A reader writes, apropos my Slate piece,

Canada cannot have crime rate ten times lower than the crime rate in the U.S. It can have crime rate of one tenth the crime rate of the U.S.

I've heard this objection before, but I'm just not sure I understand its foundation. Indeed, if "X times lower" meant "lower by X times the original amount," "ten times lower" would make little sense (except if for some reason you said that -9 was ten times lower than 1). Or if you somehow just defined "times lower" as an error, it would be, by definition, an error.

What I don't grasp is what justification, besides the objector's own view of what the language should be, there is for this. This is, to my knowledge, a common part of normal English usage. It's not confusing. It's not illogical unless one defines "lower" in a pretty strange way.

Even if one is a prescriptivist, who argues that a statement is bad English if it doesn't conform with The Authorities, what Authorities actually condemn this? There might be some, and please let me know if there are, but I just don't know of any, and my quick and dirty search didn't come up with any.

Naturally, if you think that this usage is ugly or annoying, I can't really argue with that. And if enough people think that, one might want to avoid the usage simply to avoid annoying one's readers. But I took the "cannot" to mean "cannot, without violating the rules" rather than "cannot, without annoying me." Where are those rules set down?