Thu, 23 Aug 2007 09:28:01 -0700 Steve Gray <stevebg@adelphia.net> I agree that it's a bad usage, rather like "500% discount!" which I never see here in the U.S. That could be taken to mean that they give you money, and it's not that different from "five times less." I agree that it is bad usage because it may be confusing, but I don't think it is quite *AS* bad as misusing percent discounts. 500% discount is always meaningless (unless, as you say, they pay you 4 times the original price to take it), because we have a convention that already defines the meaning of N% discount. In contrast, there is no accepted convention that defines "a is X times less than b". Part of the reason I think "times less than" is bad (although I have to confess that I've caught myself using the phrase) is that I don't think there *is* a good way to conventionally define "a is X times less than b", because the common usage (i.e. that "a is X times less than b" is equivalent to "b is X times as much as a") is not consistent with the English language connotations of the phrase "less than". "Less than" could/should imply subtraction --- just as "2 times more than" could be the same as "3 times as much". On the other hand, defining it to be strict about "less than" implying subtraction would violate the colloquial usage, so would introduce more confusion than it would clear up. As far as RWG's original topic, I am sickened by what I see in my kids' official math textbooks [luckily my 12 and 14 year olds read other ("real") math texts recreationally]. Even when the texts aren't wrong, they rigidly mandate rules that must be followed or else the student is "wrong". We just moved coasts and the kids are entering a school which is switching to "Singapore Math" --- a curriculum that seems at odds with mathematics (it seems to really be against abstraction of any sort) and promises to be even more mind-numbingly prescriptive than the crap we've gone through until now. I am too depressed about the general topic to want to start this thread, though, unless people have useful suggestions (and home schooling is not practical for us). Science textbooks are bad in a different way: they are not as clearly *wrong* as the math books I've seen, but usually so unclear and vague that they convey *no* information whatsoever, except for some fuzzy feeling that _something_ is being explained. The specifics are never clear, it isn't quantitative (unless it is an extreme oversimplification), no causal relationships are ever described, and the notion that an experiment demonstrates or disproves something cannot be found. The entire notion that science is a way of answering real questions about the real world (one of the things that I found so exciting as a kid) is gone. In any case, this is not math "fun" --- it is math "pain" --- so doesn't belong on this list. Christoph Pacher wrote:
[...] Those books weighed maybe five times less, and contained way more than twice the algebra.
How do people feel about this construction, in which you use the phrase "five times less" to colloquially mean what a formal description would have to call "one fifth as much" or the like?
This came up on a blog I read, in which commenters seemed about equally divided between "This is just fine, it's completely obvious what the construction means" and "that's literally meaningless, no reasonable person should produce such a statement." At the time I wondered what the breakdown would be among a mathematician audience, and this seems like a chance to find out.
My vote is against "x times less", where x>1. I do not use it (but it is used by German speaking people as well).
Christoph
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