Found a great article on the math of checkout lines. It does a great job of showing a concrete example of some fancy math concepts, and also shows the difference between thinking something is correct and having proof of it.
Given the picture below, which line do *you* think is faster? Click the image to find out.
Thanks to Corey for this.
This guy, Evan Miller, put together some proper Math to produce a better way for ordering things with positive and negative ratings. You know, things like music lists, movies, products, anything that gets rated.
Also, I see his site says he’s a PhD student in University of Chicago’s Economics program. That’s supposed to be a good school for econ. Seems bright, got some good-looking writings on his homepage.
Science!!
There’s this idea I’ve had rolling around my head for a while now. I call it the Law of Small Numbers, but it’s not really a law, and it’s apparently not called that either, at least according to Wikipedia.
Basically, it’s that small numbers increase easier than big numbers. It’s an idea that’s become popular with investors — small businesses can double your money easier than big ones. A tiny store can easily double it’s business, WalMart can’t.
Simply put, if you’ve got 2 units, and you increase that by 1, you’ve increased by 50%. If you’ve got 20 units, and you increase by 1, it’s only 5%. That’s the Law of Small Numbers. Maybe I should call it the Law of Increases of Small Numbers.
It’s something that’s popped into my head lately, thinking about gas prices. I’ve been trying to collect some gas mileages in my car, so that I can have hard data to look at. The way I see it, your gas mileage is a function of your gear, and your RPMs. Assuming constant gear (let’s say 4th — you’re cruising). If you are going from 2000 RPM to 4000 RPM when accelerating, you are literally cutting your gas mileage in half. If you can travel 55 MPH at 2000, but 60 MPH at 2500, is it worth decreasing your mileage by 25%? What if the corresponding speed increase only gets you there 90 seconds faster?
On a side note, one of the pages linked from that Wikipedia page discusses the Strong Law of Small Numbers
“There aren’t enough small numbers to meet the many demands made of them.”
I see this as the reason that things always seem to happen in twos and threes, but that doesn’t mean that they’re related.