3 of 3 people found the following review helpful
I received this free through the Amazon Vine review programme.
I'm not by any means a Mathematician, however I did 'A' Level Maths, and occasionally have had recourse to statistics in producing a Linguistics-based PhD, I've also bought several titles from the 'Very Short Introduction' series in the past... so I didn't expect to find this entry quite as challenging as it proved.
This is far from a brief work. The 160 pages to this work are densely crammed with theory that goes far beyond 'A' level standard. The book is written in a really small, dense font face - it could easily and quite respectably have been produced in a much larger format. The topic is interesting, but quickly becomes quite complex. An introduction it might be, but perhaps only if this is being assessed at the academic level.
For the retail/Amazon price this can be an extremely good value work. But it most assuredly is NOT an accessible introductory title.
3 of 3 people found the following review helpful
I would have liked books like this when I was studying at university nearly forty years ago. This one provides a useful commentary on the concept of symmetry. However, the brevity of the book's coverage is both a strength and a weakness. You don't purchase a book in thie excellent OUP series expecting to read a comprehensive and revelatory discussion on the concept. What these books do provide is an excellent summary. The clue is in the strap line: 'very short introductions'. So I would argue any volume in the series should be reviewed with this caveat in mind - hence my five stars. The book provides an insightful summary of the concept of symmetry, and it is more than evident that Ian Stewart knows about this subject. So if you're not studying for a degree or even revising for an exam but want a starting point for finding out more about this subject then this slim volume provides an excellent starting point. It is well written, erudite and engaging.
2 of 2 people found the following review helpful
You may be under the misapprehension that this book is an introduction to symmetry for laymen with no knowledge of mathematics. That is wrong! Pretty early on, it is clear that you will at least have to Google what a catenary is (the shape of a hanging chain held at two ends) and know what a sine wave is (a basic periodic curve, with period 2π radians). This is pretty elementary stuff, but if you aren't prepared for it you will get lost almost immediately.
Having said that, Stewart lost me temporarily on page 9 with his rainbow explanation. The problem is a lack of diagrams at this point, and I think he should either expand or drop this example. This is true for a lot of other examples: if you don't know what a catenary is, it is introduced in a joking way and is not essential to what follows. (Square wheels on inverted catenary rutted roads!)
Chapter 2 introduces the reader to the idea of a mathematical Group. Symmetries form groups, groups are all permutation groups, and can all be represented by matrices, at least in the finite case, but can be treated in the abstract, with any general properties then saying something fundamentally useful about permutations and symmetries.
In Chapter 3, probably the most accessible chapter, we see the fundamental frieze and wallpaper patterns, as well as the regular solids like the icosahedron. Frieze patterns are perhaps old-fashioned now, but people used to stick things called borders on their walls. These were thin strips with a repeating pattern. There are only 7 types. At this point, there is a blip in the book, where these 7 are illustrated, and due to the way they are compressed onto one page, with no indication where one ends and another starts, there appear only to be 6. Dividers should have been inserted. However, those horizontal lines that appear to be dividers are in fact part of the friezes, so to get 7 patterns, take the following rows: 1, 2+3, 4+5, 6, 7, 8+9, 10.
When it comes to wallpapers, with repeating patterns, there are just 17 of them. Yes, I know, the catalogues show far more but in terms of regular repetition, ignoring the actual pattern that is repeated, there are just 17. There are just 5 regular solids, and when it comes to crystal structures, just 14. These are fascinating bits of trivia to bore your friends with!
Chapter 4 looks at the abstract structure of groups and an important idea, conjugacy. You may not know this, but if you have learned how to solve a Rubik cube, you already know about conjugacy. This is in fact covered in Chapter 5, which also looks at Sudoku grids and their number. Don't believe any App that says it gives unlimited numbers of grids!
Chapter 6 covers natural symmetries, and the layman will have no trouble with understanding it. Unfortunately, there follow Chapters 7 and 8 that again become too technical, introducing the symmetries of particles and the classification of so-called simple groups.
So, a mathematician will understand everything in this book apart from that wretched rainbow explanation. For the layman, read it, but skip over anything you don't understand, as it is unlikely to come back and haunt you later. (The opposite is generally true for formal mathematical textbooks!)
Stewart touches briefly on some of his own research interests, including gaits, in the area of catastrophe theory.
It's cheap, it's funny, sometimes frustrating, but well worth buying, reading and leaving on the coffee table before inviting friends round.
[Oh, and for the record, I have three degrees in mathematics and found this mostly very easy reading. It is about 135 pages long but they are only A6 pages.]
3 of 3 people found the following review helpful
IS has gained a reputation for making the findings of science and mathematics but in tacking Symmetry he has taken on a difficult task. There is a Youtube video of an interview in which he demonstrated different types in everyday life starting with the human face and in the book he discusses different types of symmetry: bilateral, rotational(snowflakes), geometric and so on, but when he gets to algebra group theory and the fundamentals of physics the going gets tough and the average reader will struggle with it. However, the concept of symmetry underlies so many things that the effort is well worth it.
Rating 4 out of 5
2 of 2 people found the following review helpful
I like the very short introduction series - I've read a few. They're not beginners' guides but rather dense and complete overviews.
I found this one to be below par. The beginning, discussing rainbows, relied heavily on a particular model of light (wave theory, rather than particle and let's not forget QED) and to be honest I wasn't sure it was a good way in nor clearly about symmetry. If one knew anything of the topic there was no need for such a soft intro, if a soft intro was considered necessary then the Open University got it right in M336 groups and geometry when using tesellations from Roman and Greek friezes (and, bizarrely, Heathrow)
From then on the book didn't create a journey I could follow. Which is not to say it was content free.
I've developed a very keen interest symmetry in my design work the past few months and whilst I use complicated processes it never really enters into the deep maths that I always knew were behind it but never really looked into. And I'm glad I did look further because I'm gradually getting more and more into it.
It would however be very foolish for someone to pick this up expecting an easy read leading to an easy understanding, this stuff you really need to spend time over getting to know.
The design of the whole series of 'Very short introductions' is very good, very simple and doesn't distract from the content, and I love the idea of these being an introduction mainly because they will either make or break your interest into each subject, it may sound strange but they really are that involving (I also bought the one on Astronomy). But saying this, symmetry is introduced to the reader through a series of very common objects/natural occurrences; wheels, waves and rainbows being the first to be explained and then on to rock, paper, scissors shortly after, and that is where the book takes a leaning on mathematics to get across the complexity and often simplicity of symmetry.
It may be an introduction but its very complicated and like learning anything, it requires proper investment into the subject, if you're not naturally adept at maths like me you should, like me look forward to discovering this brilliant subject through time. I'm looking forward to taking a look at the fractals addition after.
The Very Short Introduction series are written by professors of the subject and are aimed at provoking cross-discipline intrigue in the reader that may incite further investigation and reading - and boy are they good at achieving exactly that; often they leave more questions than answers.
Symmetry is all around us, in the patterns we love, the symbols we use (religious and corporate) and even in our own bodies and that is what inspired me to pick up this book. What followed was one of the more intriguing reads as Ian Stewart gracefully spans the origins of the investigation into symmetry arising from planar graphs & equations, through nature and chemistry right the way down to the Unitary theory.
At several points the maths [far] surpassed my understanding and I would find it incredible if anyone but Stewart himself understood every aspect of the book in the depth explained as it draws upon many, many overlapping fields including mathematics, chemistry, physics, biology and quantum theory. But that is how deeply symmetry is ingrained into our universe - that it pops up again and again in all disciplines and their overlaps. It is the prevalence that astounded me and there are many examples in life, counterweighted by all of the instances it pops up in mathematical, geometric and algebraic theory.
Recommended for a truly intriguing & fascinating read into the nature of symmetry that sells itself as an introduction but is pretty comprehensive in its scope; weighing in at 130 or so A6 pages with many diagrams to explain the principles and references for further-reading.
5 of 6 people found the following review helpful
I'm not sure for whom this book is intended - I can't imagine that a non-mathematician would go beyond the first few pages. As someone who once did a course entitled 'Topics in pure mathematics' I'm familiar with most of the material, and was dismayed to find the name of Galois appearing right at the beginning - Galois theory was the summit of my course. Also, I'm not sure that using symmetry to lead into simple group theory is really the right way round - and here, as in so many places, the reader is plunged far too rapidly into notation which may not be familiar, and terms suddenly appear without definition (and there's no glossary); I'm not convinced, for example, that the general reader suddenly coming across 'asymptotic' will understand it, and we encounter, later on, summary notation (unexplained) and plenty of other detail to drown in. We are told that there are 17 types of wallpaper, however - wasting space which could have been more profitably used. I'm relieved that this wasn't one of my textbooks. This introduction could use its own introduction.