MM: How did you come up with the idea for Fifteen Furlongs? How long did it take to program?
KW: I came up with the idea while helping some of my friends study. Some of their answers were obviously wrong if you understood what the units meant, but they didn’t, so that level of checking wasn’t there for them. As a result, I thought of this idea of having “sensible” units that you could compare to to get a better understanding of what units mean. The entire site took a week to program and I worked on entering equivalences for the next few weekends.
MM: How does it work? (How many units of measure does it consider? How does it choose what to report?)
KW: It works by taking your input and splitting it into the scalar and the units. Then, it converts the units to SI base units and multiplies that conversion factor by the scalar. Finally, it checks against the list of known equivalences for the SI unit combination and picks the one that is closest to “one” equivalence.The site itself accepts 107 different units and 24 different SI prefixes, so 2568 total units possible. It even accepts units like knots, joules, amperes, newtons, and Sieverts. I think my favorite feature is that you can type kg*m/s^2 and it’ll interpret it correctly as a Newton.
MM: What made you decide to study mathematical subjects like physics, economics, and computer science?
KW: Mostly they were subjects I was interested in. As a kid, I got hooked on computer science when I learned programming, but it was more of the algorithms and math that drew me in. Physics and economics interested me because they use math to explain the real world, which I thought was awesome.
MM: What was math like for you as a kid? Did you ever do mathy things outside of school?
KW: Math was pretty competitive for me. I personally found my school’s math program to be too simple, so I ended up learning more advanced concepts outside of school. This worked well for me in competitions like the American Math Competition, Michigan Mathematics Prize Competition, and others. I think as a kid though, I found the competitions to be the main motivating factor to get me to learn more math.
MM: Was there ever a downside to the competitive side of math for you?
KW: At a certain point near the end of high school, the math became extremely difficult and lost the intuition and applications that drew me in in the first place, so it took a lot more effort to keep trying. That ended up being pretty exhausting for me and it actually made me lose interest in math for a bit, but I realized that that was just the competitive edge, and there was a lot more beyond competition that I enjoyed.
MM: Do you have a favorite mathematical fact/tidbit that you can explain?
KW: A fact that I really like is the fact that miles per gallon is a unit of inverse area. That is, if you think of gallons per mile, gallons per mile is actually just area. Gallons is volume and miles is length, so gallons per mile actually represents the cross-sectional area of the gasoline you’d use if you stretched it out over the course of the entire route. xkcd did a great job of explaining it here.
MM: Our site is for middle schoolers and up. Do you have any tips or a message for young mathematicians?
KW: A lot of my friends in primary school found math to be boring without knowing any practical applications, but math is everywhere, and it’s those applications that are interesting! I like to think about the most random things while waiting, like figuring out the speed of an elevator. You know how tall the floors are and you can count the seconds, so you should be able to find the average speed of an elevator pretty easily. I’ll bet most people will be pretty impressed if you tell them the speed of the elevator car they’re in, even though it isn’t too difficult to find out.