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3Sep/110

Review: Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction

Great stories. Interesting and challenging problems. Instructive MATLAB code. Lots of physics. That's my in-a-nutshell assessment of Princeton University Press's hot-off-the-press Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction.

Paul Nahin is a great story teller. Some of you might recall my review of an earlier book of Nahin's An Imaginary Tale where I noted Nahin's enjoyable writing style. Nahin has, in fact, written quite a number of books.

Nahin takes on the subject of using computers to solve difficult problems, many in physics, that couldn't be solved before computers. The publisher's page introduces some of the problems.

How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.

Nahin explains that physicists can't always find elegant equations that describe a problem and, if they can, those equations may not be solvable. Plus, even when a scientist can solve an equation it's very important to back up the solution of an equation "in the abstract" with numerical values, i.e. numbers obtained through crunching a model.

Nahin illustrates his approach to solving problems with MATLAB code. While I'm not a MATLAB programmer, the examples are short and simple enough that they should be easily portable to Mathematica or other number crunching environment.

Nahin's strength to a general reader (I consider myself one of those in relation to this book) is that he paints the historical landscape remarkably well. As someone who grew up using punch cards with an IBM mainframe (I'm dating myself) I love stories of early computers. Nahin shares a number of these. That makes the book deeply enjoyable for me.

I have to confess, physics is not one of the subjects I enjoy. Thus, I can't speak to the interest that the many discussions of mathematical physics may have for readers. This is one of those books that one can read as a spectator, enjoying the scenery, taking in the landscape, appreciating the rich stories -- my relationship with the book -- or one can dive in, study the many equations, run the code, and have a personal experience of how problems that were unsolvable just a few decades ago have succumbed to computers.

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