How many needles does a pine tree have? This and hundreds of similar questions are spread throughout this unconventional book by S. Mahajan, a professor of applied sciences working at Olin and MIT. Why should anyone bother about the number of needles of a pine tree (problem 1.19), or how much power a person would have to put out in order to hover by flapping his or her arms (problem 3.36)? And what do these questions have to do with computer science? The ultimate answer is insight: an ability that makes the difference between those who stop when facing a problem without an immediate answer and those capable of whetting their natural curiosity and eagerness to see beyond the obstacles and exert the fine art of problem solving by using conventional and unconventional reasoning tools.
This book teaches how to train our brain (and our gut, as the author loves to say) in order to use reasoning schemas that go beyond logical deduction. It consists of three main parts. Part 1 covers two topics dear to computer scientists: divide-and-conquer and abstraction. They are used to show how to organize complexity in problems. The author shows, with vivid examples, how these cognitive tools help us in solving problems that are apparently intricate at first sight. The explanatory approach is very pragmatic, with some problems used as clues to explain concepts. Not all problems are mere thought exercises: some of them have a practical aspect that helps the reader to appreciate the problem-solving tools provided by the author. The estimation of human power output during a physical activity is just an example among many others.
Part 2 of the book concerns a bunch of techniques for discarding complexity in problems without losing information. Concepts like symmetry, conservation laws, proportional reasoning, and so on are exposed in ways that are very easy to understand, although many of the reported examples fall in the area of physics. The trick used by the author is to avoid heavy mathematical formulations in favor of intuitive explanations that go directly to the heart of the problem to be solved. A constant concept used throughout all of the chapters of this part is invariance, an indispensable tool for computer scientists too, which the author shows everywhere by using an adage found in Engel’s book on problem solving [1].
Finally, Part 3 is still on discarding complexity in problems, but now admitting a partial loss of information. Here, the main topics are: lumping (that is, approximation), probabilistic reasoning, and reasoning with easy cases. A fourth chapter on spring models strictly pertains to the world of physics. In the chapter on probabilistic reasoning in particular, the subjective approach is well explained and confronted with the frequentist approach, again with several examples to show the effectiveness of Bayes’ rule to make probabilistic deductions.
Most of the examples of the book (and some entire chapters) are based on physics topics, and few of them face problems specifically centered on computer science or pure mathematics. Nevertheless, this book teaches how to think: in a world where Google is always under our fingers to give us solutions made by others, I find this book extremely valuable for teaching students (of any scientific discipline) to reason autonomously. The only danger I see in this book is the temptation to put scientific methods, mathematical modeling, and rigorous thinking aside in favor of more pragmatic approaches. This is a risk that could be averted by a proper balancing of insight and rigor, which is outside the scope of the book.
More reviews about this item: Amazon
