Thursday, April 24, 2008

For Carrie: Maybe Americans aren't so good at math

Knowing that Citizen Carrie "enjoys" chronicling the hilarity of the American auto industry, I point her (and anyone else who's reading) to this story from The Numbers Guy at the Wall Street Journal. Essentially, the CEO of Ford, in claiming that his cars simply have too many options for consumers, said that the 128 console options for the Lincoln Navigator would ultimately disappoint the customer, because there was no way the dealer could stock "128 factorial" different cars. So Ford is going to simplify the process by cutting the number of options.

[What I guess this means is that Ford will bundle more of their options, so the customer will be forced to take things they don't want in order to get the things they do want. To their credit, Ford admits that this is a move to cut costs, but, to their detriment, they're also trying to spin it into a benefit for choice-beleaguered consumers. If there's anything which symbolizes the problems of our automakers, it is that, at a time when businesses are trying to customize the "shopping experience" for each customer, the Big 3 are retreating to one-size-fits-all. No, Mr. Mulally, we are not looking for a Model T.]

The problem, of course, is that factorial refers to the arrangements of things. For example, if you have a red, a yellow, and a blue pencil, you can line them up in 3! (! is the symbol for factorial) different ways: RYB, RBY, YRB, YBR, BRY, and BYR. But you can't go to your dealer and ask for the options to be moved around ("I want the speedometer here, the A/C control here,..."), the situation in which factorial would apply.

For car options, the relevant calculation depends on the existence, not the placement. So the ways you can ask for, say, three options are (using * to indicate the lack): RYB, RY*, R*B, R**, *YB, *Y*, **B, or ***. There are 8, and we could find that without listing them by calculating 2^3 (each option is presumably independent of the others, so you can either have it or not, thus there are 2 options, yes or no, for each of the three slots: 2*2*2).

So we are looking at the difference between 128! and 2^128, and the former is much, much bigger (see the article for further discussion). When The Numbers Guy contacted Ford:
“Essentially, your reader is right,” Ford spokesman Mark Truby told me Thursday afternoon, adding that the true number is probably lower. Mr. Mulally “was trying to make a point.”
And here is the epitome of corporate-think. First, the spokesman sticks in an "essentially," a null word that does qualify the statement to a degree. Second, it's explained away by, "trying to make a point"; in other words, the factual content is unimportant as long as the point was made successfully.

One wonders (but not very long) how tolerant Mr. Mulally is when a VP walks into his office and says, "We sold a bunch of cars this month, but the number is unimportant as long as we sold some, 'cause that's my point." Or, perhaps even more importantly, if Mr. Mulally's check comes in minus a couple of zeros.

1 comment:

Citizen Carrie said...

OK,OK, you dragged it out of me. In the first grade, I was the best reader in my class but second worst in math.

Clicky Web Analytics