A little bit of knowledge is a dangerous thing.

There’s no shortage of stupidity in the world. And, alas, it comes in many, many different kinds. Among the ones that bug me, pretty much the worst is the stupidity that comes from believing that you know something that you don’t.

This is particularly dangerous for people like me, who write blogs like this one where we try to explain math and science to non-mathemicians/non-scientists. Part of what we do, when we’re writing our blogs, is try to take complicated ideas, and explain them in ways that make them at least somewhat comprehensible to non-experts.

There are, arising from this, two dangers that face a math or science blogger.

1. There is the danger of screwing up ourselves. I’ve demonstrated this plenty of times. I’m not an expert in all of the things that I’ve tried to write about, and I’ve made some pretty glaring errors. I do my best to acknowledge and correct those errors, but it’s all too easy to deceive myself into thinking that I understand something better than I actually do. I’m embarrassed every time that I do that.
2. There is the danger of doing a good enough job that our readers believe that they really understand something on the basis of our incomplete explanation. When you’re writing for a popular audience, you don’t generally get into every detail of the subject. You do your best to just find a way of explaining it in a way that gives people some intuitive handle on the idea. It’s not perfect, but that’s life. I’ve read a couple of books on relativity, and I don’t pretend to really fully understand it. I can’t quite wrap my head around all of the math. That’s after reading several entire books aimed at a popular audience. Even at that length, you can’t explain all of the details if you’re writing for non-experts. And if you can’t do it in a three-hundred page book, then you certainly can’t do it in a single blog post! But sometimes, a reader will see a simplified popular explanation, and believe that because they understand that, that they’ve gotten the whole thing. In my experience, relativity is one of the most common examples of this phenomenon.

Todays post is an example of how terribly wrong you can go by taking an intuitive explanation of something, believing that you understand the whole thing from that intuitive explanation, and running with it, headfirst, right into a brick wall.

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One of my pet peeves about people and math is that most
people don’t really have a clue of what math is. I’ve been writing
this blog for something over three years, and by the standards of
a lot of people, I’ve almost never written about math.

Yesterday, my son’s kindergarten class had a picnic. On my way home,
I was listening to the local NPR station, which was interviewing some
crossword puzzle writer whose name I cannot remember; I will therefore refer
to him as “crossword-boy”. (It was not Will Shortz; Shortz is much smarter than the
guy they were interviewing.) At one point, they asked him something about
Sudoku.

His response was a bit disjointed – he couldn’t decide whether to talk about
the history of Sudoku or about his opinion of it. His opinion is that it’s
incredibly dull and pointless, and that designing good Sudoku doesn’t require as
much creativity as designing good crosswords. (Just that much is annoying: I’m
a Sudoku addict, and I’ve definitely noticed dramatic differences in Sudokus
from different places. Will Shortz’s Sudoku books have great ones; most computerized
Sudoku games generate rather boring ones; the ones in most newspapers are
obviously computer generated.)

In the course of babbling about how uninteresting, non-creative, and
unsatisfying Sudoko puzzles are, he let loose with the real stupidity: “You know,
Sudoku doesn’t even have to use numbers, it can use any 9 symbols. It’s not a
mathematical puzzle at all.

Because it doesn’t rely on arithmetic, according to crossword-boy,
it’s not mathematical at all. He went on to say that it’s
just a logic puzzle, not a math puzzle at all.

Sorry pal, but logic is math.

Sudoku is an incredibly mathematical puzzle. It’s not an
arithmetic puzzle, but it’s a highly mathematical one.
In computer science terms, it’s a moderately
complex constraint-solving puzzle.

Math is more than arithmetic. It’s more than numbers. Math
is really the formal study of logic and structure. Numbers and arithmetic
are one kind of structured system described using logic which can be
studied and understood using math. But pretty much everything
with a precise, formal structure to it has at least an element of
mathematics. The structure of crossword-boy’s crossword puzzles
is fundamentally mathematical.

A bunch of readers, and one commenter in another thread, have all hit me with a pathetic
monstrosity of a purported proof of God. Several have even been misled by the URL where the
dreadful thing is posted, thinking that ScienceBlogs have picked up a creationist. Rest assured, this bozo and his blog have nothing to do with our beloved ScienceBlogs (note the “S”); it’s just some jerk who wants to try to capitalize on our reputation.

If you want to find the original page, you can go to “scienceblog.com” yourself and find it. I’m not going to link to this slime – his blog name is an attempt to use SBs reputation to pump up his credibility, so I’m not going to send hits his way.

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