillations, swinging first up, then down; but with hardly any pattern to them.
Using the curve, you can predict the value of the next peak in z provided you know the value of the current peak. In this sense, at least some of the dynamics is predictable. But it's only a short-term prediction.
Figure 57 The butterfly effect: a numerical simulation of one variable in the Lorenz system. The curves represent initial conditions differing by only 0.0001. At first they appear to coincide, but soon chaotic dynamics leads to independent, widely divergent trajectories.
any physical system that behaved nonperiodically would be unpredictable.
from its attractor, then it rapidly homes back on to it. So chaos is a strange and beautiful combination of stability
If you want to predict whereabouts on its attractor a chaotic system will lie in the distant future, and all you know is where it is now, then you've got problems. On the other hand, you can safely predict that even after a random disturbance the system will quickly return to its attractor – or, if it has several attractors, it will return to one of them.
What the butterfly does is disturb the motion of the point in phase space that represents the Earth's weather. Assuming that this point lies on an attractor, albeit a highly complex multidimensional one, then the tiny flapping of the butterfly can divert the point off the attractor only very briefly, after which it rapidly returns to the same attractor. However, instead of returning to the point A that it would have reached if undisturbed, it returns to some nearby point B. The trajectories of A and – then diverge exponentially, but because they lie on the same attractor, they generate time-series with the same texture. In particular, a hurricane – which is a characteristic weather motif – cannot occur in the perturbed time-series unless it was (eventually) going to occur in the original one. So what the butterfly does is to alter the timing of a hurricane that – in a sense – was going to happen anyway.
Given all this, it is an exaggeration to claim the butterfly as the cause of the big changes that its flapping wing sets in train. The true cause is the butterfly in conjunction with everything else. There are billions of butterflies in the world, and the lazy agitation of their wings is just one source of tiny vortices in our atmosphere. The weather is determined by the combined effect of all such influences. The proverbial butterfly is just as likely to cancel out a hurricane as to create one – and it may just raise the average temperature of India by a hundredth of a degree, or generate a small grey cloud over Basingstoke.
In there somewhere is a butterfly, but it is just one of a trillion factors (I underestimate) that have contributed, since the dawn of time and the birth of space, to the presence of that mass of humid air now, here, using these molecules of water and gas. It is no more sensible to blame the flapping of a butterfly's wing than it is the flipping of a quark's quantum state.
Where does this sensitivity come from? It's a mixture of two conflicting tendencies in the dynamics. The first is stretching. The mapping x → 10x expands distances locally by a factor of ten. Nearby points are torn apart. The second is folding. The circle is a bounded space, there isn't room to stretch everything. It gets folded round itself many times, that's the only way to fit it in after you've expanded distances by ten. So, although points close together move apart, some points far apart move close together.
Y aquí vienen los notes que he tardado un poqutín demasioda para sentarme y escribirlo o ejem más bien copiar los highlights del kindle y editarlo para acabar con un resumen que es un poquitin demasiado largo y estonces aca solo pongo lo q cabe y el resto esta guardado en el forder de books en el escritorio
Chaos occurs when a deterministic (that is, non-random) system behaves in an apparently random manner.
An inherent feature of mathematical equations in dynamics. The ability of even simple equations to generate motion so complex, so sensitive to measurement, that it appears random.
Slight change in the starting value: lose track completely of where it's going.
Out of chaos emerges pattern. Determinism for simple systems with few degrees of freedom, statistics for complicated systems with many degrees of freedom.
Poincaré founded the modern qualitative theory of dynamical systems. His greatest creation was topology – the general study of continuity. He called it analysis situs – the analysis of position.
Topology has been characterized as ‘rubber sheet geometry’. More properly, it is the mathematics of continuity. Continuity is the study of smooth, gradual changes, the science of the unbroken. Discontinuities are sudden, dramatic: places where a tiny change in cause produces an enormous change in effect.
In other words, instead of looking at all initial states, you can look at just Figure 24 If a point in phase space traces out a closed loop, then it will repeat the same motion periodically for ever. a few. Imagine a whole surface of initial states, and follow the evolution of each until (if it ever does) it comes back and hits the surface again (Figure 25). Can you find one state that returns exactly to where it started? If so, you've bagged a periodic solution.
Neptune, Pluto, and a grain of interstellar dust, the three -body problem
The piece of dust moves within the rotating mutual gravitational field of the two planets. It thinks of itself not as a member of a three-body system, but as a tiny ball rolling around on a rotating but fixed landscape. That's Hill's reduced model.
Chaotic motion obeys exactly the same laws as simple motion, it is just that even small internal variables and force must be accounted for precisely and individually
The nature of randomness and superpositions has meant it is physically impossible to know both velocity and position of particles. There must always be uncertainty.
in quantum mechanics uncertainty is physically manifested and probability waves are thought by some to have physical existence in our reality.
the arrows on nearby curves are fairly closely aligned. This means that the notional fluid, whose flow is represented by the lines, doesn't get torn apart: the motion is continuous.
First, on the left-hand side, there's a point towards which all nearby Figure 36 Phase portrait of a flow in the plane, showing (left to right) a sink, a saddle, a limit cycle, and a source. flow-lines spiral. This is known as a sink. It's rather like a plughole down which the fluid is gurgling, hence perhaps the name. Over on the right-hand side is a plughole in reverse, a point from which fluid spirals away. This is called a source. Think of fluid bubbling up from a spring. In between is a place where flow lines appear to cross. This is known as a saddle. Actually the lines don't cross; something more interesting happens, which I'll describe below. If two jets of a real fluid run into each other, you see saddles. Finally, surrounding the source on the right is a single closed loop. This is a limit cycle. It resembles an eddy, where fluid goes round and round. A whirlpool. In a few pages' time we'll see that, roughly speaking, flows in the plane possess (some or all of) these features, and typically nothing else. There can be several of each feature, but you won't find anything more complicated. I'll also explain why I use the word ‘typically’ here. But first, let's acquaint ourselves more closely with these four fundamental features of flows in the plane – differential equations with two degrees of freedom. Figure
Saddles (Figure 39) are more interesting. They're also the sort of thing that only a mathematician would think of – except that Mother Nature has an even more vivid imagination. In a sense, they're steady states that are stable in some directions and unstable in others.
The one shown is a stable limit cycle: nearby points move towards it. There is also an unstable limit cycle: nearby points move away.
limit cycles are really interesting. If you start on one (Figure 40), you go round and round and round forever, repeating the same motion over and over again. The motion is periodic. There are two basic kinds of limit cycle. The one shown is a stable limit cycle: nearby points move towards it. There is also an unstable limit cycle: nearby points move away.
quasiperiodicity. Here several different periodic motions, with independent frequencies, are combined together.
the criterion for the combination to be periodic is that the ratio of the periods should be a rational number – an exact fraction p/q where p and q are whole numbers.
structurally stable to mean a flow whose topology doesn't change if the equations describing it are altered by a small enough amount. This is a quite different idea from a stable state of a given equation.
So what does a general dynamical system do in the long run? It settles down to an attractor. An attractor is defined to be… whatever it settles down to!
‘Almost all’ numbers in the interval 0 to 1 have decimal expansions that are random. This was proved by an American mathematician called Gregory Chaitin, who studied the limitations of computability. It's believable if you say it right: a number chosen ‘at random’ will have random digits. So the deterministic dynamical system that we've constructed behaves in this random fashion, not just for a few weird initial points, but for almost all of them!
every continuous mapping of a line segment to itself must have at least one fixed point: a point that maps to itself.
Let me recap. If there's a line segment, such that every point starting on it eventually comes back to it, then there is at least one periodic solution passing through that segment.
to build a Cantor set you start with an interval of length 1, and remove its middle third (but leaving the end points of this middle third). This leaves two smaller intervals, one-third as long: remove their middle thirds too.
are now ready for an electrifying discovery. Not only does the wrap-ten-times mapping have the four curious properties noted – sensitivity to initial conditions, existence of random itineraries, common occurrence of random itineraries, and cake-mix periodicity/aperiodicity. So do the solenoid and its corresponding differential equation.
In 1950 the American ENIAC computer made the first successful calculations in weather prediction. By 1953 the Princeton MANIAC machine had made it clear that routine weather-prediction was entirely feasible.
Numerical weather-prediction is like a huge game of three-dimensional chess. Imagine a fine grid of points drawn on the surface of the Earth, at several heights to track the up–down motion of the atmosphere as well as north–south and east–west.
what are the rules of the game? The rules are the equations of motion of the atmosphere.
Thousands upon thousands of repetitive calculations based on explicit and deterministic rules.
the number of variables involved in the atomic model is far too large for a computer to handle. It can't track each individual atom of the atmosphere.
Institute of Technology in 1944, is cunning and surprising. The model is deliberately coarsened, to filter out the sound waves. You don't use the most accurate possible equations: you deliberately make them less accurate – to
the convection cells, going round and round in a periodic fashion. In a manner typical of classical applied mathematics, Saltzman guessed an approximate form of the solution, substituted it into his equations, ignored some awkward but small terms, and took a look at the result. Even his highly truncated equations were too hard to solve by a formula, so he put them on a computer. He noticed that the solution appeared to undergo irregular fluctuations: unsteady convection. But it didn't look at all periodic.
system of equations that has now become a classic: Here x, y, z are his three key variables, t is time, and d/dt is the rate of change. The constants 10 and 8/3 correspond to values chosen by Saltzman; the 28 represents the state of the system just after the onset of unsteady convection,
is paper shows the first 3,000 iterations of the value of the variable y (Figure 54). It wobbles periodically for the first 1,500 or so, but you can see the size of the wobble growing steadily. Lorenz knew from his linear stability analysis that this would happen: but what happened next? Madness. Violent oscillations, swinging first up, then down; but with hardly any pattern to them.
Using the curve, you can predict the value of the next peak in z provided you know the value of the current peak. In this sense, at least some of the dynamics is predictable. But it's only a short-term prediction.
Figure 57 The butterfly effect: a numerical simulation of one variable in the Lorenz system. The curves represent initial conditions differing by only 0.0001. At first they appear to coincide, but soon chaotic dynamics leads to independent, widely divergent trajectories.
any physical system that behaved nonperiodically would be unpredictable.
from its attractor, then it rapidly homes back on to it. So chaos is a strange and beautiful combination of stability
If you want to predict whereabouts on its attractor a chaotic system will lie in the distant future, and all you know is where it is now, then you've got problems. On the other hand, you can safely predict that even after a random disturbance the system will quickly return to its attractor – or, if it has several attractors, it will return to one of them.
What the butterfly does is disturb the motion of the point in phase space that represents the Earth's weather. Assuming that this point lies on an attractor, albeit a highly complex multidimensional one, then the tiny flapping of the butterfly can divert the point off the attractor only very briefly, after which it rapidly returns to the same attractor. However, instead of returning to the point A that it would have reached if undisturbed, it returns to some nearby point B. The trajectories of A and – then diverge exponentially, but because they lie on the same attractor, they generate time-series with the same texture. In particular, a hurricane – which is a characteristic weather motif – cannot occur in the perturbed time-series unless it was (eventually) going to occur in the original one. So what the butterfly does is to alter the timing of a hurricane that – in a sense – was going to happen anyway.
Given all this, it is an exaggeration to claim the butterfly as the cause of the big changes that its flapping wing sets in train. The true cause is the butterfly in conjunction with everything else. There are billions of butterflies in the world, and the lazy agitation of their wings is just one source of tiny vortices in our atmosphere. The weather is determined by the combined effect of all such influences. The proverbial butterfly is just as likely to cancel out a hurricane as to create one – and it may just raise the average temperature of India by a hundredth of a degree, or generate a small grey cloud over Basingstoke.
In there somewhere is a butterfly, but it is just one of a trillion factors (I underestimate) that have contributed, since the dawn of time and the birth of space, to the presence of that mass of humid air now, here, using these molecules of water and gas. It is no more sensible to blame the flapping of a butterfly's wing than it is the flipping of a quark's quantum state.
Where does this sensitivity come from? It's a mixture of two conflicting tendencies in the dynamics. The first is stretching. The mapping x → 10x expands distances locally by a factor of ten. Nearby points are torn apart. The second is folding. The circle is a bounded space, there isn't room to stretch everything. It gets folded round itself many times, that's the only way to fit it in after you've expanded distances by ten. So, although points close together move apart, some points far apart move close together.
lukewhitestone's review against another edition
3.0
Chapters 15 and 16 are quite insightful, and the main thing I was looking for in this book. Quantum mechanics is frustrating to everyone, and this book takes a skeptical and undogmatic view of irreducible randomness which is surprisingly hard to find. Explaining the keystones of QM such as the EPR Paradox and Bell's Inequality is done clearly and intuitively, and even though I can't say I've grasped every concept, I'm glad to have this book on my shelf for reference.
The discussion of Tim Palmer's ideas on the possible reconciliation of determinism in science and QM is interesting, but seems quite incomplete. Perhaps it is too in depth a topic for a book like this, but I think a discussion of superdeterminism (Palmer's newest theory) and the upsides and downsides to that brand of approach would elevate this book for me. As it is I remain unconvinced of Palmer's theories and find it equally unsatisfying to the conventional view.
I realize this book is from 2002... Maybe time for a new edition then? :)
The discussion of Tim Palmer's ideas on the possible reconciliation of determinism in science and QM is interesting, but seems quite incomplete. Perhaps it is too in depth a topic for a book like this, but I think a discussion of superdeterminism (Palmer's newest theory) and the upsides and downsides to that brand of approach would elevate this book for me. As it is I remain unconvinced of Palmer's theories and find it equally unsatisfying to the conventional view.
I realize this book is from 2002... Maybe time for a new edition then? :)
hanadibeg's review against another edition
Does God play dice? No ... or, yes. The answer doesn't matter, because dice's dynamics is deterministic chaos.
bakudreamer's review against another edition
3.0
Ought to be a DVD ( wish I'd discovered Ian Stewart a long time ago ) Overall great ~
emlo's review against another edition
informative
slow-paced
1.5
Star rating based purely on my enjoyment of the book, rather than the book's quality, which is excellent. It took me a whole year to read. The history of the subject and the real world applications were fascinating. I really tried to understand the math but it just boggled my tiny brain.
futurelegend's review against another edition
4.0
It's a thankless task trying to write for a general audience about a subject as rich, varied and profound as mathematics. Especially in a culture where maths is so badly taught many adults take great pride in not being any good at it (hint: there's a lot more to maths than endlessly adding and dividing fractions!) Some fail by being too superficial, but Ian Stewart can't be accused of that. Here he takes on the relatively new field of chaos, the mathematics of systems where very small changes in parameters lead to huge differences in outcome that, to the uninformed, appear random. These chaotic systems are the true building blocks of the real world rather than the neat, straightforward formulae that create smooth, regular shapes, yet generations of mathematicians and physicists have shied away from them until very recently. Stewart shows how even the most shapeless systems, when looked at from the right angle, exhibit the most exquisite patterns and symmetries. His style is informal, chatty, sometimes iconoclastic, but be warned: it's not a book for mathematical novices. Some of the concepts are mind-twisting!
charbel14's review against another edition
4.0
Before we start with the review, let's take a moment to appreciate how good of a science communicator Ian Stewart is.
Now on with the nitty gritty.
When faced with accepting Quantum Mechanics, Einstein famously said: "God does not play dice with the universe", to which Stephen Hawking wittily replied: "Not only does God play, but he sometimes throws them where they cannot be seen". Quantum Mechanics, you see, cannot be handled with simple every day linear mathematics. Instead we attempt to explain it using probability. The reason behind this is chaos.
Chaos may not be apparent in the overview of things, but when the smaller details add up, chaos becomes the main force behind them. It is the reason why so many behaviours seem unpredictable, or even random. To understand chaos, we cannot rely on classical linear mathematics, in fact just to glimpse it mathematicians had to become absorbed in the world of topology; a world of saddles, sinks, sources, and attractors; where a hole is not the lack of something but is in itself something (I love that!). I admit that before reading this book I underestimated topology, thinking that it could not rival calculus, statistics, and probability. But once I was asked to visualise an object in four dimensions, let alone fix or six, I understood my own ignorance. In the end, what we end up with is that chaos is not only unpredictable, but also stable; making it one of the most dazzling paradoxes around.
Now enough about chaos and topology, let's talk about the book; after all that's what a review is for. Now, can you read this book without an advanced background in mathematics? Yes, I did. Will it be easy? Not particularly. The larger part of Does God Play Dice is conceptual. You have to put in an effort. If I had to compare this book to something, I'd say that it's close to an introductory course on chaos. It explains a whole lot, but it leaves you with so many questions. The best aspect of this book is that some of the most difficult things to understand are explained clearly with Ian Stewart's subtle sense of humour. And so even when I had my eyes closed trying to visualise something, like attractors, or writing down notes on the Butterfly Effect ( which is pretty useful to me), it was still fun. Challenging, but fun!
Best of all, the book prepares you to read more about chaos. Because let's face it, when you finally finish this book, you're going to have one of two reactions: either "Wow, I'm so glad I read this! I need to learn more about chaos!" or "I don't even want to hear the C word again! Now where's the aspirin?".
Fortunately for me, I had the former reaction. Some chapter were fantastic (chapter 16 comes to mind), others, like the pendulum chapter, could have used more "bling".
So would I recommend this book? Yes, definitely. But a word of advice: take your time with it. Let the new concepts sink in first. Don't rush through it; read the sentence (or the chapter) multiple times if you have to, until you get it. Because once you do, it's worth it.
If you do decide to pick it up, I hope you enjoy it. Have fun, and sorry about the long review.
Now on with the nitty gritty.
When faced with accepting Quantum Mechanics, Einstein famously said: "God does not play dice with the universe", to which Stephen Hawking wittily replied: "Not only does God play, but he sometimes throws them where they cannot be seen". Quantum Mechanics, you see, cannot be handled with simple every day linear mathematics. Instead we attempt to explain it using probability. The reason behind this is chaos.
Chaos may not be apparent in the overview of things, but when the smaller details add up, chaos becomes the main force behind them. It is the reason why so many behaviours seem unpredictable, or even random. To understand chaos, we cannot rely on classical linear mathematics, in fact just to glimpse it mathematicians had to become absorbed in the world of topology; a world of saddles, sinks, sources, and attractors; where a hole is not the lack of something but is in itself something (I love that!). I admit that before reading this book I underestimated topology, thinking that it could not rival calculus, statistics, and probability. But once I was asked to visualise an object in four dimensions, let alone fix or six, I understood my own ignorance. In the end, what we end up with is that chaos is not only unpredictable, but also stable; making it one of the most dazzling paradoxes around.
Now enough about chaos and topology, let's talk about the book; after all that's what a review is for. Now, can you read this book without an advanced background in mathematics? Yes, I did. Will it be easy? Not particularly. The larger part of Does God Play Dice is conceptual. You have to put in an effort. If I had to compare this book to something, I'd say that it's close to an introductory course on chaos. It explains a whole lot, but it leaves you with so many questions. The best aspect of this book is that some of the most difficult things to understand are explained clearly with Ian Stewart's subtle sense of humour. And so even when I had my eyes closed trying to visualise something, like attractors, or writing down notes on the Butterfly Effect ( which is pretty useful to me), it was still fun. Challenging, but fun!
Best of all, the book prepares you to read more about chaos. Because let's face it, when you finally finish this book, you're going to have one of two reactions: either "Wow, I'm so glad I read this! I need to learn more about chaos!" or "I don't even want to hear the C word again! Now where's the aspirin?".
Fortunately for me, I had the former reaction. Some chapter were fantastic (chapter 16 comes to mind), others, like the pendulum chapter, could have used more "bling".
So would I recommend this book? Yes, definitely. But a word of advice: take your time with it. Let the new concepts sink in first. Don't rush through it; read the sentence (or the chapter) multiple times if you have to, until you get it. Because once you do, it's worth it.
If you do decide to pick it up, I hope you enjoy it. Have fun, and sorry about the long review.
santirv's review against another edition
3.0
I am not sure if I have understood every mathematical detail... well I pretty confident that I did not understand many things. But it is a really good book and address questions about the limits of Science to comprehend natural phenomena that are important to keep in mind.