Wu on rates expressed as percents
[W]hen the National Mathematics Advisory Panel reviewed two widely used algebra textbooks to determine their “error density” (which was defined a the number of errors divided by the number of pages in the book), it found that one had an error density of 50 percent and the other was only slightly better at 41 percent. (p. 4)
What I think he is saying
- All rates are expressible as percents. A Toyota Prius’s mileage, for example could be expressed as a “mileage density” of 5100 percent. Or conversely, as a “gasoline density” of 2 percent.
- My argument sounds more impressive if I support it with an abstract measure. Saying, “There are half as many errors as pages,” or even, “On average, every other page contained an error,” is much less impressive than “an error density of 50 percent”.
- American textbooks have too many errors and should be more carefully produced.
I actually agree with this last one.
The error density business is garbage intended to mislead though. The takeaway message for a casual reader is “50% of what’s in a typical math textbook is wrong!” I’m not sure whether it’s just bad writing or intentional deception.
But Wu’s gotta be careful here.
Yesterday’s Daily Wu counted two errors (a mistaken “no more than” when it should be “more than” and a false claim that the only possible number system using 10 digits is our Hindu-Arabic decimal system).
Wu now has a minimum error density of 18%. Good thing he wrote a long article.