Infinity is a naturally compelling subject, and the apparent convergence of this sequence of similar iron posts brings to mind an infinite geometric series, where each term is a scaled-down version of the previous one.
Appreciation
A Tiny Triumph for Mathematical Consistency
Compared to most people, I have a heightened sense of math. One of the ways this manifests itself is through discomfort with mathematical inconsistency.
For example, inconsistent menu pricing drives me crazy (like on this Wendy’s Menu), and consistent menu pricing leaves me with a warm, fuzzy feeling (like on this Five Guys’ Menu). A recent example of this mathematical discomfort occurred at a studio where I often play music.
The owner of the studio is liquidating his library of VHS Tapes, which include a lot of rare concert videos. The tapes are nicely displayed in a glass case, and a sign displayed the prices:
I’m friendly with the staff, so I felt comfortable going off on a mathematical rant in front of them. I started in on their pricing structure.
“These prices don’t make sense,” I said. “If someone buys 4 tapes, the cost is $2.50 per tape; for 8 tapes, it’s still $2.50 per tape. Shouldn’t you be offering a larger discount for 8 tapes?”
I continued. “And look, if you buy 8 tapes, tapes 5, 6, 7,and 8 each cost $2.50, the same as tapes 1, 2, 3, and 4. But if you buy 12 tapes, tapes 9, 10, 11, and 12 each cost $1.25! The marginal cost of a tape should be strictly decreasing!”
The staff humored me by sharing a laugh over my mathematical discomfort, and that was the end of it. Until I returned to the studio.
As I was packing up and checking out of my session, a staffer approached me. “I thought about what you said last time; it made a lot of sense.” I responded with a quizzical look, unsure of what he was talking about. “The cost of the tapes,” he said. He pointed to the glass case. “I changed the pricing system because of you.”
I slept a little easier that night, knowing that I had struck a blow for mathematical consistency.
Statistics Teaching
Math and Science Education: State-by-State Rankings
This report from the American Institute of Physics ranks U.S. states by their proficiency in Math and Science education:
https://www.aip.org/press_release/state_outcomes_math_science_education_reveal_big_disparities.html
The study uses student performance in physics and calculus courses (measured by various standardized exams) as well as teacher certification requirements to rate each state.
Massachusetts comes in first, with New York placing a respectable fifth. Mississippi is dead last by a wide margin.
I originally came upon this story in the Huffington Post, and readers posted some interesting responses. One comment compared and contrasted these rankings with the average math SAT scores for each state. And another person remarked how closely these state rankings in math and science education align with state voter preference!
Challenge NYT
Math Quiz: NYT Learning Network
Through Math for America, I am part of an on-going collaboration with the New York Times Learning
https://learning.blogs.nytimes.com/2011/07/20/test-yourself-math-july-20-2011/
This math problem is based on the difference in earning potential between high school and college graduates. It adds up!
Application Appreciation
Yet Another Car Rental Scam
As a car-less person in a car-driven world, I occasionally need to rent a car to move sofas, bring home large plants, or just get away from all my car-less neighbors for the weekend. A long history of distrust of car-related business people (sales, repair) makes me approach my car-rental interactions with cynicism. Here’s yet another reason that cynicism is justified.
Car rental agencies offer a Pre-Pay for Gas option when you pick up your vehicle. “Pay now, and you won’t have to worry about filling the tank when you return the car. It’s less hassle for you! ” says the salesperson. “You even get a discounted rate on gas!” It’s not emphasized initially, but you won’t be charged what it costs to fill the tank when you return the car; you will be charged for a full tank of gas, regardless of how much gas is in the tank.
This is actually a good deal for you if you can arrange your travel in such a way as to roll into the lot on an empty tank of gas. But if you pre-pay and then return the car with half a tank of fuel? You just gave the rental agency 8 gallons X $4 per gallon = $32 worth of gas. That’s a nice little bonus for them!
And for the record, the sort of meticulous, obsessive planning required to return a rental car on empty tends to detract from the fun of your road-trip. Not for me, necessarily, but potentially for your passengers.