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Fearful Symmetry: Is God a Geometer?
This sequel to the bestselling Does God Play Dice? will open your eyes to the broken symmetries that lie all around you, from the shapes of clouds to the drops of dew on a spider's web, from centipedes to corn circles. It will take you to the farthest reaches of the universe and bring you face-to-face with some of the deepest questions of modern physics.
287 pages, Hardcover
First published June 1, 1992
8 people are currently reading
291 people want to read
About the author
Ian Stewart
270 books758 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 - 15 of 15 reviews
February 16, 2016
Going back to the beginning of the universe, we see examples of symmetry breaking-- from quarks to the various forms comprised of them. There seems to exist a fractal nature in how symmetry of any kind is broken. The breaking of symmetry that gave tigers their stripes is the same phenomenon that gave mass to energy (though the Higgs was discovered after Stewart's book). Ian Stewart examines the symmetry of life and non-life as it exists throughout the universe. I read this in tandem with Sean Carroll's lecture series on the Higgs. It was a great paring because Stewart focused on the history of symmetry, particularly highlighting Turing, as well as a plethora of examples of symmetry breaking. Carroll focused on how symmetry brought about mass in the first place. If I had read Stewart alone, I would have already been impressed with the wide survey of the symmetry and symmetry breaking that exists all around us and how it is connected to emergence. Coupled with Carroll's lectures, which provide the most up to date research on symmetry in fields, Stewart's book was even more enjoyable.
Stewart provided his reader with an understanding of what symmetry is, how to recognize it, and how to understand group theory. Each symmetry relies on gradients. Various perturbations can cause a symmetry to break. Often the patterns are hard to pin down. For example, unless you understand all the forces that act upon the object in question, you will have a difficult time understanding the full pattern. For example, if there is a periodicity at work, but there is another force or disturbance that affects the periodicity, you must understand it all as a system.
While reading examples that have been known about since Turing's time, I could not help but think about how the same pattern is at work in how cells forms memories so that, even though cells all have the same DNA, they know to develop into various cells such as a liver cell, a heart cell, and so on.
Stewart has a great talk that is more current than this book. I highly recommend it.
https://www.youtube.com/watch?v=_nZX4...
Stewart provided his reader with an understanding of what symmetry is, how to recognize it, and how to understand group theory. Each symmetry relies on gradients. Various perturbations can cause a symmetry to break. Often the patterns are hard to pin down. For example, unless you understand all the forces that act upon the object in question, you will have a difficult time understanding the full pattern. For example, if there is a periodicity at work, but there is another force or disturbance that affects the periodicity, you must understand it all as a system.
While reading examples that have been known about since Turing's time, I could not help but think about how the same pattern is at work in how cells forms memories so that, even though cells all have the same DNA, they know to develop into various cells such as a liver cell, a heart cell, and so on.
Stewart has a great talk that is more current than this book. I highly recommend it.
https://www.youtube.com/watch?v=_nZX4...
May 5, 2019
There's a fairly high probability that anyone who's interested in mathematics - either professionally or simply out of curiosity - has read one or more books by Ian Stewart. He's an accomplished professional mathematician with interests in many branches of the subject. But he's also a very good writer and expositor of diverse mathematical topics. Most of his books have been intended for general readers with an interest in mathematics. These include popular topics like chaos theory, the mathematics of biology, mathematical recreations, and mathematical curiosities. (His Wikipedia page lists about 36 books of this type.) But he's also written well about more advanced topics such as Galois theory and algebraic number theory.
One of Stewart's particular interests is "symmetry", which makes a lot of sense, because symmetry is a pervasive theme in mathematics - and has been for some time. Mathematically, symmetry is usually studied in terms of "transformations" that can be performed on an object and which leave the object essentially the "same", in some sense. Plane geometry (or geometry in any number of dimensions, for that matter) provides some of the most obvious examples. Consider an equilateral triangle (all of whose sides are the same length). Such a triangle can be rotated about its center in either 120 or 240 degrees and will look identical to how it did before rotation. Mathematically, a non-rotation (i. e. by 0 degrees) is also considered and, trivially, doesn't change a thing. The triangle can also be reflected across a line from any vertex to the middle of the opposite side. This is known, naturally, as "reflection" symmetry. Clearly, too, it makes no change at all to the triangle's appearance.
However, symmetry can also be considered in a more general sense in which a transformation does make some change to the appearance of an equilateral triangle, yet still leave it the "same" in a more relaxed sense. A transformation that only moves the triangle from one place to another changes nothing but the position, yet is still considered a transformation - one which could be applied to almost anything, not just an equilateral triangle. For example, a wallpaper design. A rotation about the center by any number of degrees can be considered a "symmetry" of the triangle - if you don't care about the direction the vertices point with respect to anything else in the plane. Expansion or contraction of the triangle changes only its size, and that doesn't affect any of its abstract geometric properties, such as the fact that the sum of the interior angles of the vertices is always 180 degrees. (That's true for any type of triangle with straight sides, not necessarily an equilateral one.)
It's possible to make even more drastic transformations to a triangle which can also be considered symmetries in a looser sense. For instance, the lengths of two sides could be doubled (or multiplied by any positive number), but the object would still be a triangle, with many properties unchanged, such as the sum its interior angles, or simply continuing to be a 3-sided polygon. Even more interestingly, transformations can be combined with each other and still yield a symmetry in the abstract sense. A certain limited number of combined transformations may still leave an equilateral triangle completely unchanged - reflections and rotations by multiples of 120 degrees, for example.
Sets of transformations that can be combined with each other are very important mathematical objects themselves - known as "groups". Stewart devotes the second chapter to a brief discussion of "group theory", but doesn't say much more about abstract groups in the remainder of the book. Groups are very interesting - but their theory can quickly become quite complicated and "deep". Group theory is a pervasive topic in modern mathematics, and has been for almost 200 years. Stewart doesn't go further with the subject or its history in the present book, but does in a later book: Why Beauty is Truth .
Instead, most of the book presently under discussion is concerned with cases where symmetry is "broken" - that is, when the appearance or some other aspect of a real-world object becomes different in some way. The object no longer has a perfect symmetry of some sort, but only one that is merely "approximate" - generally for understandable reasons. Consider an automobile - practically any kind. Almost all cars have a left-right mirror symmetry, which is a reflection in a vertical plane that runs through the center of the car from the front to the back. But it's not perfect, because the steering wheel and various switches and gauges on the dashboard are only on one side or the other. That's because hardly any cars now provide for anything except one single driver. (In addition, the layout of things under the hood is usually not symmetric either, since most cars have only one battery, alternator, etc.)
Humans and most other higher animals don't have perfect left-right symmetry either, for similar reasons. They typically have only one heart, liver, stomach, etc. - not in the exact center of the body - even though a few organs like kidneys and lungs are duplicated symmetrically, and the redundancy is useful. In principle, a car could be built that had nearly perfect bilateral symmetry. The seats for driver and passengers could be located in a straight line from front to back - as with fighter planes with more than one occupant. But the vehicle would then probably be much narrower (to avoid wasted space) - and consequently more likely to tip over when making sharp turns. So the upshot is that nature often finds it convenient to break "perfect" symmetries, even if only slightly.
Most of the rest of Stewart's book goes into many examples of this symmetry breaking. For instance, although most land animals with legs have, externally at least, bilateral symmetry, they are mostly unable to move at all unless the legs don't all move the same way at the same time. (Hopping animals like kangaroos are an exception, of course.) There's a whole chapter in the book about the different ways that animals move their legs in order to walk or run - and the pattern may change depending on how fast the animal needs or wants to go.
There's a whole chapter on the symmetry of crystals. A fascination with crystals (whether or not taken to unreasonable extremes) has been common in humans from prehistoric times - even before homo sapiens (as Stewart points out). All crystals have some sort of symmetry, at least in principle, though often "broken" - because of how their constituent atoms arrange themselves. The study of crystal symmetries was historically almost the earliest example of the use of group theory in science. Different minerals are in fact characterized by the types of symmetries their crystals may exhibit. The symmetries are usually slightly broken, due to asymmetries of the chemical environment in which the crystal grew. Randomness is pervasive in nature, but often leads to its own symmetries - such as the way that smoke entering one side of a room will quickly become distributed fairly evenly within the room.
Natural laws, such a gravity, have symmetries too. A rock tossed upwards at an angle will follow a symmetric parabola. A deep theorem, due to the mathematician Emmy Noether, explains how conservation laws (such conservation of energy and momentum, which govern the motion of tossed rocks) are a result of symmetries in the equations of physics.
Crystals aren't alive, but animals are, and they have symmetries too, even though usually only approximate (as noted above). Consider the stripes of a tiger. They are arranged, albeit rather irregularly, in a periodic sequence along the length of the animal's body - literally from head to tail. It turns out that this symmetry is a lot like the symmetry of ocean waves approaching a beach. (Periodic phenomena have deep mathematical generalizations: "harmonic analysis", in which group theory is of central importance. Consider how combinations of different frequencies of sound waves are what constitute music.) Animal patterns such as tiger stripes result from waves of chemical densities in the liquid medium inside very young embryos, because they affect gene expression. Alan Turing - the early computer scientist who conceived "Turing machines" - was apparently the first to suggest this, even before "genes" were actually understood. This story is told in another chapter of Stewart's book.
One of Stewart's particular interests is "symmetry", which makes a lot of sense, because symmetry is a pervasive theme in mathematics - and has been for some time. Mathematically, symmetry is usually studied in terms of "transformations" that can be performed on an object and which leave the object essentially the "same", in some sense. Plane geometry (or geometry in any number of dimensions, for that matter) provides some of the most obvious examples. Consider an equilateral triangle (all of whose sides are the same length). Such a triangle can be rotated about its center in either 120 or 240 degrees and will look identical to how it did before rotation. Mathematically, a non-rotation (i. e. by 0 degrees) is also considered and, trivially, doesn't change a thing. The triangle can also be reflected across a line from any vertex to the middle of the opposite side. This is known, naturally, as "reflection" symmetry. Clearly, too, it makes no change at all to the triangle's appearance.
However, symmetry can also be considered in a more general sense in which a transformation does make some change to the appearance of an equilateral triangle, yet still leave it the "same" in a more relaxed sense. A transformation that only moves the triangle from one place to another changes nothing but the position, yet is still considered a transformation - one which could be applied to almost anything, not just an equilateral triangle. For example, a wallpaper design. A rotation about the center by any number of degrees can be considered a "symmetry" of the triangle - if you don't care about the direction the vertices point with respect to anything else in the plane. Expansion or contraction of the triangle changes only its size, and that doesn't affect any of its abstract geometric properties, such as the fact that the sum of the interior angles of the vertices is always 180 degrees. (That's true for any type of triangle with straight sides, not necessarily an equilateral one.)
It's possible to make even more drastic transformations to a triangle which can also be considered symmetries in a looser sense. For instance, the lengths of two sides could be doubled (or multiplied by any positive number), but the object would still be a triangle, with many properties unchanged, such as the sum its interior angles, or simply continuing to be a 3-sided polygon. Even more interestingly, transformations can be combined with each other and still yield a symmetry in the abstract sense. A certain limited number of combined transformations may still leave an equilateral triangle completely unchanged - reflections and rotations by multiples of 120 degrees, for example.
Sets of transformations that can be combined with each other are very important mathematical objects themselves - known as "groups". Stewart devotes the second chapter to a brief discussion of "group theory", but doesn't say much more about abstract groups in the remainder of the book. Groups are very interesting - but their theory can quickly become quite complicated and "deep". Group theory is a pervasive topic in modern mathematics, and has been for almost 200 years. Stewart doesn't go further with the subject or its history in the present book, but does in a later book: Why Beauty is Truth .
Instead, most of the book presently under discussion is concerned with cases where symmetry is "broken" - that is, when the appearance or some other aspect of a real-world object becomes different in some way. The object no longer has a perfect symmetry of some sort, but only one that is merely "approximate" - generally for understandable reasons. Consider an automobile - practically any kind. Almost all cars have a left-right mirror symmetry, which is a reflection in a vertical plane that runs through the center of the car from the front to the back. But it's not perfect, because the steering wheel and various switches and gauges on the dashboard are only on one side or the other. That's because hardly any cars now provide for anything except one single driver. (In addition, the layout of things under the hood is usually not symmetric either, since most cars have only one battery, alternator, etc.)
Humans and most other higher animals don't have perfect left-right symmetry either, for similar reasons. They typically have only one heart, liver, stomach, etc. - not in the exact center of the body - even though a few organs like kidneys and lungs are duplicated symmetrically, and the redundancy is useful. In principle, a car could be built that had nearly perfect bilateral symmetry. The seats for driver and passengers could be located in a straight line from front to back - as with fighter planes with more than one occupant. But the vehicle would then probably be much narrower (to avoid wasted space) - and consequently more likely to tip over when making sharp turns. So the upshot is that nature often finds it convenient to break "perfect" symmetries, even if only slightly.
Most of the rest of Stewart's book goes into many examples of this symmetry breaking. For instance, although most land animals with legs have, externally at least, bilateral symmetry, they are mostly unable to move at all unless the legs don't all move the same way at the same time. (Hopping animals like kangaroos are an exception, of course.) There's a whole chapter in the book about the different ways that animals move their legs in order to walk or run - and the pattern may change depending on how fast the animal needs or wants to go.
There's a whole chapter on the symmetry of crystals. A fascination with crystals (whether or not taken to unreasonable extremes) has been common in humans from prehistoric times - even before homo sapiens (as Stewart points out). All crystals have some sort of symmetry, at least in principle, though often "broken" - because of how their constituent atoms arrange themselves. The study of crystal symmetries was historically almost the earliest example of the use of group theory in science. Different minerals are in fact characterized by the types of symmetries their crystals may exhibit. The symmetries are usually slightly broken, due to asymmetries of the chemical environment in which the crystal grew. Randomness is pervasive in nature, but often leads to its own symmetries - such as the way that smoke entering one side of a room will quickly become distributed fairly evenly within the room.
Natural laws, such a gravity, have symmetries too. A rock tossed upwards at an angle will follow a symmetric parabola. A deep theorem, due to the mathematician Emmy Noether, explains how conservation laws (such conservation of energy and momentum, which govern the motion of tossed rocks) are a result of symmetries in the equations of physics.
Crystals aren't alive, but animals are, and they have symmetries too, even though usually only approximate (as noted above). Consider the stripes of a tiger. They are arranged, albeit rather irregularly, in a periodic sequence along the length of the animal's body - literally from head to tail. It turns out that this symmetry is a lot like the symmetry of ocean waves approaching a beach. (Periodic phenomena have deep mathematical generalizations: "harmonic analysis", in which group theory is of central importance. Consider how combinations of different frequencies of sound waves are what constitute music.) Animal patterns such as tiger stripes result from waves of chemical densities in the liquid medium inside very young embryos, because they affect gene expression. Alan Turing - the early computer scientist who conceived "Turing machines" - was apparently the first to suggest this, even before "genes" were actually understood. This story is told in another chapter of Stewart's book.
January 16, 2016
A very nice book explaining the mathematical concept of symmetry and its application to patterns formations in physics, biology, astronomy etc. I really love that the authors begin the discussion with Curie's principle - a question somewhat fundamental to all sciences, also of important philosophical connotations: whether symmetric cause has symmetric effect? In my layman's understanding, symmetry is some transformation that leaves a particular structure invariant. The structure can be a geometric figure, or more interesting to physicists, equation of motion. A particular solution of the equation often do not have as many symmetries as the equation itself (symmetry is broken). However the symmetries are preserved by the set of all solutions. I think it's beautiful in the sense that it resonates with our experience with Nature: you see one piece of her work somewhere, then you know what else there could be, and they are all from same cause or origin - one cannot be if others are not.
Another thing I found interesting is to compare this book side by side with Hermann Haken's books on Synergetics. Lots of examples are the same. But just from the keywords, you see different traditions of pattern formation studies. One is about how things are broken from one, the other is about how many things (e.g. degree of freedoms) come to be one. The contrast worth much contemplation.
I also love the final part on symmetric chaos. This teased me on a question I always think about - what's the relationship between perfect symmetry breaking and statistical symmetry breaking. It seems that there were hints but not yet conclusions when the book was written. I played with some programs myself. So much fun!! I'm very grateful that the authors provided equations and pseudo-code for curious readers. I just started another book by Field and Golubitsky on this topic.
I read this book because it was referred to in another book of Golubitsky called the symmetry perspective, which I think is more inspiring. Sometimes, greater pleasure comes with greater precision, especially for a math topic. I recommend that book for any one who wants to dig deeper into the formalism.
Another thing I found interesting is to compare this book side by side with Hermann Haken's books on Synergetics. Lots of examples are the same. But just from the keywords, you see different traditions of pattern formation studies. One is about how things are broken from one, the other is about how many things (e.g. degree of freedoms) come to be one. The contrast worth much contemplation.
I also love the final part on symmetric chaos. This teased me on a question I always think about - what's the relationship between perfect symmetry breaking and statistical symmetry breaking. It seems that there were hints but not yet conclusions when the book was written. I played with some programs myself. So much fun!! I'm very grateful that the authors provided equations and pseudo-code for curious readers. I just started another book by Field and Golubitsky on this topic.
I read this book because it was referred to in another book of Golubitsky called the symmetry perspective, which I think is more inspiring. Sometimes, greater pleasure comes with greater precision, especially for a math topic. I recommend that book for any one who wants to dig deeper into the formalism.
July 26, 2013
Nice book, easily accessible even to people with no mathematical background, and with very interesting insights and very good explanations and examples of what is symmetry and symmetry breaking. I thoroughly enjoyed reading this book.
The only small defect is that the influence of symmetry and symmetry breaking in particle physics and in quantum mechanics (where these concepts play a huge role) was addressed only quite superficially.
The only small defect is that the influence of symmetry and symmetry breaking in particle physics and in quantum mechanics (where these concepts play a huge role) was addressed only quite superficially.
September 2, 2025
Stewart and Golubitsky describe the book in the preface, "[Fearful Symmetry] is about the role of symmetry in pattern formation." The book illustrates the concept with examples of symmetries almost exclusively from nature. The authors take their "[emphasis on] dynamic processes [as opposed to static states] in which which symmetry can either be destroyed or created" to be the main difference between their book and others written on the topic.
They consider a given physical object's type of symmetry. Which depends on the transformations (rotation, reflection, translation) that can performed on an object that leave the object looking the same as before, "a symmetry is a transformation that leaves the object invariant - that is, it looks the same after applying the symmetry as it did to begin with, it is replaced into the same space that it started from." A circle has an infinite number of rotational and reflectional symmetries (because there are an infinite number of rotations through tiny degrees).
A symmetry group is "a closed system of transformations: whenever two of them are combined, the result is another member of the same group. We call this particular group the symmetry group of the object." To illustrate the idea, they imagine a starfish with 5 identical arms and mention that (assuming the arms really ARE identical) any two symmetry transformations can be combined and since neither transformation will make the object look different, a combination of two symmetry transformations can itself be considered a symmetry transformation. The importance of the group concept is that it is exhaustive (all possible symmetry transformations are included in the 'symmetry group') so that certain symmetry groups can be compared to others.
They also introduce the concept of symmetry breaking, by which they "mean that some of the symmetries" are "removed from consideration... If one group is a part of another group, then we say that the smaller one is a subgroup. When symmetry breaks, the symmetry of the resulting state of the system is a subgroup of the symmetry group of the whole system." One goal of the book is to explore the explanatory power that the symmetry concept has to help explain physical phenomena (a smaller goal is to be clear about what symmetry can't do).
This book explains the different ways that symmetry can be applied to systems in the physical world and used to make predictions about those systems. Symmetry helps model physical reality but Stewart is careful to caveat, "Nature behaves in ways that look mathematic, but nature is not the same as mathematics. Every mathematical model makes simplifying assumptions; its conclusions are only as valid as those assumptions. The assumption of perfect symmetry is excellent as a technique for deducing the conditions under which symmetry-breaking is going to occur, the general form of the result, and the range of possible behavior." Reality can't be ignored completely (since that is what's supposed to be explained).
____
I've left out a lot of the specific physical phenomena like walking patterns, spirals on snail shells, spiral galaxies, the standard model of physics, and tigers' stripes that are explored from a 'symmetry standpoint' and are very interesting, but I hope I've summarized the main ideas.
Stewart and Golubitsky make a very strong case for the power of symmetry to simplify the mathematics and help make scientific predictions. This book also seems to me to show what it is about mathematics that can make people want to become mathematicians in the first place. It is fascinating how powerful mathematical models of reality can be and taking this book as an example, symmetry and group theory seems to be one of the most powerful techniques mathematicians have.
They consider a given physical object's type of symmetry. Which depends on the transformations (rotation, reflection, translation) that can performed on an object that leave the object looking the same as before, "a symmetry is a transformation that leaves the object invariant - that is, it looks the same after applying the symmetry as it did to begin with, it is replaced into the same space that it started from." A circle has an infinite number of rotational and reflectional symmetries (because there are an infinite number of rotations through tiny degrees).
A symmetry group is "a closed system of transformations: whenever two of them are combined, the result is another member of the same group. We call this particular group the symmetry group of the object." To illustrate the idea, they imagine a starfish with 5 identical arms and mention that (assuming the arms really ARE identical) any two symmetry transformations can be combined and since neither transformation will make the object look different, a combination of two symmetry transformations can itself be considered a symmetry transformation. The importance of the group concept is that it is exhaustive (all possible symmetry transformations are included in the 'symmetry group') so that certain symmetry groups can be compared to others.
They also introduce the concept of symmetry breaking, by which they "mean that some of the symmetries" are "removed from consideration... If one group is a part of another group, then we say that the smaller one is a subgroup. When symmetry breaks, the symmetry of the resulting state of the system is a subgroup of the symmetry group of the whole system." One goal of the book is to explore the explanatory power that the symmetry concept has to help explain physical phenomena (a smaller goal is to be clear about what symmetry can't do).
This book explains the different ways that symmetry can be applied to systems in the physical world and used to make predictions about those systems. Symmetry helps model physical reality but Stewart is careful to caveat, "Nature behaves in ways that look mathematic, but nature is not the same as mathematics. Every mathematical model makes simplifying assumptions; its conclusions are only as valid as those assumptions. The assumption of perfect symmetry is excellent as a technique for deducing the conditions under which symmetry-breaking is going to occur, the general form of the result, and the range of possible behavior." Reality can't be ignored completely (since that is what's supposed to be explained).
____
I've left out a lot of the specific physical phenomena like walking patterns, spirals on snail shells, spiral galaxies, the standard model of physics, and tigers' stripes that are explored from a 'symmetry standpoint' and are very interesting, but I hope I've summarized the main ideas.
Stewart and Golubitsky make a very strong case for the power of symmetry to simplify the mathematics and help make scientific predictions. This book also seems to me to show what it is about mathematics that can make people want to become mathematicians in the first place. It is fascinating how powerful mathematical models of reality can be and taking this book as an example, symmetry and group theory seems to be one of the most powerful techniques mathematicians have.
April 23, 2021
Libro sobre la simetría, como ente matemático y como explicación física de multitud de hechos. Una simetría no es (o no es solamente), como intuitivamente pueda parecernos, la similitud de una figura geométrica cuando la rotamos o la reflejamos. Una simetría en general es una invariancia ante una transformación. Esa transformación puede ser geométrica, (girar, reflejar en un espejo, rotar) o matemática, no necesariamente realizable con nuestras manos. Desde el principio (del libro y del Universo), en el que se nos cuenta cómo la rotura de la simetría electrodébil da lugar a la fuerza electromagnética (la mediada por fotones, la electricidad, la luz, todo) y la fuerza débil (responsable de algunas desintegraciones nucleares), vamos avanzando en el tiempo y encontrando un montón más de simetrías, físicas y biológicas. El libro es interesantísimo, y en algunos momentos requiere de lectura reposada. Ejemplo: el teorema de Noether, que dice que en todo sistema en el que haya una simetría, podemos encontrar unan magnitud conservada. Y así es: si en un sistema hay simetría temporal, es decir, el sistema vuelve a ser el mismo si nos trasladamos en el tiempo, entonces se conserva la energía. En física de partículas la existencia de una simetría ante transformaciones gauge significa que se conserva la carga eléctrica. En el libro emplean más páginas en contarlo y por supuesto lo hacen mejor, pero la cuestión principal es que la simetría es la fuente de un huevo de hechos que observamos en el mundo.
Libro recomendabilísimo.
Libro recomendabilísimo.
September 2, 2025
מענין וקולח. לפעמים נראה שההסבר לא מספיק ברור והרצון להמנע מפורמליסטיקה מוגזם עד לפגיעה בהבנה
September 1, 2013
Breaking symmetry to uncover one theory that rules them all
Breaking Symmetry is certainly a magic term in this book. With the use of innumerable real-life examples and the use of dozens of pictures Stewart and Golubitsky try to illustrate the basic concept of the "Theory-That-Covers-Everything". Being confronted with the dissection of physical phenomenon into degrees of symmetry, gives the reader enough reason to believe that the "big theory" might ultimately be uncovered by using the mathematical tool of Breaking Symmetry. But this book also points out that scientists are still far away from reaching this ultimate goal.
The patterns discussed in this book takes you to the invisible world of quarks, then shows you the wonderful stripes on the fur of a tiger and finally let you surf the spiral-arms of our Galaxy. Clearly it gives the reader the opportunity to have a taste from more than one scientific discipline: Biology, Physic, Chemistry, Maths, they are all addressed in this book.
But be aware: you must keep yourself very alert while reading it, because the train of thought is not always easy to follow. Apart from the sometimes strange jumps, the narration is very clear and easy to understand, which will certainly enable you to get more insight into the fascinating world of symmetry.
Breaking Symmetry is certainly a magic term in this book. With the use of innumerable real-life examples and the use of dozens of pictures Stewart and Golubitsky try to illustrate the basic concept of the "Theory-That-Covers-Everything". Being confronted with the dissection of physical phenomenon into degrees of symmetry, gives the reader enough reason to believe that the "big theory" might ultimately be uncovered by using the mathematical tool of Breaking Symmetry. But this book also points out that scientists are still far away from reaching this ultimate goal.
The patterns discussed in this book takes you to the invisible world of quarks, then shows you the wonderful stripes on the fur of a tiger and finally let you surf the spiral-arms of our Galaxy. Clearly it gives the reader the opportunity to have a taste from more than one scientific discipline: Biology, Physic, Chemistry, Maths, they are all addressed in this book.
But be aware: you must keep yourself very alert while reading it, because the train of thought is not always easy to follow. Apart from the sometimes strange jumps, the narration is very clear and easy to understand, which will certainly enable you to get more insight into the fascinating world of symmetry.
September 20, 2009
This is a wonderful book about the things that BREAK symmetry. Lots and lots of illustrations that truly bring the topic to life. The very first photograph is of a milk drop falling into a saucer of milk. The circular wave centered around the point where the drop hit the surface rises as a crown. The crown has 24 spikes and droplets--so there is 24-fold symmetry. The reason there is ALWAYS a 24-fold symmetry seems to be a mystery.
The book covers so many different subject areas; geometry, astronomy and cosmology, fluid dynamics, biology, nonlinear dynamics, and more. One of the most fascinating chapters was about the gaits of animals, and how animals change from one gait to another (like from trot to canter, and so on). Highly recommended to everyone who is interested in the natural world.
The book covers so many different subject areas; geometry, astronomy and cosmology, fluid dynamics, biology, nonlinear dynamics, and more. One of the most fascinating chapters was about the gaits of animals, and how animals change from one gait to another (like from trot to canter, and so on). Highly recommended to everyone who is interested in the natural world.
June 12, 2015
Part of my job includes teaching quantum mechanics to other people, so when I find a math book that not only offers up insightful takes on mathematical concepts I'm not already nauseatingly familiar with but does so in humorous and accessible prose, I get truly excited. Not only have I enhanced my own learning, I've found a teaching example to look up to. That said, not even Ian Stewart could make me care about the biology sections.
April 7, 2011
Another of Ian Stewart's wonderful books.
This one (at least, my edition) is apparently available only from UK, in a Penguin edition, although my copy (ordered through Amazon U.S.) came quickly and inexpensively.
This one is another fascinating read.
Highly recommended!
This one (at least, my edition) is apparently available only from UK, in a Penguin edition, although my copy (ordered through Amazon U.S.) came quickly and inexpensively.
This one is another fascinating read.
Highly recommended!
January 14, 2010
"Interesting treaty on symmetry"
Want to read
November 7, 2010Crítica de las simetrías de la Naturaleza... como si a la Naturaleza le importara lol.
Pasta dura. Costo aproximado >$300 MN (México).
Editorial Drakontos.
Pasta dura. Costo aproximado >$300 MN (México).
Editorial Drakontos.
February 4, 2015
Expected more interesting examples from a person like Golubitsky!
December 25, 2025
Authors' commentary was a drag.
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