April 03, 2013
Welcome to this month’s PragPub magazine, available at pragprog.com/magazines.
Real and complex numbers extend the rational number system, providing solutions to equations like x^2 = 2 and x^2 = -2. They’re pretty handy things to have around. But real and complex numbers are not the only way to extend the rational numbers. P-adic numbers also do the job. P-adic math has some really peculiar properties, but because it encodes congruence information very naturally, it turns out to be easier to do certain things in P-adic math than in real/complex math.
Like proving that no three positive integers a, b, and c can satisfy the equation a^n + b^n= c^n for any integer value of n greater than two.
But P-adic math is worthy of your attention even if you’re not trying to come up with your own proof of Fermat’s Last Theorem. Because it will stretch your mind. Mark Chu-Carroll’s introduction to the bizarre world of P-adic math, where numbers run backward and closeness doesn’t mean what you think it means, is a mind-stretcher.
The other articles in this issue should give your mind some exercise, too. Like our lead article by Ron Jeffries on estimation. Two months ago in these pages Ron convinced you that estimation is evil. He’s back this month to tell you that estimation is necessary. And he’s right both times.
Paul Callaghan will stretch your mental muscles with his article on dependent types. Paul’s done a lot of work on dependent types and thinks the idea is so powerful and important that it could just be a whole new programming paradigm.
Two articles this month focus on career topics: Johanna Rothman warns about the questions you should never ask when interviewing prospective team members. And Matthias Günther continues his exploration of The Pomodoro Technique, looking at ways to tailor this technique to your particular situation. And there’s more. Steven K. Roberts continues sharing his secrets for pursuing your crazy dream without going broke in the process. John Shade puts in a good word for fear. And our new “Coming Up” page describes one of the new departments we have in the works.
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Andy & Dave
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