Hooray for New Age Maths

There was this fantastic article on the Green Economics of SUVs in the New York Times of all places:

The argument is that the saving in fuel from 14 to 24 MPG (from a big SUV to a smaller one) is a better saving than from 24 to 46 MPG (from small SUV to Prius), and thus one should exchange one's Hummer for a new Toyota RAV4, not a Toyota Pious.

Actually, no. In fact, upgrading the inefficient S.U.V. to a more efficient one would save a lot more fuel — 372 gallons per year — than the 250 gallons saved from the switch from an efficient S.U.V. to the most fuel-efficient car on the market.

Why does 10 m.p.g. matter more than 22? The reason is that the relationship between m.p.g and fuel savings is not linear but curvilinear. Ten m.p.g. at the bottom of the range matters a lot more than 22 m.p.g. higher up.

And apparently:

This is a hard concept for us to get our brains around. Richard B. Larrick and Jack B. Soll, reporting in Science (gated) found that only 1 percent of college students studied correctly perceived that an improvement from 14 to 24 m.p.g. saves considerably more fuel than an improvement from 24 to 46.

That only 1% of college students got it right tells me more about the sort of kids they let into college these days, and is in my view indicative of the underlying problem in that (i) only 1% are capable of doing high school maths and (ii) less than 1% are studying Maths, Science or Engineering. (If its the M,S,E lot that got it wrong lord help us.....). But hey, if everyone is studying New Age subjects, Finance or Economics who wants numbers that add up, the taxpayer bails you all out anyway, right?

So one is somewaht resigned to it when he says:

The trick is one that even fourth-graders can master: invert the fraction. Let’s consider not miles per gallon but gallons per mile (or, to make the numbers prettier, gallons per hundred miles). By this metric, we get an unclouded picture: the Prius uses 2.17 gallons per hundred miles, the RAV4 uses 4.17, and the Range Rover uses 7.14.

Good heavens - that means to go 100 miles there is a 2 gallon difference between Pious and RAV4, but a 3 gallon difference between RAV4 and monster SUV. Who woulda thunk it.

Anyway, his thesis is that one should therefore substitute one's Hummer for a RAV4, not one's RAV 4 for a Pious to be having the biggest impact. Can you see the problem in his argument?

Aha, I hear you say - why not just substitute your Hummer straight for a Pious and then get all that fuel saving benefit and be truly Green and Pious.

Buzzzzz. Wrong!!!!!

Wrong?

Yup, wrong - because the BIG EQUATION here is Total Lifetime Energy Usage, and the Hummer is already built - its called a Sunk Cost, I've already raped the planet for it. However, if I buy a new RAV4 or a Pious I have to rape the planet again for all the materials, labour, energy etc to build the new car.

And guess what - the energy absorbed in building that new car will far outweigh the energy absorbed in the difference in fuel consumption for the 100,000 miles or so I will drive.

Allow me to calculate this - thats roughly 5,000 gallons of fuel - $ 12,500 at $1.50 a gallon - difference between Hummer and Pious over a lifetime.

Now, the cost of a car can pretty much be thought of as the sum of its energy inputs, so a Pious at c $24,000 (margins on smaller cars are wafer thin, that's mostly real costs) is about double the $12,500 figure.

So, by buying that new Pious rather than keeping the existing Hummer you have just burnt nearly double the amount of energy as you would in driving Ol' Gas Guzzler another 100,000 miles.

Now if you were to buy a Second Hand Pious, then that would be fine. But hey, you may as well buy a second hand car you actually like driving, as the marginal difference is far lower than buying a new car

Anyway, for your enjoyment I have put up the YouTube vid of Tom Lehrer's "New Maths" as done by RonfarZ3

Here endeth the lesson.