I was going to follow up yesterday's comments on matrix representations of graphs and linear operators, with a discussion of Markov chains. I still might. But I think this evening I'll write about something different.
I've already linked to Joel on
Software. I think I wrote that I liked the book with the same
title (the subtitle is
And on Diverse and Occasionally Related
Matters that Will Prove of Interest to Software Developers, Designers,
and Managers, and to Those Who, Whether By Good Fortune or Ill Luck,
Work with Them in Some Capacity). One of the things I like about
it, of course, is that the author had the good sense to agree with me
on so many issues. I also like his writing style. A few days ago I
was happy to see a new
article on the JoS site. As usual, I was entertained, and found
myself agreeing -- mostly. You might guess where our opinions differ
from this snippet:
The trouble is, we don't really have professional schools in software development, so if you want to be a programmer, you probably majored in computer science. Which is a fine subject to major in, but it's a different subject than software development.
If you're lucky, though, you can find lots of programming-intensive courses in the CS department, just like you can find lots of courses in the History department where you'll write enough to learn how to write. And those are the best classes to take. If you love programming, don't feel bad if you don't understand the point of those courses in lambda calculus or linear algebra where you never touch a computer. Look for the 400-level courses with Practicum in the name. This is an attempt to hide a useful (shudder) course from the Liberal Artsy Fartsy Administration by dolling it up with a Latin name.
He's right that software development isn't the same as computer science (and neither software development nor computer science is the same as helping an acquaintance troubleshoot Windows problems, regardless of what the world might think). Software development isn't linear algebra, either, except in a few cases. Software development also isn't reading, writing, arithmetic, or the scientific method. But if you're a software developer and you never learned to read efficiently, to write clearly, to estimate intelligently, or to construct an experiment, then you didn't get as much out of your education as you should have. Of course, you're unlikely to get very far in the most programming-intensive courses I know about -- courses in compilers, operating systems, and computer networks -- without drawing on some fairly sophisticated mathematics. Actually, a compiler course is a really good example of what I mean. Writing a compiler involves a lot of programming, but programming competence is only the start. To write a compiler, you need to know all sorts of things about regular languages and finite state machines, various classes of more complicated grammars and corresponding push-down automata, recursion, graph theory, complexity theory, and some basic logic. For that matter, it's awfully useful to know a little about -- you guessed it -- lambda calculus. None of these topics is any less abstract than, say, a similar list of topics drawn from a first course in linear algebra.
Of course, most of the programmers in the world don't write compilers,
any more than most of the programmers in the world write numerical
linear algebra software. And, much as I might grouse about it, I do
understand that lots of people will program for a living without ever
understanding linear algebra. Hey, you can write some pretty
interesting programs without really understanding recursion (though a
programmer who has never heard of recursion is sort of like a
mathematician who has never heard of Gauss -- you have to wonder about
his education, and you might think twice before hiring him). The
people who really bother me are not those who don't understand the
point: it's those who don't understand that there is a point
or, worse yet, those who scoff at the notion that something they don't
know about might be of practical import. This attitude reminds me of
the old quote that
if the King's English was good enough for Jesus,
it's good enough for me.
Gauging from his writing, though, I guess Joel would probably agree with me (maybe not about linear algebra). If you're one of the handful of people reading this, I suspect you agree, too.