The Power of Computational Thinking

The world hardly needs a new book on mathematical thinking aimed at the general reader. I have a bookshelf full of them. So The Power of Computational Thinking, by Paul Curzon and Peter W. McOwan, both of Queen Mary University of London, hardly breaks new ground. It is well written, however, and it seems appropriate for a high school student or an undergraduate who would like to look past rote computations to see the big picture. And it even holds some surprises for the jaded professional with a shelf full of similar books.

Take, for example, their first in-depth example, developed in Chapter 2. If I were writing a book similar to this, I’m not sure where I would start, but it almost certainly wouldn’t be with locked-in syndrome. This chapter is focussed on Jean-Dominique Bauby, author of The Diving Bell and the Butterfly. Bauby has locked-in syndrome, which means that he is perfectly intelligent, and aware of his surroundings, but almost entirely unable to move. He is able to communicate only by blinking one eye.

Curzon and McOwan take up Bauby’s communication system, and ask how it could be improved. In the course of exploring it, they introduce the major themes of their book — algorithmic thinking, pattern matching, generalization, abstraction, decomposition, and evaluation. They contrast Bauby’s system with existing systems, such as Morse code and various binary representations of letters. They connect it to predictive text algorithms. Their final lesson is that what constitutes the “best” system depends heavily on context, in this case on Bauby and his care givers, and what works for them. It’s an intriguing introduction to their topic, and completely unique in my experience.

There are several other fresh ideas in the book. In Chapter 4, they discuss Cut Hive puzzles, a type of puzzle loosely related to sudoku, which I had never seen before. They develop some simple rules for starting to solve the puzzles, and encourage the reader to develop more rules using similar techniques. In Chapter 11, they talk about the basic mathematics behind a CAT scan, and make an extended analogy to the board game Battleship.

Of course, there are a lot of old friends in the book as well. There are discussions of the Bridges of Königsberg, John Conway’s Game of Life, and even John Searle’s Chinese Room. I may have seen better discussions of some of these topics in other places, but Curzon and McOwan are always clear and they discuss the topics in enough depth for the uninitiated reader to get the idea. They are very deliberate about tying each topic into their overall discussion of computational thinking.

Curzon and McOwan are computer scientists, and they write from that perspective. However, they carefully avoid getting bogged down in details, so pretty much everything they say about “computational thinking” can be viewed as talking about mathematical thinking in general.

Any book of this sort demands a delicate balance between clarity and depth. Simple examples are easier to explain, but too many of them, and the book feels superficial. On the other hand, real-world applications are highly motivating, but to do them justice may demand a level of detail that’s hard for the beginner. Curzon and McOwan lean a little towards the simple and superficial end, but as a whole, I think they do a good job of making connections to the deep problems facing today’s software engineers.

Overall, I believe that this book achieves its goals. It discusses a wide variety of problems from the perspective of computer scientists, and introduces the big ideas that underlie the mathematical way of thinking. I would certainly recommend it to a young person who has mathematical aptitude and needs insight into what computational thinking really means.

Benjamin V. C. Collins has been on the faculty at the University of Wisconsin-Platteville since 2000. His mathematical interests include the history of math, recreational math, and discrete math. When he’s not in class (or in a meeting) you might find him working the New York Times crossword puzzle or running long distances slowly.