(Cross-posted at Gifted Exchange) I’m recently back from a week-long vacation at Disney World with my three small children. It was a lot of fun (if not exactly relaxing). My inner geek was on display, though, as I kept pondering the logistics of line management.
Disney has huge crowds for the popular rides. In a keen bit of psychological insight, Disney understands that people tolerate waits better if there’s transparency on time. The powers that be also know that some people detest lines enough that they will give something up (like complete flexibility) in order to be guaranteed a short wait.
So all popular rides have two options: a stand-by line, with a posted wait time, and a “Fast Pass” option. To get a Fast Pass ticket, you go to a machine by the ride and insert your park pass. The ticket gives you an appointed window to show up in order to bypass the line. The catch is that there are only a certain number of Fast Pass tickets per day, and they are given out in chronological order. If you show up at 9am, you might get a fast pass time of 10am-11am. Show up at 1pm and your time window might be 8pm-9pm, with the downside that you probably can’t get another fast pass ticket until you return yours to the ride in question. So you’re shut out of other popular rides for the day, unless you wait in the 60-plus minute standby line.
Making best use of all this information involves optimizing various variables: how much you dislike lines, how long the lines actually are (often a function of time of day and day of week), and how much you care about this particular ride in comparison to other rides. For example, “Soarin'” is by far the best ride at Epcot. Our first day at Epcot, we got Fast Pass tickets for the ride for a roughly 8pm return. That was fine, because there weren’t very many other popular rides at Epcot. Once we learned that Jasper really liked that ride, though, we showed up the next day when Epcot opened. He and I made a beeline for Soarin’ and got on the first run. Meanwhile, my husband got us all Fast Passes for the 9:45-10:45 window. So we got to go on the ride twice with no wait. By the time we got on for the second time, the standby line was up at 30 minutes, and it hit 60 very shortly. Fast Passes sold out by afternoon. Score!
Optimizing in a world of multiple variables is, of course, a real world application of math. Amusement parks are one thing, but many other fields make use of this knowledge as well: economics (and business forecasting in general), engineering, logistics. Not having a background in advanced math would make getting jobs in any of these fields rather difficult. That’s why I was quite disturbed to read (in Marian Wright Edelman’s Huffington Post column) about the results of the Department of Education’s Office of Civil Rights survey of public schools in America. Edelman has her own opinions on tracking and funding that I don’t share. But regardless, these are some disturbing statistics: “Fifty-five percent of the low-minority high schools surveyed offer calculus but only 29 percent of high-minority high schools do. Similarly, 82 percent of low-minority schools offer Algebra II compared to 65 percent of the high-minority schools.”
While some enterprising students might take Algebra II or Calculus during the summer or petition the school for an online course (or do Khan Academy on their own), a school’s course offerings pretty much set the tone for what a student is expected to know. That such a low percentage of high schools offer calculus — and an appallingly low percentage of schools serving mostly minority kids — does not bode well for a mathematically promising future. That’s a far worse outcome than a 75-minute wait in the line for Space Mountain.
Did you take calculus in high school? What’s your favorite real world application of math?
photo courtesy flickr user Tia Eliane Turismo e Intercambio