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Nature's Numbers - Discovering Order and Pattern in the Universe
Mathematics has the power to open our eyes to new and unsuspected regularities in nature - the secret structure of a cloud or the hidden rhythms of the weather. This book aims to equip the reader with a mathematician's eye, changing the way we view the world.
176 pages, Paperback
First published January 1, 1995
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About the author
Ian Stewart
261 books750 followersIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
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Displaying 1 - 30 of 79 reviews
April 17, 2015
An interesting book on mathematics and mathematicians. Accessible and easy to read (it even ditched the word 'reification' in favour of 'thingification of processes' because the former sounds pretentious. And the latter doesn't? Hmm. It was interesting that the very next book I read - and which I'm bogged down in - Lyotard on postmodernism, used 'reification' in the foreword. I was pleased Stewart had explained it here.)
I was a little disappointed that Stewart presented the book in a way that suggested all mathematicians would be agreement with his views. For instance, on pg 39, he describes mathematicians as creators. That's certainly a valid perspective. However, many other mathematicians would see it differently: they see themselves as explorers. They see mathematics as being 'discovered', not 'invented'. There's a huge philosophical chasm there.
Stewart points out the meaning of "solve" has undergone change over time. (pg 56) His comments on Keynes' comments about Isaac Newton as the last wonderchild of the old order, rather than the first of the new, reminded me strongly of Arthur Koestler's comments on Copernicus in the brilliant The Sleepwalkers: A History of Man's Changing Vision of the Universe.
I would have liked to have seen more on the Feigenbaum constants, including their possible approximation by expressions involving the golden ratio.
A fine introduction, whether you know a lot or a little about mathematics.
I was a little disappointed that Stewart presented the book in a way that suggested all mathematicians would be agreement with his views. For instance, on pg 39, he describes mathematicians as creators. That's certainly a valid perspective. However, many other mathematicians would see it differently: they see themselves as explorers. They see mathematics as being 'discovered', not 'invented'. There's a huge philosophical chasm there.
Stewart points out the meaning of "solve" has undergone change over time. (pg 56) His comments on Keynes' comments about Isaac Newton as the last wonderchild of the old order, rather than the first of the new, reminded me strongly of Arthur Koestler's comments on Copernicus in the brilliant The Sleepwalkers: A History of Man's Changing Vision of the Universe.
I would have liked to have seen more on the Feigenbaum constants, including their possible approximation by expressions involving the golden ratio.
A fine introduction, whether you know a lot or a little about mathematics.
May 14, 2008
Most people look at math these days - or I did, at least, for a long time - as something alienating and cold that professionals and quasi-sociopaths do because they're maladjusted and tend to enjoy escaping into abstraction. I guess that's a reactionary stereotype to the complementary idea that mathematicians are clairvoyant mystics who, in a process that involves obviously superior intellect and talents, transcribe the secrets of nature into a string of ever-impressive feats of accomplishment, usually serving the interests of freemasons and the illuminati. Either way they're reduced into comic book characters who are simultaneously grotesque, villainous and brilliant. Maybe they have to be that in order to capture the public imagination, for sinister purposes as yet unseen and also to assure at least a little bit of grant money. This is also a very States-based reading of myth creation. Ian Stweart is British, and in this book he runs around talking excitedly about for example the fact that the number of petals on a flower is regularly a part of the fibonacci sequence and how amazing a thing that is for all of us to think about with no more sinister intent than your pot-smoking friend in highschool had in coercing you to take a hit before he threw on "The Wall". They're both efforts at insisting that there are fascinating dimensions of experiencing reality worth exploring, and although they may not leave you with much else other than a dumbfounded expression , at least it was a well earned and very amused one.
January 10, 2017
This entertaining and very readable little book describes the relevance of mathematics for describing and appreciating nature. In the process it supplies quite a lot of curious information, some of which feeds into serious issues if you really want it to, but most of which is purely entertaining and easily accessible. It points out that mathematics is not simply about numbers, but also about shapes, patterns, regularities, transformations, and evolutions. There is nothing here to intimidate those with a maths phobia, a cuff about the ears for so called pragmatists who only want to hear about so called “applied” or “useful” mathematics, and a stern reproof for those scientists too arrogant to acknowledge the contribution mathematics makes to their fields.
A few signs of the book’s age are amusing but do not affect its quality at all. “But the next time you go jogging wearing a Walkman, or switch on your TV, or watch a videotape, pause for a few seconds to remember that without mathematics none of these marvels would ever have been invented.” [p72]
It can be amusingly gross: “Nature prefers the icosahedrons above all other viral forms: examples include herpes, chickenpox, human wart, canine infectious hepatitis, turnip yellow mosaic, adenovirus and many others.” [p82]
Mathematics is not only about numbers.
“It’s time we started pulling the bits together, Because only then will we truly understand nature’s numbers – along with nature’s shapes, structures, behaviours, interactions, processes, developments, metamorphoses, evolutions, revolutions...” [p150]
“Notice that this approach again changes the meaning of “solve.” First that word meant “find a formula.” Then its meaning changed to “find approximate numbers.” Finally, it has in effect become “tell me what the solutions look like.” In place of quantitative answers, we seek qualitative ones. ... Why did people want a formula in the first place? Because in the early days of dynamics, that was the only way to work out what kind of motion would occur. Later, the same information could be deduced from approximations. Nowadays, it can be obtained from theories that deal directly and precisely with the main qualitative aspects of the motion. ... For the first time we are starting to understand nature’s patterns in their own terms.” [p59]
It is suitably irate about popular notions of ‘usefulness.’
“... two of the main things that mathematics is for: providing tools that let scientists calculate what nature is doing, and providing new questions for mathematicians to sort out to their own satisfaction. These are the external and internal aspects of mathematics, often referred to as applied and pure mathematics. (I dislike both adjectives and I dislike the implied separation even more.) “ [p17]
“Engineers designing a bridge are entitled to use standard mathematical methods even if they don’t know the detailed and often esoteric reasoning that justifies these methods. But I, for one, would feel uncomfortable driving across that bridge if I was aware that nobody knew what justified those methods. So, on a cultural level, it pays to have some people who worry about pragmatic methods and try to find out what really makes them tick.” [p18]
“One of the strangest features of the relationship between mathematics and the “real world,” but also one of the strongest, is that good mathematics, whatever its source, eventually turns out to be useful.” [p18]
“...it is ...very tempting to assume that the only useful part of mathematics is applied mathematics; after all, that is what the name seems to apply... But it gives a very distorted view of the origins of new mathematics of practical importance. Good ideas are rare, but they come at least as often from imaginative dreams about the internal structure of mathematics as they do from attempts to solve a specific, practical problem.” [p62]
I was interested in a brief comment on mathematical reasoning.
“A great deal of work in philosophy and the foundations of mathematics has established that you can’t prove everything, because you have to start somewhere; and even when you’ve decided where to start, some statements may be neither provable nor disprovable.”
Textbooks of mathematical logic say that a proof is a sequence of statements, each of which either follows from previous statements or from agreed axioms – unproved but explicitly stated assumptions that in effect define the area of mathematics being studied. This is about as informative as describing a novel as a sequence of sentences, each of which either sets up an agreed context or follows credibly from previous sentences. Both definitions miss the essential point: that both a proof and a novel must tell an interesting story.” [p39]
A nice aside about the nature of creativity:
“ ... some of the emotional experiences of the creative mathematician: frustration at the intractability of what ought to be an easy question, elation when light dawned, suspicion as you checked whether there were any holes in the argument, aesthetic satisfaction when you decided the idea really was O.K. and realized how neatly it cut through all the apparent complications. Creative mathematics is just like this - ...” [p43]
A long account of symmetry and the breaking of symmetry is capable of informing many debates about cosmology. Sadly I have abandoned such internet debates as a waste of my time.
“In short, nature is symmetric because we live in a mass-produced universe ... Every electron is exactly the same as every other electron, every proton is exactly the same as every other proton, every region of empty space is exactly the same as every other region of empty space, every instant of time is exactly the same as every other instant of time. And not only are the structures of space, time and matter the same everywhere: so are the laws that govern them. ... At the instant of the universe’s formation, all places and all times were not only indistinguishable but identical. So why are they different now? [p84,85]
The answer is the ... principle of symmetry breaking... The evolving universe can break the initial symmetries of the big bang... Potentially, the universe could exist in any of a huge symmetric system of possible states, but actually it must select one of them. In so doing, it must trade some of its actual symmetry for unobservable, potential symmetry... the important point is that the tiniest departure from symmetry in the cause can lead to a total loss of symmetry in the resulting effect – and there are always tiny departures. ... Small disturbances cause the real system to select states from the range available to the idealized perfect system. "[p85, 86]
“There is so much symmetry ... in our mass produced universe that there is seldom a good reason to break all of it. So rather a lot survives... the symmetries we observe in nature are the broken traces of the grand, universal symmetries of our mass produced universe. “ [p85]
“This universality of symmetry breaking explains why living systems and non-living ones have many patterns in common. Life itself is a process of symmetry creation – of replication: the universe of biology is just as mass-produced as the universe of physics... The most obvious symmetries of living organisms are those of form – icosahedral viruses, the spiral shell of Nautilus, the helical horns of gazelles, the remarkable rotational symmetries of starfish and jellyfish and flowers.” [p88]
“In short there is an ideal mathematical universe in which all of the fundamental forces are related in a perfectly symmetrical manner – but we don’t live in it.” [p90]
I was fascinated by an account of the way animals deploy their limbs in order to move about efficiently. It actually has a bearing on a quite significant problem in the history of art, which was the difficulty artists had painting a realistic horse in action. The fact is that, up to the nineteenth century, nobody knew in sufficient detail how they moved their legs. Really, I was tempted to type up even more of this material but there has to be some limit.
“Two biologically distinct but mathematically similar types of oscillator are involved in locomotion. The most obvious are the animal’s limbs ... The main oscillators that concern us here, however, are to be found in the creature’s nervous system... A lot of what we do know has been arrived at by working backward – or forward if you like – from mathematical models.” [p98, 99]
Some animals possess only one gait... The elephant, for example, can only walk... Other animals possess many different gaits; ... The seven most common quadrupedal gaits are the trot, pace, bound, walk, rotary gallop, transverse gallop and canter. ... There is also a rarer gait, the plonk, in which all four legs move simultaneously.... sometimes seen in young deer. The pace is observed in camels, the bound in dogs, cheetahs use the rotary gallop to travel at top speed. Horses are among the more versatile quadrupeds, using the walk, trot, transverse gallop and canter, depending on circumstances.” [p99, 100].
In general, we can learn a lot about nature by thinking in mathematical language. This is a necessary corrective, for example, to the excessive claims made for genetics, still the easy, fashionable answer to everything and hence to nothing.
“...mathematics can illuminate many aspects of nature that we do not normally think of as being mathematical. This is a message that goes back to the Scottish zoologist D’Arcy Thompson, whose classic but maverick book On growth and Form set out, in 1917, an enormous variety of more or less plausible evidence for the role of mathematics in the generation of biological form and behaviour. In an age when most biologists seem to think that the only interesting thing about an animal is its DNA sequence, it is a message that needs to be repeated, loudly and often.” [p105]
“Plants don’t need their genes to tell them how to space their primordia: that’s done by the dynamics. It’s a partnership of physics and genetics and you need both to understand what’s happening.” [p142]
In short, Ian Stewart has the gift of being able to make mathematics accessible and relevant in an entertaining manner. A short enough book, this was a pleasure to read and will remain on my shelves for future reference.
A few signs of the book’s age are amusing but do not affect its quality at all. “But the next time you go jogging wearing a Walkman, or switch on your TV, or watch a videotape, pause for a few seconds to remember that without mathematics none of these marvels would ever have been invented.” [p72]
It can be amusingly gross: “Nature prefers the icosahedrons above all other viral forms: examples include herpes, chickenpox, human wart, canine infectious hepatitis, turnip yellow mosaic, adenovirus and many others.” [p82]
Mathematics is not only about numbers.
“It’s time we started pulling the bits together, Because only then will we truly understand nature’s numbers – along with nature’s shapes, structures, behaviours, interactions, processes, developments, metamorphoses, evolutions, revolutions...” [p150]
“Notice that this approach again changes the meaning of “solve.” First that word meant “find a formula.” Then its meaning changed to “find approximate numbers.” Finally, it has in effect become “tell me what the solutions look like.” In place of quantitative answers, we seek qualitative ones. ... Why did people want a formula in the first place? Because in the early days of dynamics, that was the only way to work out what kind of motion would occur. Later, the same information could be deduced from approximations. Nowadays, it can be obtained from theories that deal directly and precisely with the main qualitative aspects of the motion. ... For the first time we are starting to understand nature’s patterns in their own terms.” [p59]
It is suitably irate about popular notions of ‘usefulness.’
“... two of the main things that mathematics is for: providing tools that let scientists calculate what nature is doing, and providing new questions for mathematicians to sort out to their own satisfaction. These are the external and internal aspects of mathematics, often referred to as applied and pure mathematics. (I dislike both adjectives and I dislike the implied separation even more.) “ [p17]
“Engineers designing a bridge are entitled to use standard mathematical methods even if they don’t know the detailed and often esoteric reasoning that justifies these methods. But I, for one, would feel uncomfortable driving across that bridge if I was aware that nobody knew what justified those methods. So, on a cultural level, it pays to have some people who worry about pragmatic methods and try to find out what really makes them tick.” [p18]
“One of the strangest features of the relationship between mathematics and the “real world,” but also one of the strongest, is that good mathematics, whatever its source, eventually turns out to be useful.” [p18]
“...it is ...very tempting to assume that the only useful part of mathematics is applied mathematics; after all, that is what the name seems to apply... But it gives a very distorted view of the origins of new mathematics of practical importance. Good ideas are rare, but they come at least as often from imaginative dreams about the internal structure of mathematics as they do from attempts to solve a specific, practical problem.” [p62]
I was interested in a brief comment on mathematical reasoning.
“A great deal of work in philosophy and the foundations of mathematics has established that you can’t prove everything, because you have to start somewhere; and even when you’ve decided where to start, some statements may be neither provable nor disprovable.”
Textbooks of mathematical logic say that a proof is a sequence of statements, each of which either follows from previous statements or from agreed axioms – unproved but explicitly stated assumptions that in effect define the area of mathematics being studied. This is about as informative as describing a novel as a sequence of sentences, each of which either sets up an agreed context or follows credibly from previous sentences. Both definitions miss the essential point: that both a proof and a novel must tell an interesting story.” [p39]
A nice aside about the nature of creativity:
“ ... some of the emotional experiences of the creative mathematician: frustration at the intractability of what ought to be an easy question, elation when light dawned, suspicion as you checked whether there were any holes in the argument, aesthetic satisfaction when you decided the idea really was O.K. and realized how neatly it cut through all the apparent complications. Creative mathematics is just like this - ...” [p43]
A long account of symmetry and the breaking of symmetry is capable of informing many debates about cosmology. Sadly I have abandoned such internet debates as a waste of my time.
“In short, nature is symmetric because we live in a mass-produced universe ... Every electron is exactly the same as every other electron, every proton is exactly the same as every other proton, every region of empty space is exactly the same as every other region of empty space, every instant of time is exactly the same as every other instant of time. And not only are the structures of space, time and matter the same everywhere: so are the laws that govern them. ... At the instant of the universe’s formation, all places and all times were not only indistinguishable but identical. So why are they different now? [p84,85]
The answer is the ... principle of symmetry breaking... The evolving universe can break the initial symmetries of the big bang... Potentially, the universe could exist in any of a huge symmetric system of possible states, but actually it must select one of them. In so doing, it must trade some of its actual symmetry for unobservable, potential symmetry... the important point is that the tiniest departure from symmetry in the cause can lead to a total loss of symmetry in the resulting effect – and there are always tiny departures. ... Small disturbances cause the real system to select states from the range available to the idealized perfect system. "[p85, 86]
“There is so much symmetry ... in our mass produced universe that there is seldom a good reason to break all of it. So rather a lot survives... the symmetries we observe in nature are the broken traces of the grand, universal symmetries of our mass produced universe. “ [p85]
“This universality of symmetry breaking explains why living systems and non-living ones have many patterns in common. Life itself is a process of symmetry creation – of replication: the universe of biology is just as mass-produced as the universe of physics... The most obvious symmetries of living organisms are those of form – icosahedral viruses, the spiral shell of Nautilus, the helical horns of gazelles, the remarkable rotational symmetries of starfish and jellyfish and flowers.” [p88]
“In short there is an ideal mathematical universe in which all of the fundamental forces are related in a perfectly symmetrical manner – but we don’t live in it.” [p90]
I was fascinated by an account of the way animals deploy their limbs in order to move about efficiently. It actually has a bearing on a quite significant problem in the history of art, which was the difficulty artists had painting a realistic horse in action. The fact is that, up to the nineteenth century, nobody knew in sufficient detail how they moved their legs. Really, I was tempted to type up even more of this material but there has to be some limit.
“Two biologically distinct but mathematically similar types of oscillator are involved in locomotion. The most obvious are the animal’s limbs ... The main oscillators that concern us here, however, are to be found in the creature’s nervous system... A lot of what we do know has been arrived at by working backward – or forward if you like – from mathematical models.” [p98, 99]
Some animals possess only one gait... The elephant, for example, can only walk... Other animals possess many different gaits; ... The seven most common quadrupedal gaits are the trot, pace, bound, walk, rotary gallop, transverse gallop and canter. ... There is also a rarer gait, the plonk, in which all four legs move simultaneously.... sometimes seen in young deer. The pace is observed in camels, the bound in dogs, cheetahs use the rotary gallop to travel at top speed. Horses are among the more versatile quadrupeds, using the walk, trot, transverse gallop and canter, depending on circumstances.” [p99, 100].
In general, we can learn a lot about nature by thinking in mathematical language. This is a necessary corrective, for example, to the excessive claims made for genetics, still the easy, fashionable answer to everything and hence to nothing.
“...mathematics can illuminate many aspects of nature that we do not normally think of as being mathematical. This is a message that goes back to the Scottish zoologist D’Arcy Thompson, whose classic but maverick book On growth and Form set out, in 1917, an enormous variety of more or less plausible evidence for the role of mathematics in the generation of biological form and behaviour. In an age when most biologists seem to think that the only interesting thing about an animal is its DNA sequence, it is a message that needs to be repeated, loudly and often.” [p105]
“Plants don’t need their genes to tell them how to space their primordia: that’s done by the dynamics. It’s a partnership of physics and genetics and you need both to understand what’s happening.” [p142]
In short, Ian Stewart has the gift of being able to make mathematics accessible and relevant in an entertaining manner. A short enough book, this was a pleasure to read and will remain on my shelves for future reference.
May 31, 2021
An interesting concept, a book about mathematics with almost no math in it. Instead, it is about how mathematics reveals itself in the symmetries that exist at every scale. Like evolution, symmetry is not consciously directed, but is the result of underlying forces which arrange themselves according to fundamental laws of physics. Snowflakes may appear beautiful to our eyes (which brings to mind another question: why do our minds find symmetry appealing?), but they are that way because of their hydrogen/oxygen structure, which limit the ways they can bond together with other water molecules.
There are number patterns, such as the Fibonacci sequence, and shape patterns, such as the spirals in a seashell. Each has a story to tell, and some interesting ideas to reveal about the deep structure of matter. It is startling to think that some of the same self-symmetries revealed in atomic structures repeat at the level of galaxies. There is a chapter on chaos theory, irreverently called, “Do Dice Play God,” which looks at the the forces that shape the world around us. It would be interesting to use it as a starting point for a discussion of free will versus determinism.
The book does not spend time on philosophical discussions, so its main appeal is in its examples of patterns and symmetries. The author does a good job on these, and manages to add some interesting facts to each of them, so the reader frequently pauses and thinks, “Hmm, I didn’t realize that.” For instance, there is the idea of broken symmetry; a perfectly flat pond is not very interesting, but toss a pebble into it and the second order symmetry of the the waves expanding outward easily holds our attention.
Math provides the structure that helps us understand nature’s patterns; it reveals clues that we can follow to help unlock secrets. This book is a fun excursion for anyone with an interest in the deep symmetries of time and space.
There are number patterns, such as the Fibonacci sequence, and shape patterns, such as the spirals in a seashell. Each has a story to tell, and some interesting ideas to reveal about the deep structure of matter. It is startling to think that some of the same self-symmetries revealed in atomic structures repeat at the level of galaxies. There is a chapter on chaos theory, irreverently called, “Do Dice Play God,” which looks at the the forces that shape the world around us. It would be interesting to use it as a starting point for a discussion of free will versus determinism.
The book does not spend time on philosophical discussions, so its main appeal is in its examples of patterns and symmetries. The author does a good job on these, and manages to add some interesting facts to each of them, so the reader frequently pauses and thinks, “Hmm, I didn’t realize that.” For instance, there is the idea of broken symmetry; a perfectly flat pond is not very interesting, but toss a pebble into it and the second order symmetry of the the waves expanding outward easily holds our attention.
Math provides the structure that helps us understand nature’s patterns; it reveals clues that we can follow to help unlock secrets. This book is a fun excursion for anyone with an interest in the deep symmetries of time and space.
September 18, 2014
Worthwhile account of mathematic's vital role in describing natural parameters that shape processes including evolution, genetics and the formation of matter. Stewart argues passionately that it's math damn it that reveals the fundamental, inescapable foundation of the universe.
While the book was uneven, going occasionally on long detours and other times brief stops at interesting patterns, the overall effort was rewarding. I like the fact that Stewart is more interested in the future of math, what he hopes will be new ways to look at shapes and patterns in what he terms 'morphomatics'.
I was hoping he would get into Fibonacci numbers and the golden ratio and he did, explaining not only the facts but how they were discovered and ongoing experiments surrounding them. There is a chapter on broken symmetry which I found fascinating. I can't explain it but I found it fascinating.
The book is very concerned with chaos theory which was emerging around the time this was written, 1995. The idea that apparent chaos can be recognized as having a deterministic origin was well explored. He gives as an example a ping pong ball in an ocean storm. Without knowing where the ball was released and without any ability to predict where the ball will go next, this seeming chaos has some qualities we can recognize. The ball will always be on the surface of the ocean. The surface is its 'strange attractor'.
While the book was uneven, going occasionally on long detours and other times brief stops at interesting patterns, the overall effort was rewarding. I like the fact that Stewart is more interested in the future of math, what he hopes will be new ways to look at shapes and patterns in what he terms 'morphomatics'.
I was hoping he would get into Fibonacci numbers and the golden ratio and he did, explaining not only the facts but how they were discovered and ongoing experiments surrounding them. There is a chapter on broken symmetry which I found fascinating. I can't explain it but I found it fascinating.
The book is very concerned with chaos theory which was emerging around the time this was written, 1995. The idea that apparent chaos can be recognized as having a deterministic origin was well explored. He gives as an example a ping pong ball in an ocean storm. Without knowing where the ball was released and without any ability to predict where the ball will go next, this seeming chaos has some qualities we can recognize. The ball will always be on the surface of the ocean. The surface is its 'strange attractor'.
February 9, 2011
Interesting and very simple explanation of how basic mathematics (not addition, multiplication, etc. but rather patterns, symmetry, rhythms, and chaos) are essential to the structure of nature. It was written in a very accessible manner and kind of reminded be of a NOVA episode. Best of all, I put the book down feeling like I actually understand what chaos theory is about (at a very basic level). I almost gave this 4-stars; but it's simplicity and lack of depth kind of knocked it down to "like it" rather than "really liked it" for me, but it really is a great succinct book on how math is the base of nature.
January 27, 2012
This is a math book with hardly any math in it. The author (whom I normally enjoy) attempts to use solely prose to prove mathematical concepts inundated with numbers and calculations. Trying to side-step the math actually makes the book a lot drier than it could have been. A simple equation or graph in the right place would have made the book more succinct in places. (Of course, this is coming from a confessed math nerd.)
Books on chaos and Fibonacci numbers abound... I'd steer away from this if that's your interest.
Books on chaos and Fibonacci numbers abound... I'd steer away from this if that's your interest.
January 27, 2019
For someone like me who stopped formally learning mathematics around trigonometry, this book was a remarkable next step in my math education. I finally understood what calculus actually is, and got a good introduction to Chaos Theory (hint: it's not really chaotic, it just appears to be.)
Highly recommended for people who want to understand math better, and how it is actually applied in the "real" world.
Highly recommended for people who want to understand math better, and how it is actually applied in the "real" world.
January 8, 2024
Disclaimer: another charity shop pick
A great book for anyone with an idea of mathematical theory, unfortunately I don’t. The imagery is really good and it kept my attention just enough to finish it (thank god it was only 170pages or something.)
Not every charity shop book is a good fit.
Can’t win ‘em all, just most of ‘em
A great book for anyone with an idea of mathematical theory, unfortunately I don’t. The imagery is really good and it kept my attention just enough to finish it (thank god it was only 170pages or something.)
Not every charity shop book is a good fit.
Can’t win ‘em all, just most of ‘em
March 4, 2024
good book if you want to fall asleep quickly
February 14, 2023
I found this book really interesting. As a book on mathematics goes it isn't very technical. You don't need a math background to understand the book and its concepts. The book basically demonstrates how math is engrained in the world around us. If you are more familiar with mathematics there isn't going to be anything new or novel addressed in the book. But it is a nice summary of how different branches of mathematics, such as chaos theory, are used to describe the world around us. It will make you think about the structure of nature and the hidden rules that make things look and act like they do. I definitely recommend it.
September 1, 2017
I always felt atracted to the simple question weather math was created or invented. Although I'm pretty convinced it's an invention, created to serve as a tool that establishes the bridge between man and nature, I wanted some arguments on the question and to learn more about it, so this book seemed a good way to do that.
I think the autor covers very interesting subjects, much of them unknown to me to the date, and does what he proposes to do in the beginning of the book. More importantly, I really liked that he assumes a position instead of being just a narrator in his text. That way I feel more attracted to the discussion, by having to deal with certain positions that the author assumes, which some of them I agree, others I don't.
Other thing, although he clearly made an effort to slowly increase the complexity of the themes he was discussing, so that the reader can adapt better to the subjects and to be "readable" also by people who are not so familiar with mathematics in general, maybe he had passed a little bit to much here and there the simplicity desirable on this kind of texts. But that's just my opinion, and I read in other reviews that some people think that some parts of the text are to basic. I think that's not the case, since people who are not famialrized with these terms must first be confronted with the "basic" to maybe understand more complex parts.
Even though, I think it's a fun book where you can learn some new stuff and give some thought to matters who are apperntly absent, but in fact, very present in our daily lives.
I think the autor covers very interesting subjects, much of them unknown to me to the date, and does what he proposes to do in the beginning of the book. More importantly, I really liked that he assumes a position instead of being just a narrator in his text. That way I feel more attracted to the discussion, by having to deal with certain positions that the author assumes, which some of them I agree, others I don't.
Other thing, although he clearly made an effort to slowly increase the complexity of the themes he was discussing, so that the reader can adapt better to the subjects and to be "readable" also by people who are not so familiar with mathematics in general, maybe he had passed a little bit to much here and there the simplicity desirable on this kind of texts. But that's just my opinion, and I read in other reviews that some people think that some parts of the text are to basic. I think that's not the case, since people who are not famialrized with these terms must first be confronted with the "basic" to maybe understand more complex parts.
Even though, I think it's a fun book where you can learn some new stuff and give some thought to matters who are apperntly absent, but in fact, very present in our daily lives.
June 14, 2017
It says something when I find it hard to put down a book about math and silently promise myself, "Just one more page, then I'll go to sleep...". Fortunately, the author breaks the topics up well between chapters, so it prevented me from pulling an all nighter...I won't say there are no cliffhangers in math and science, but, at least, there were no cliff hangers in this book.
Still, this book was riveting and eye opening. As a person who is recently reforming a lifelong disillusionment with math and trying to build a relationship of mutual understanding, this book did wonders to show me, well, the wonder of mathematics. It was fascinating to see just how many things in nature are governed by the rules of the universe which can be explained through the language of math. The author does a great job of explaining complex theories and concepts in a way that is easy to understand using real world examples, They don't go too in depth, but hey, it's a 150 page book. It has left me with a long list of things for further study!
Still, this book was riveting and eye opening. As a person who is recently reforming a lifelong disillusionment with math and trying to build a relationship of mutual understanding, this book did wonders to show me, well, the wonder of mathematics. It was fascinating to see just how many things in nature are governed by the rules of the universe which can be explained through the language of math. The author does a great job of explaining complex theories and concepts in a way that is easy to understand using real world examples, They don't go too in depth, but hey, it's a 150 page book. It has left me with a long list of things for further study!
May 3, 2013
The highest level of math I learned was Statistics -- which I thought was easier than Algebra II. Even at my level of understanding of mathematics, this book was totally lucid, not to mention it was a flat out blast to read. I never knew I could like math this much! I felt as if I was taken on an adventure through the strange realities of the universe, and I didn't want it to end. There was something worth remembering in every chapter. I will definitely be picking up any book by Ian Stewart in the future.
August 15, 2018
Interesting book although it is quite old now. The chaos theory and butterfly effect has rekindled my interest in pure mathematics and science. There is also mention of very interesting nature's numbers like pi, Fibonacci numbers, golden number/golden angle (√5-1)/2 or 137.5° and Feigenbaum's number (~4.669) and how these numbers form patterns in nature. Some facts like how flower petals are usually Fibonacci numbers were quite interesting. Overall I felt the book was a bit short. I will definitely consider reading more of Ian Stewart's work in future.
This entire review has been hidden because of spoilers.
February 10, 2022
Incredible.
When I picked up my first Ian Stewart book about "popular" mathematics I had no idea what I was in store for. Now, some 5 (or more) books of his later, I am happy to report that his works are excellent.
If you're in the field or study for fun, then Stewart's books can help fill in a lot of blanks. Regularly do historical examples he cites pop up in other books I am simultaneously reading/listening to.
This one is grand, and holds some very interesting nuggets. This book was where I first heard of the Chaos constant, the transcendental Feigenbaum number.
Read it!
Rav.
When I picked up my first Ian Stewart book about "popular" mathematics I had no idea what I was in store for. Now, some 5 (or more) books of his later, I am happy to report that his works are excellent.
If you're in the field or study for fun, then Stewart's books can help fill in a lot of blanks. Regularly do historical examples he cites pop up in other books I am simultaneously reading/listening to.
This one is grand, and holds some very interesting nuggets. This book was where I first heard of the Chaos constant, the transcendental Feigenbaum number.
Read it!
Rav.
February 1, 2018
I am not a mathematician; the highest course I have had is introductory calculus. Stewart explores the role of mathematics in nature (or perhaps its the other way round), starting with counting numbers and working up to chaos theory. The first four chapters were intelligible, and in fact his explanation of calculus made more sense to me than anything I have previously encountered. Much of the rest was an interesting narrative, but just a bit beyond my grasp.
December 5, 2020
This book helped me understand what math actually aspires to, which is very different from anything I learned in school. I found interesting the discussion on how deviations in symmetry magnify exponentially over time - which I think is another (more rigorous) way of saying something Coach K once said - “everything you do is important because you do it”. Very true. Also interested in learning more about applications of phase space
November 8, 2020
I did find a few concepts quite interesting such as the idea of broken symmetry and phase space. However, I found the examples and ideas were a bit disconnected sometimes. Long narrative of instances did not sound very appealing to me.
I do believe the author tried a good story telling but I found it a bit not as interesting
I do believe the author tried a good story telling but I found it a bit not as interesting
January 27, 2012
As stated on the back cover, a book "aimed at the educated but non specialist reader". Although I don't see myself as a specialist, I didn't learn much from it. It is more a long article for a scientific magazine than a real book.
December 25, 2021
A really cool book to appreciate mathematics without getting bogged down in technicalities, and also a fast read. I found his explanations of chaos theory and locomotion to be less clear than the other chapters
January 18, 2022
I do not like math and I only ever use it with statistics which sucks or art which is tedious but this book made me appreciate its beauty. I still don’t want to do math but I dislike it less thanks to this book
November 3, 2016
I've been thinking of the cicadas ever since I put this book down.
September 5, 2020
Easy to read, but I liked Ian Stewart's "Concepts of Modern Mathematics" much more.
August 31, 2021
love it
January 3, 2022
Enjoyed the concept of spontaneous symmetry breaking.
June 19, 2022
This popular mathematics book reflects upon the ways in which patterns appear in nature and how mathematics can shed light on said patterns. It explores why tides are predictable while weather patterns are anything but. It investigates why flowers disproportionately have a number of petals that is in the Fibonacci sequence (a list of numbers in which each is formed through the addition of the previous two numbers.) It shows one how an eyeball can evolve, and how long it would be expected to take. It describes where and how we see calculus, probability and statistic, chaos theory, and complexity in nature.
It’s unambiguously a pop math book, there’s not an equation in sight. It does use diagrams and various graphics to convey ideas, and these help to simplify and visualize the topic. If anything, I would say the book could have benefited from more graphics [and might even have benefited from a less strict rule about sticking to colloquial prose.] (Meaning, some of the analogies and attempts to relate clarified ideas better than others.)
I found the book highly readable, and believe that – overall – the author did a fine job of providing food for thought without getting too complicated for the general reader. There were points at which the author seemed to lose his train. For example, he off-ramped into criticisms of the division of mathematics into applied and theoretical branches and the tendency to more greatly value the applied side of this false dichotomy. I have no doubt this is a worthwhile subject of discussion, but not necessarily in this book.
If you’re looking for a readable discussion of how mathematics is used in the study of nature, this book is worth reading – especially if you are equation-phobic.
It’s unambiguously a pop math book, there’s not an equation in sight. It does use diagrams and various graphics to convey ideas, and these help to simplify and visualize the topic. If anything, I would say the book could have benefited from more graphics [and might even have benefited from a less strict rule about sticking to colloquial prose.] (Meaning, some of the analogies and attempts to relate clarified ideas better than others.)
I found the book highly readable, and believe that – overall – the author did a fine job of providing food for thought without getting too complicated for the general reader. There were points at which the author seemed to lose his train. For example, he off-ramped into criticisms of the division of mathematics into applied and theoretical branches and the tendency to more greatly value the applied side of this false dichotomy. I have no doubt this is a worthwhile subject of discussion, but not necessarily in this book.
If you’re looking for a readable discussion of how mathematics is used in the study of nature, this book is worth reading – especially if you are equation-phobic.
April 21, 2021
Trăim Într-un univers de forme. În fiecare noapte, stelele se mişcă pe cer pe traiectorii circulare. Anotimpurile au cicluri anuale. Nici un fulg de zăpadă nu este exact identic cu vreun altul, dar toţi fulgii au o simetrie hexagonală. Tigrii şi zebrele sînt acoperiţi cu desene dungate, leoparzii şi hienele au pete. Trenuri de unde complicate străbat oceanele; forme asemănătoare de valuri traversează deșertul. Arce colorate de lumină împodobesc cerul sub formă de curcubee şi un halou circular strălucitor înconjoară uneori luna în nopţile de iarnă. Din nori cad picături sferice de apă. Mintea si cultura omului au dezvoltat un sistem formal de gândire pentru recunoaşterea, clasificarea şi folosirea formelor, sistem pe care l-am numit matematică. Folosind matematica pentru organizarea şi sistematizarea ideilor noastre despre forme, am descoperit un mare secret: formele naturii nu se află acolo tocmai pentru a fi admirate, ci sînt de fapt indiciile vitale ale regulilor care guvernează procesele naturale.
July 6, 2019
A really cool popscience book about mathematics. Unfortunately it was butchered mercilessly by the Polish translator. I need to get a copy in English to finish it, because it's unreadable in Polish...
Świetna książka popularnonaukowa. Przedstawia pojęcia i zagadnienia matematyczne w bardzo przystępny sposób.
Niestety tłumaczenie to koszmar. Nie da się tego czytać. Miejscami miałam wrażenie, że tłumacz używał Google Translate.
Na przykład:
1.Zabawa Statek/Dok (gra słów: 'doprowadzenie statku do doku'...) przetłumaczona na Statek/Szczaw...
2."Hand-waving argument" przetłumaczone na "argumentacja oparta na wymachiwaniu rękoma"...
3. √2 zapisane jako V2 ?! (Czy tę książkę edytowano w notatniku?)
Na koniec tłumaczenie, po którym książkę odłożyłam (i już do niej w tej wersji językowej nie wrócę): "all is flux, all is change" -> "wszystko jest PRZEPŁYWEM i zmianą".
Naprawdę CCPress? Naprawdę?!
Świetna książka popularnonaukowa. Przedstawia pojęcia i zagadnienia matematyczne w bardzo przystępny sposób.
Niestety tłumaczenie to koszmar. Nie da się tego czytać. Miejscami miałam wrażenie, że tłumacz używał Google Translate.
Na przykład:
1.Zabawa Statek/Dok (gra słów: 'doprowadzenie statku do doku'...) przetłumaczona na Statek/Szczaw...
2."Hand-waving argument" przetłumaczone na "argumentacja oparta na wymachiwaniu rękoma"...
3. √2 zapisane jako V2 ?! (Czy tę książkę edytowano w notatniku?)
Na koniec tłumaczenie, po którym książkę odłożyłam (i już do niej w tej wersji językowej nie wrócę): "all is flux, all is change" -> "wszystko jest PRZEPŁYWEM i zmianą".
Naprawdę CCPress? Naprawdę?!
December 24, 2019
Niektóre rozdziały tej książki czytało mi się niezwykle przyjemnie. Mimo, iż nie znam się za bardzo na matematyce ani fizyce, nie byłam zagubiona i czerpałam radość z czytania.
Niestety znalazło się też kilka rozdziałów, w których od początku nie umiałam się odnaleźć.
Największą zaletą tej publikacji jest to, że autor w przystępny sposób wyraża swoje myśli; podaje czytelnikowi klarowne informacje. Jeżeli dana kwestia jest "bardziej skomplikowana" przedstawia ją na prostych przykładach, zaczerpniętych z życia codziennego.
Jak każdej książki popularnonaukowej, nie radzę czytać "na raz", ale podzielić sobie jej lekturę, aby jak najwięcej z niej przyswoić.
Jeżeli nie interesuje Was sam temat; matematyka oraz fizyka, odradzam- wówczas możecie się wymęczyć.
Lektura tej książki bardzo mi się spodobała i mam nadzieję, że często będę do niej wracać.
Niestety znalazło się też kilka rozdziałów, w których od początku nie umiałam się odnaleźć.
Największą zaletą tej publikacji jest to, że autor w przystępny sposób wyraża swoje myśli; podaje czytelnikowi klarowne informacje. Jeżeli dana kwestia jest "bardziej skomplikowana" przedstawia ją na prostych przykładach, zaczerpniętych z życia codziennego.
Jak każdej książki popularnonaukowej, nie radzę czytać "na raz", ale podzielić sobie jej lekturę, aby jak najwięcej z niej przyswoić.
Jeżeli nie interesuje Was sam temat; matematyka oraz fizyka, odradzam- wówczas możecie się wymęczyć.
Lektura tej książki bardzo mi się spodobała i mam nadzieję, że często będę do niej wracać.
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