## Archive for July 5, 2011

### Twice the Sum of Its Digits

As my sons and I were doing a 6 × 6 KenKen puzzle today, we needed two numbers with a product of 18. “What two numbers multiply together to give 18?” I asked the boys.

Eli answered, “4 and 4½.”

“Um, yeah,” I responded. “How do you know that?”

“Well,” he said exuberantly, “4 × 4 is 16, and 4 × 5 is 20, so 4 × 4½ is 18.”

By the look on my wife’s face, I could tell that she was as shocked as I was. “Holy sh*t,” I said. “He just did linear interpolation!”

Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?

That’s the Law of Spline Demand.

As it turns out, our paths crossed the number 18 several times today. While brushing their teeth, Eli explained that he had to floss 18 times. “There are 4 spaces between my fingers, so there are 9 spaces between my teeth. So I have to floss 18 spaces on the top and bottom.”

The number 18 walks into a bar. “I’d like a beer,” he says.

“Sorry, I can’t serve you,” says the bartender.

“Why not?” asks 18.

“Because you’re under 21.”

After each night’s bedtime story, either my wife or I count to the boys before they go to sleep. Tonight, Eli asked mommy to count to 198 by the Phibby (pronounced *fee*‘-*bee*) numbers, which is Eli’s word for the multiples of 11. Nadine said, “That seems like a lot of counting,” to which Eli responded, “Not really — 198 is only the 18th Phibby number.”

**[Footnote]** As I was doing “research” for this post, I did a Google search for “joke interpolation.” I was directed to *Joke Retrieval: Recognizing the Same Joke Told Differently*, an academic paper that codifies jokes independent of context, characters, and location; instead, jokes are compared by punch line, and professions/countries are viewed as interchangeable. The result is a model that attempts to identify two different versions as the same joke. Several variations of the following joke appeared within that paper:

An engineer driving westbound collides with a mathematician driving eastbound on the same highway. Their cars are completely demolished, yet neither driver has even a scratch. They each crawl from the wreckage, and they begin to marvel at what just transpired. “This is a miracle!” says the engineer. “Can you believe that neither of us got hurt?”

“I know!” says the mathematician. “And look! This bottle of whiskey in my back seat is still intact. Such an amazing occurrence calls for a celebration,” he says, as he unscrews the cap and hands the bottle to the engineer.

The engineer swigs half the bottle, then hands it back to the mathematician. The mathematician puts the cap back on and sets the bottle on the ground.

“Aren’t you having any?” asks the engineer.

“Nah,” says the mathematician. “I think I’ll wait till after the police arrive.”