We like the sense that things ultimately will add up

By Tom Stafford, Staff Writer 4:30 PM Saturday, February 4, 2012

1. Write any three-digit number. (I’m taking 100.)

2. Switch the digits around to create a second number. (010 or 10)

3. Subtract the smaller from the larger. (100-10.)

In this case, the result, 90, can be divided by 9. But what are the chances that doing this with any three numbers will produce a number divisible by 9?

As Adam Parker showed a dozen or so high school students last month at Wittenberg University’s Saturday Science program, the chances are 100 percent.

At one level, the assistant professor of mathematics and computer sciences showed off a mere math trick. And many folks know 9 is a tricky number.

Eighteen is not only two times 9, but if you add its two digits, 1 and 8, they add up to 9.

Every number divisible by nine, 27, 36, 45, 54, 63, 72, 81, 90 and 99, to name a few, either add up to or can be divided by nine.

That test turns out to be more than a trick. It’s a way we can check whether a number is divisible by 9 without the long division.

So it’s part of a pattern — one that doesn’t and won’t change. Finding those and more sophisticated unchangeable patterns in numbers and shapes is at the heart of mathematics, which is Parker’s point.

Just as Einstein said, “God doesn’t play dice with the world,” mathematics is not left to chance, he said.

“You tend to think of these things as random, but there’s a lot of structure under them.”

To illustrate, Parker draws a doodle.

He counts all the points at which the line of the doodle runs over itself. He then counts the number of spaces or holes inside the doodle and adds one for the space outside the doodle.

The number of holes minus the number of intersections always has the same answer: two.

Like Polly-Wolly, you can doodle all the day, and that will never change.

At this point someone’s bound to wonder what kind of simpleton would spend all day figuring this out.

A smart one, it seems.

“When you understand simple things really deeply, that’s where there’s interesting stuff,” Parker said.

Interesting turns fascinating when we can connect a simple thing that holds true in one area of mathematics, combine it with one that works in another, and find that the two can work together.

Springfield’s own Homer Simpson licks his fingers over one of the most famous of math problems.

The Poincare Conjecture is a problem involving a shape called a torus that Homer immediately would recognize as a donut.

Even without icing or sprinkles, the problem was round for nearly a century when a reclusive Russian solved it in 2006.

A final note.

Many of us met Pythagoras in school and even remember his theorem about right triangles (a² + b² = c²). Fewer know that his followers saw in mathematical order the expression of a deeper, mystical order in the universe, one that inspired their faith.

Most other faiths rely on words. But all believe in a more pleasing order than the one we live in.

Like modern day people, Pythagoreans lived their lives in the hope that things ultimately add up.

Contact this reporter at (937) 328-0368.

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