### Units of Folly

During the week after the article came out, my conversations on hybrid cars went something like this:

Person 1: "blah-blah-blah hybrid cars blah-blah-blah"

Person 2 : "Speaking of hybrids, did you hear that there are people who are working on cars and getting 250 miles per gallon?"

Nate: "Yeah, but they made a mistake. They're not just running gas, they're plugging the cars into electrical outlets."

Nate takes one of those pauses that he takes to breathe, and then doesn't get a chance to finish his thought before Person 1 or Person 2 patronizingly explains to him, as if he does not know it, "Yes, they plug into the walls, and that means that they are getting some of their power from outside the car, so they are really just transferring pollution to the power plants, but we can solve that by finding cleaner sources for electricity. And running off of wall charging is good enough for most people's commutes, but since it actually has an engine and can be called a hybrid people won't be turned off from buying it. So you're wrong, Nate. There's no problem with what they are doing."

Nate, perturbed that he's having yet another person explain what he already knows about there being no problem with plug-in cars and upset that he's trying to point out a mistake being made in a calculation, not a problem with what the people are doing, takes time to compose himself.

"I know all of that," Nate grumbles. "I'm just trying to point out that they aren't getting 250 miles per gallon of gas if over three quarters of their miles are coming from a source other than gas. They're getting under 50 miles per gallon of gas and 200 from charging batteries in the wall. That's not 250 miles per gallon of gas, it's less than 50 miles per gallon of gas."

Another example of the same mistake that I've had trouble explaining to the same people is cost of vehicle ownership. My wife and I added up all of our vehicle expenses, including gas, oil changes, repairs, inspections, registartion, and the price we paid for the car. Then we divided by the distance we've driven since buying the car.

A number of my fellow graduate students were perfectly fine with this, but they objected to my comparison of this result to what people with car loans pay per mile for their cars. I include monthly car payments and inital loan payemnts and fees as part of the cost off ownership, but the objecters did not. So they conclude that my wife and I pay more per mile than a person with a car laon, because gas is abit more and there ar emroe repairs, while I say we pay less because we don't shell out hundreds of doallrs a month jsut on payments. Yet the same people who won't include car payments in teh vehicles cost find it perfectly logical, and in one case necessary, to include the purchase price for a vehicle bought without a loan. It goes without saying that I didn't even bring up the word depreciation with these people, even though in fact the current value of the car is held as an asset that you can liquidate and so can be included as such in the calculation.

The common mistake in these two examples is in the units, but it's not one of the normal mistakes that we make with units. Normally when we do a calculation we take all of the numbers, we do the math, and then we accidently use the wrong units. NASA has lost space probes in this way. It happens.

In my examples above, though the mistake is different. In the examples, we have an idea of what we want to quantify and the units we need to get some desired bit of quantitative information. The mistake is that in striving towards an answer with those units we may not make sure that the units are the correct ones to give us the answer we want to know or we may not have starting numbers that represent all of the things that must be oconsidered to properly give a number to go with the desired units.

In the second example, which is easier, we want to know the costs per distance but the example makes a mistake. The cost per mile of ownin ga car must include the cost of the car. If you have a house, you don't say that the cost of owning a house is simply the utilities plus the maintainence, do you? No, you include the mortgage. And you can do a lot of other number fudging by including or excluding equity, which basically measures depreciation, and remaining balance on the loan, giving you a host of numbers to pick and choose as your calculation's result (although I would only count two of them as correct, and if I did the numbers then I would label which number I used). Your dog does not cost you food, shots, and vet bills. Your dog also costs you the price you paid for the dog. Your trip to Dairy Queen is not free just because the ice cream you bought required you to pay no extra money between purchase and complete consumption. Your trip to Dairy Queen costs more than the gas you paid to drive there, too.

Do you get it? You don't even need to think about opportunity cost.

Shifting gears, in the first example we want to know the distance traveled per unit of fuel consumed. The mistake here is not accounting for all of the fuel and coming to the ridiculous number of 250 miles per gallon of gasoline. Sure, that is indeed how many miles said cars get on one gallon of gasoline. But how many miles would it get for two gallons? It's nowhere near 500 miles per gallon unless you stop the car and plug it in for a while. If you just keep driving for another gallon, you'll only go an extra 40 or 50 miles. And so on until the tank is empty. It's only the first gallon that gets the extra miles.

Miles per gallon is an excellent representation of miles per unit fuel only when gasoline is the only fuel being used. After all, if you have a horse pull your car for 100 miles and then drive a gallon of gas, you don't claim that your car gets 130 miles per gallon of gasoline, do you? It's technically correct, but it doesn't provide the information you want to know. So the problem with the 250 miles per gallon hybrids is that the value of 250 miles per gallon does not represent what we want to know, miles per units of fuel consumed. We need to include all fuel sources in some way and no matter how we do it we will need to convert some units. No economic, technological, ecological or sociological argument is going to change this, although the infomation provided once we get the calculation correct is good for forming and evaluating those types of arguments. (I can't do the conversion, by the way, because I don't have all of the numbers I need.)

The only reason why I still have respct for my fellow sciencey types who make these sorts of mistakes is that, as I said, these aren't the normal mistakes that are made with units. They are more abstract mistakes and they are easy to make. The potential to make them is all around us. You can make 8 cakes with a five pound bag of flour, unless you make other things with the flour, too. The eight cakes will weigh eleven pounds, more than a bag of flour, because there are other ingredients. The only reason why we don't make these mistakes is because figuring out how many cakes we'll get form a bag of flour, or how much one bag of flour's worth of cakes will weigh, isn't something we do every day. Neither is figuring out how fuel efficient our vehicles are or crunching the price per mile that we pay for our cars.

So, I forgive my fellow nerds. I just wish they'd let me finish my thoughts before they tell me what I already know about hybrids.