Is anyone else bothered by idioms like "twice as close" or "twice as small"? I understand what these phrases mean and how they're used to indicate the inverses of "twice as far" and "twice as big", but they still bother me. If (A) is two miles away and (B) is one mile away, (A) is twice as far away as (B), but (B) is 50% closer than (A), not "twice as close". If distance in miles is the metric for "closeness", how can "twice" and "50%" mean the same thing? "Twice as far" indicates that the magnitude of the distance to (A) is 200% the magnitude of the distance to (B). The concept "twice" should be independent of what is being measured. If (A) is "twice as floober" as (B), then we should know to take the magnitude of (B)'s floober and multiply by two.
Do other languages have corresponding idioms that make illogical use of "twice" or other relative modifiers?
I too am bothered by this. It's one of those things that doesn't make sense (if you want to be logical about it) but that has become acceptable. I think it happened gradually. The way I imagine it happened goes like so: First, "twice as fast" was used when referring to speeds or rates (number of something per unit time), which makes perfect sense. Then, "twice as fast" was used to mean "in half the time", which makes sense in some situations ("This printer can print 1000 pages twice as fast as that one") but not others ("You can get to the Sushi place on California Street twice as fast as the one in Clement Street" - implying "same speed & half the distance -> half the time). Once the illogical use of "twice as fast" became acceptable (it snuck in, since the phrase "twice as fast" is not inherently illogical), then this opened the gates for inherently illogical things like "twice as small" and "twice as close".
While this particular kind of thing sounds very odd when you say in in Portuguese (then again, I have not lived in Brazil since 1999, so it may have become acceptable since then for all I know), we do say plenty of illogical things. Like double negatives. The equivalent of "I didn't do nothing" is THE way to say "I didn't do anything" in Portuguese. This weird way of saying it is so consistent across the language that I did not realize it was illogical until I started to learn English and had to be told when to use "nothing" and when to use "anything". It was then that I realized that every Portuguese sentence that in English translates into "... not ... anything ..." is stated in a way that, if you're strict about it, says the opposite of what the speaker means.
In other words, give it a generation or two and people will look at you funny when you point out that saying it this way makes no sense.
End break.
Bernardo
Okay, one more thing:
"If (A) is two miles away and (B) is one mile away, (A) is twice as far away as (B), but (B) is 50% closer than (A), not..."
I'm not even sure if I agree with that. If "closer" means "at a shorter distance away", then "50% closer" can mean "at twice the distance" (since it's "less closer", or not as close) just as it could mean "at 50% the distance". In other words, "half as small a distance" could mean "half the distance" or "a distance not as small". Does that make sense? Not much. Therefore, adjectives/adverbs that mean "not as _ _ _" should not be modified by things like "less", "more", "twice as", or "50%". Since those adjectives imply negation, modifying their magnitude with "less", "more", "twice as", or "50%" could mean increasing OR decreasing the magnitude of the property you're talking about, it's just not clear.
(That's the difference between the logician/philosopher/CS-researcher person and the engineer. The engineer can say "this just doesn't work, so can we just not do it this way and do it THAt way instead?").
Ok, I better stay a little late today otherwise I'm going to feel guilty. Nick, stop sending me links to your brother's blog during workday hours!
BNM
To be fair, I just remembered that the link that landed me on Mike's blog today was sent to me quite a while ago, I was just going through old-ish email...