Coding Notes

I was recently visiting my library’s math section looking for some interesting recreational math reading. I enjoy exploring math because, while some people may not think so, I find that the same problem solving skills that go into math also seem to be utilized in programming, especially in algorithm development. With a math minor my idea of recreational math reading may be a little different from those that aren’t directly involved with math however, Ian Stewart’s book The Magical Maze sounded interesting and intriguing. I had seen Ian Stewart’s name previously while perusing my local bookstores however, I had never read any of his books. The reason that I chose The Magical Maze over the other books in my library was because of its subtitle “Seeing the World Through Mathematical Eyes” this intrigued me and upon reading Stewart’s introduction to the book I understood what he meant.

Stewart wrote the book as another form of his lectures at the Royal Institution’s 1997 Christmas Lectures for young people. Naturally, and as Stewart points out, the book takes a different form than the lectures and includes more material than he covered in his lectures. That being said Stewart’s intent, as the subtitle states, was to present the book as an overview of how to see various aspects of the world from a more mathematical standpoint. Furthermore the book is one of mathematical recreation and was not meant to be inapproachable by those that aren’t in the field of mathematics. This same recreation must have been apparent in his lectures at the Christmas Lectures as they are not a math specific lecture series. Ultimately, it seems, that Stewart set out to present the reader with a way to approach the world with math and not to require the reader to understand too much complex math ahead of time.

I found the book to be a refreshingly light and yet detailed exploration of various more complex and applied mathematical subjects. Stewart structures the book as if the reader is wandering through a maze and thus he creates a very enjoyable story like appeal throughout the book. This helps to create a constant longing to get to the next junction of this magical maze. Stewart explores the mathematics that go into many of the magicians math tricks (or number guessing games) and the history and math behind calendars and flowers in his first chapter. The ease of use of the book is apparent from this very first chapter as several of its topics deal with complex modulus operations, and yet Stewart approaches them from a beginners standpoint, explaining the modulus, while continuing to keep it intriguing for the non-beginner. This ease of use and intriguing nature of the first chapter is constant throughout the book as Stewart explores further topics.

After the first chapter it becomes apparent that each junction of the maze is to discuss a different topic. Stewart approaches almost all of the topics from a very applied manner allowing the reader to understand where they would encounter this particular topic in their everyday world. The book talks briefly on many topics including decision graphs and indirectly finite automata, symmetry, probability and statistics, exposing some of its trickery, Stewart even touches on chaos theory.

Something that delighted the computer scientist in me was the way in which Stewart approached Turing machines, while I already understood the topic Stewart approached it from a perspective that every one could understand. By first approaching very simple logical paradoxes and proofs Stewart quickly and understandably moved into a universal way to solve any problem, the Turing machine. Stewart even went into the topic of the halting problem and the logical paradox that creates the unsolvable nature of the problem.

Stewart goes into the topic of symmetry in quite a bit of detail as well and yet by exploring it from a more applicable standpoint he allows for anyone to approach its complexity. Employing mirrors and animal movements Stewart describes how symmetry can be both three dimensional and four dimensional (time being the fourth dimension). Throughout the book Stewart uses other people’s work as well as his own to apply the math in an approachable way to the real world. For instance he uses others work with train sets to explain the existence of a universal Turing machine, by structuring a train set in a certain way one can simulate a computer and create a train network that exhibits the traits of the halting problem! Oh the joy a train set designer could have with that!

Overall I found the book to be incredibly refreshing in that it covered so many topics and did so with application as its main focus, leaving the reader longing to understand more of how the world is mathematically inclined. Stewart very much accomplished his goal of providing an excellent applicable mathematical overview in an approachable by anyone format. I would highly suggest any computer scientist read it because Stewart is a mathematician thus he approaches many of the same topics that computer science students approach and yet he does so from a different perspective than the computer science classroom’s perspective. This different perspective allows for a broadening of understanding in the various topics that The Magical Maze touches on. For the non computer science reader, I would still suggest the book if only to discover why sunflowers have spiraling seeds, the book allows anyone to open their eyes to the incredible mathematical universe that we live in, and provides a general appreciation for its mathematical complexity.