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# Symmetry: About Mathematicians, Translators and Writers

Amit Ben Best from Ben Gurion University, in a guest appearance onRoey Tsezana's blog in Tafuz, tells about his impression of the book Symmetry

He became Tom and returns to Raz and dreams of a paw

I finally finished reading the book "Symmetry" by Marcus Dusotoi, which Roy gave me. The data does not bode well for Du Sotoi. First of all, as the new head of the chair for the communication of science to the public at Oxford, he is heir to the throne of the greatest of them all, Richard Dawkins, and it is a shadow that is very difficult to get out of. Besides, the book deals with mathematics, which is a subject that is very difficult to explain to an uninformed public, because it tends to be very abstract, and people in general have difficulty dealing with such levels of abstraction. And if all this is not enough, the Hebrew version of the book was translated by Uriel Givon, who has already done targeted countermeasures in other books (for example Matt Ridley's latest book. See more here).

So the translation is pretty terrible and there are quite a few disturbing translation choices - not to mention errors - but I don't really want to talk about the translator. I want to talk about the book itself and Marcus du Sottoy. But first we need to answer a small question. What is symmetry anyway?

Most of us have a general idea about symmetry. In the eyes of most people, a symmetrical object is one that looks the same from the left as it does from the right (or whose top looks like the bottom). As mathematicians see it, this popular understanding represents one type of symmetry, called reflection symmetry; Things that look like a mirror has been placed in the middle. In mathematics, symmetries are displacements - such that at the end of the displaced object looks the same as it did before the displacement. This definition allows us not only to determine whether an object is symmetric or not, but also to count symmetries.

Think about some natural object, like a stone. The stone has a complicated shape that does not repeat itself. Now let's count symmetries. In how many ways can you move a typical stone and get the same stone back in the same position in the same place? The answer that may come to your mind is zero. The stone is completely asymmetrical and any change in the way it is placed can be distinguished. The mathematical answer is one, because in mathematics "not moving" is also considered a type of moving. So every object has at least one symmetry. Now let's look at a simple geometric beast: a straight segment of finite length (see sketch on the left). How many symmetries does a line segment have? two symmetries. You can leave it as it is, and you can reverse it (switch between A and B).

Now we will look at an equilateral triangle (see in the center of the drawing). How many symmetries does it have? Three symmetries are created as a result of rotating the triangle around its center by 0, 120, and 240 degrees. But there are additional symmetries. It is also possible to invert the triangle around the downward line between vertex A and the line to its left, and the same goes for the other vertices. This adds three more mirror symmetries to us, and a total of 6 symmetries. Small triangles were added to the triangle on the right side of the drawing that "destroy" the symmetry of the mirroring. It has only the three sliding symmetries.

So this is the symmetry, at the simple level anyway, which is what the book of Marcus de Sotoy is supposed to deal with. In symmetry, its meaning, and the mathematical theory developed to study it, the theory of bundles. And now that we understand what it is about, we can return to the book.

I did not fall out of this book. I don't like him. Don't get me wrong. Even through the weak translation, you can see that Dussotoy knows how to write not bad at all, to say the least. I learned a lot from the book and there are also quite a few passages that I enjoyed. But the book has some features I don't like.

First of all, although the book is supposed to deal with geometric symmetry and its connection to a mathematical theory called the theory of bundles, the whole is built around the author's life story. The author goes here, the author returns there. Now he takes his son, Tomer, from his marriage to an Israeli woman (yes! shout all the provincials in the chorus) to an old palace to look for symmetrical patterns. Then he meets with his German mathematician friend to talk about mathematics, and in the next chapter he meets a French mathematician. Although the autobiography is not the majority of the text, the book is structured as a book about 'Marcus du Sottoy tells about symmetry' and not as a 'book about symmetry'. Du Sotoy apparently thinks this is a way to make a book about mathematics more accessible. It's tedious for me and makes me feel that dozens of pages could have been omitted. I'm not really that interested in his travels, his loves, and his history. Even the fact that he's actually happy - because he really likes to talk about math - that the security people at the National Security Agency (chorus: Yes!) are nagging him and asking him about his research to prove that he's really a mathematician, it's not really something I need to know. I wouldn't have minded if there were some autobiographical stories in the book, but as I said, the entire book is built around Dussotoy's tedious experiences.

My next problem is a common problem in science books, and very common in math books. In many parts the book becomes a history book about the lives of mathematicians instead of a book that explains mathematics. Apparently there are people who really like it, but I want to understand things and learn things, and it's a little less important to me to know the history of all the prominent mathematicians who stopped for coffee in Paris in the 19th century, for example. I'm not really interested in the short and tormented life of Galois, nor the longer lives of Coché or Lagrange. Give me math, not mathematicians.

And it's a shame, because Dussotoy writes well, and explains well. All in all, given the difficult subject material, he managed to get me interested in groups and what they say about symmetry, and managed to make me understand even things I haven't really learned yet (I have a bit of a math background). The problem is that very quickly he is dragged into explanations of a lot of hand waving. There is nothing to be done, most of the subject is too complicated to convey to a wide audience who does not want to puzzle over formulas. Still, I think Dussotoy could have tried a little harder, and perhaps found a few more things that could be explained to the less educated audience as well (at least the book is intended for people who are not stupid and have curiosity. So they could have been challenged more). If he had spared a little on the irrelevant stories about himself and dead and living mathematicians, perhaps Dussotoy would have had more leisure to actually explain mathematics - a craft at which he undoubtedly excels. In addition, as the head of the department for explaining science to the public, I would have expected Dussuttoy to talk a little more about other scientific topics besides mathematics (out of the twelve chapters, the tenth chapter is a rare gem because it mainly deals with non-mathematical applications).

In conclusion, this is a book of almost 450 pages in which the author's writing talent is evident and there is interest in it, but at least in my opinion it could have been shortened to a book of about 350 pages that has more interest in it. So it's not a bad book, and a waiting book is actually a yes, but still... still there is this "but" that disturbs, and it's a shame.

Amit Ben-Best is a PhD student in computer science at Ben-Gurion University of the Negev specializing in evolutionary algorithms, and active in the Israeli skeptic community. In addition, he also writes on popular science topics and is a fairly mediocre mathematician at the time.

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