I’ve been an avid follower of Seth Godin ever since I watched his “why marketing is too important to be left to the marketing department” talk at the Business of Software conference. (If you haven’t made the time to see this, you really should.)
This morning his blog featured a simple quiz, which I must admit had me stumped too, despite my Bachelor of Mathematics degree:
A simple quiz for smart marketers:
Let's say your goal is to reduce gasoline consumption.
And let's say there are only two kinds of cars in the world. Half of them are Suburbans that get 10 miles to the gallon and half are Priuses that get 50.
If we assume that all the cars drive the same number of miles, which would be a better investment:
- Get new tires for all the Suburbans and increase their mileage a bit to 13 miles per gallon.
- Replace all the Priuses and rewire them to get 100 miles per gallon (doubling their average!)
Trick question aside, the answer is the first one. (In fact, it's more than twice as good a move).
We're not wired for arithmetic. It confuses us, stresses us out and more often than not, is used to deceive.
Surely, there’s a trick, I thought; I immediately started reading too deeply into the subtleties of the implicit consumption associated with new Suburbans tires vs. replacing Priuses outright – this completely missed the point!
Frustrated, I opened up Notepad and wrote it all down:
- Let m be number of miles driven by a car...
- Let s be the gas consumption (in gallons) for Suburbans (= m/10)
- Let p be the gas consumption (in gallons) for Priuses (= m/50)
- Let T be the total consumption (in gallons) (= s + p = m/10 + m/50 = 6m/50 = 0.12m)
So in Scenario #1, we have T = m/13 + m/50 = 50m+13m/650 = 63m/650 = 0.097m
And in Scenario #2, we have T = m/10 + m/100 = 11m/100 = 0.11m
Scenario #1 reduced consumption by 0.12-0.097 = 0.023; Scenario #2 only by 0.01; Scenario #1 is 2.3x more efficient! Sure, it all makes sense when it’s drawn out for you :
This very interesting article in Science, “The MPG Illusion” by Richard P. Larrick and Jack B. Soll at the Fuqua School of Business in Duke University (Vol 320, June 20, 2008, p. 1593), points out the mathematically obvious truth that gas used per mile is inversely proportional to miles per gallon, which means that you have a steeper slope at lower MPG ratings, and diminishing returns at higher MPG ratings.
Now, try to think about how this applies to your daily life and where you spend your time, particularly as an application developer.
More on this next time…