Symmetry: A Very Short Introduction

Very Short Introductions #353

by Ian Stewart

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by

symmetries in the laws of nature.



It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory.



ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Genres: Mathematics, Science, Nonfiction, Physics

161 pages, Kindle Edition

First published May 30, 2013

About the author

Ian 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.

Reviews

[Mohammed Ghoul · Rating 4 out of 5]

Symmetry is one of those subjects that seems very intuitive at its surface but the deeper you go in it the more complicated the rules get; none the less it has become a core concept in most of the modern fields of natural sciences especially in physics. This book does a great job of giving the basic idea about the subject and a very short introduction(as in the title) to many of it's mathematical implications. The book also goes into the mathematical origin of symmetry in group theory and its later applications in many mathematical areas of study and other fields(especially physics). Unfortunately the book is quite short and the author tends to get technical a lot and due to the length of the text the author must assume a certain level of mathematical knowledge in the reader part. to the author credit he points out in the beginning of the book that the this technical parts could be skipped if not properly understood without much deduction in the understanding of the core concepts. I don't think I was able to grasp like 40% of the technical mathematics, but none the less it was very informative and could open the door to further reading in the future.

[Michael · Rating 2 out of 5]

I have two major problems with this book. The first is that I thought it was specifically about super symmetry, and it's not. That's my fault for making assumptions. The other is that I, being a reasonably mathematically, geometrically, spatially, and visually acute fellow, read this book and comprehended no more than half of it. Other books in the Very Short Introduction series eschew complex mathematics in favor of a conceptual overview such that the reader understands the fundamentals of the field in question without needing much other background material. This book hinges on understanding some pretty dense math that escapes even a professional engineer like me, and so the subject remains opaque. Some figures and diagrams would have helped, especially with regard to so thoroughly visual a concept as symmetry, but these are few and far between. Instead of being informative, this book is merely frustrating.

[Justin Lynn · Rating 3 out of 5]

My brain was performing the mental equivalent of smiling blankly and nodding throughout this entire book.

[Stephen · Rating 3 out of 5]

Decently written but caveat lector: this is a mathematical book no matter how much the author tries to lighten the heavier theory and symbolism with prose explanation. So if you have a university-undergraduate level of mathematics, say, at least one class beyond calculus, it should be fine. That said, the level of rigor only really gets there by in the later two or three chapters, so there's something for the general reader as well.

The mathematical content cuts against the book in another way: ebook formatting for mathematical formulas and diagrams is awful, and when rendered as images, they don't scale properly on my Kobo reader. (This was a problem on my Kindle Paperwhite, so it's a cross-platform issue.) I try to avoid technical ebooks for this reason, and was disappointed that SYMMETRY ended up being one.

3 stars.

[Sigvald · Rating 3 out of 5]

Expecting this to be a book for laymen, I was surprised by the level of mathematical prerequisites required, which I would say is university level mathematics for engineers or scientists. Being a physicist I was proficient enough to grasp the mathematics and therefore ejoy the book. The book still only gets 3 stars simply because I didn't think the exposition was that clear or well organized.

[Abhiram Devesh · Rating 3 out of 5]

Started the book thinking that it is non-mathematical.... But alas I was overwhelmed with the depth of the mathematics needed to understand it....

[Mark · Rating 4 out of 5]

This book is well written, but its name is deceptive. It is an introductions, but I felt it went in too much depth for a first time reader on symmetry. I got a lot out of it, but I have a BS degree in Mathematics and a passion for group theory. He goes into some very deep content on the theory of groups, and I am afraid the general reader will get lost. What is does do well is show the breadth of occurrences and applications of symmetry. Even if the reader does not follow every single argument and proof, it is impossible to not come away from this book without having gained an appreciation for the diverse scope of areas where symmetry can be applied. I has clear and bountiful illustrations of symmetry in the form of creatures, the layout of wallpaper, geometry, the Platonic solids, crystals, Rubik's cube, Sudoku, snowflakes, galaxies, sand dunes, animal gaits, and the zoo of subatomic particles. A short, but slow read. It should be read quickly once to get the lay of the land, and then slowly with a pencils and stacks of paper, preferably arranged with nice symmetry.

[Nicole · Rating 1 out of 5]

Though my heart doesn’t beat higher at all when coming across algebraic equations, I am able to appreciate their usefulness when they are presented in a sophisticated way. For example, I enjoy watching the YouTube Channel “The Mathologer”.

I say this because “Symmetry” was utterly off-putting to me. It was basically an equation-dump without much of an inspiring medium around it to make it palatable to people who don’t think in algebraic equations. I skipped roughly 95% of the pages and just slowed down at the paragraphs that seemed readable to me.

It’s quite a pity, as I’m particularly interested in understanding how symmetry led physicists to develop the current model layout of the elementary particle array and why they go hunting for particles of which they don’t know for sure whether they exist. It’s just that the inherent symmetry of the standard model of elementary particles creates the expectation that a specifically described particle does exist.

So, in that way, symmetry is like a torch which can help us to discover hidden things in the darkness. I wanted to learn more about that. But it looks like I ought to find another book for that purpose.

[Tom Schulte · Rating 3 out of 5]

Oxford's Very Short Introductions are concise introductions to a wide gamut of topics. Currently available titles cover advertising, Anglo-Saxons, British politics, the Dead Sea Scrolls, folk music, and “stars”. This entry into that intriguing list is a basic, even cursory, overview of the group theory underpinnings of symmetry. I imagine it breaks the stride of voracious VSI readers. A reading of online reviews proves that to be the case: “…not a beginner's book”, “…concepts difficult to follow”, “tough slogging”, and even “abandon all hope” are all common notions from readers.

Actually, Stewart supposes very little mathematical sophistication of the reader. Giving “the mathematical skeleton of the argument”, he reduces game theoretic analysis of rock-paper-scissors to a grocery list of logical facts. When matrix algebra is about to make a cameo in defining symmetry, Stewart casually remarks “we won’t go into that.”
...

[Look for my entire review at MAA Reviews]

[Jo Bennie · Rating 2 out of 5]

Although this is a Very Short Introduction book it is not a beginner's book, I found many of the concepts difficult to follow and understand as they require a fairly high level understanding of mathematical theory: algebra, quadratic equations, string theory, game theory. However, although I was a little lost at times I was able to understand enough to get a flavour of how symmetry functions across a wide range of disciplines: chemistry, biology and geometry, from the structure of atoms in elements and planet in galaxies to Rubik's cubes, sand dune formation and the running gait of animals. Written by an expert who sees clearly how the concepts formed in high mathematics have an application in every aspect of our lives.

[Shane Hall · Rating 2 out of 5]

Tough slogging!

The VSIs are not for absolute basic beginners: while generally clear and non-technical in their intent to 'Introduce', you've got to be able to keep up (this is Oxford we're talking about).

Notwithstanding, this one is not like that. Without the prerequisite of already understanding higher-order algebra, abandon all hope. To that end, the first five of only eight chapters deal far more with the raw mechanics of Group Theory computation than with the symmetry inherent in the Theory's actual results.

Disappointing.

[Ami Iida · Rating 4 out of 5]

Symmetry is applied for everything,from rainbow to galaxy,particles,etc...........

[Ashutosh Rai · Rating 3 out of 5]

Hard to read if you are not familiar with some basic abstract algebra and mathematical reasoning, and not easy at times even if you know the basics. Extremely hard to read if you do not like mathematics. It is a small book, but not a light read by any means. Pick it up only if you are ready to spend time working out what it is trying to say. I tried to do that, but gave up at certain points. It contains way too many symbols and definitions for a "very short introduction". I did not expect it to be this hard, but did get to learn a few things.

Having said that, if group theory was introduced as a way to study symmetry when it gets taught in colleges, and the Rubik Cube and Fifteen Puzzle were shown as applications of group theory, I think a lot more students might get interested.