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(A gripe, poorly disguised as a question...) I see many instances of writing like this (actual, recent examples):
"Our telescopes are now capable of finding planets four times as small as that."
"That algorithm is more secure, but it is two times slower."
"Twice as few crimes were reported in the same period, this year."
They use what I would call the inverse of a measurable quantity. I understand something being one quarter as large because "large" substitutes for an unstated size, but "four times as small," doesn't make any sense to me, because I seem to have defined "small" as only being meaningful in comparison to how large something else is. Same with many/few: "half as many" makes sense, but "twice as few" doesn't. Is this a problem for others, or am I being to persnickity? Would a professional writer or editor find anything wrong with that kind of writing?
I've been a freelance tech writer for over 10 years now, and I totally agree with your complaint about this being sloppy writing. In order …
1. Does "four times as small" refer to area or diameter?
2. Does "two times slower" mean half the speed, or 1/2x2 = 1/4 the speed? Why not just say but it runs at half the speed?
3. For "twice as few," same comment as #2.
You are not being "persnickity." It grates on my sensibilities too. Reminds me of that current TV ad for mycleanpc.com, where the customer exclaims "My PC is running 100% faster!" Now what the hell does that mean, quantitatively?
I may not complain quite as bitterly, but I absolutely side with both of you. The general pattern is that they're measuring the lack of something rather than the something, which I've always suspected is feasible but risks confusion. If someone says "twice as slow", the only sensible thing he can mean is "half as fast"; but if I interpret it literally, "twice as slow" must mean going backward at the same speed. The same with "twice as cold" (surely means "half as hot", but if taken literally is impossible), "twice as few", "twice as dark" and so on.
The only thing I'll cavil at, Heimhenge is your question #1 above; that question applies equally to "four times as large". The right question (it seems to me) is whether "four times as small" means one quarter the size. Because if it doesn't, it sounds an awfully lot as though the speaker must have mean "400% smaller", which (like "twice as cold") is physically impossible if you take it literally.
Wait, maybe there are two things to cavil at. If the problem is measuring the lack of things rather than the thing itself, what's wrong with a PC running 100% faster? If it ran 100% slower, that would be a problem—the PC would, in fact, have stopped—but "faster" must mean something. We measure computer speed in flops—FLoating Point Operations Per Second—or more often megaflops or teraflops, so 100% faster must mean it's doing twice as many flops, no?
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Here's a related question, just for fun. Suppose you have a race track that's half a mile around. A horse runs a lap around this track in a minute, giving him an average speed of 30mph for the first lap. So how fast must the horse do the second lap in order to average 60mph for the two laps taken together? I think my dad first put this question to me, when I was a teenager, to get me thinking about the dangers of averaging figures and especially rates without careful thought; it can be done, but you have to pay attention.
Ron Draney said:
Bob, while I realize it's not really thermodynamically accurate, I think I'd be inclined to allow someone to say that twenty degrees below zero is "twice as cold" as ten below.
Now, if we can just come up with a workable reading for "twice as cheap"....
I would understand your statement if "ten degrees below zero" was used earlier in the sentence, because you're nailing down something (zero degrees) to measure against. So, "Yesterday it was ten degrees below, and tomorrow is expected to be twice as cold" means (to me, at least) "Tomorrow's temperature will be twice as far below zero as yesterday's temperature."
I think Bob clearly articulated it: It's confusing to try to measure the lack of something. Saying "It cooled down this afternoon, and tonight should be twice as cool" makes no sense because there's nothing to measure against.
I think Bob's computer speed example could be salvaged if they spoke in terms of response time, instead of FLOPS. E.g. "My computer responds in half the time" or "My computer is twice as responsive." ...And now I'm thinking that "twice as responsive" may be just as vague and confusing to others as the examples I started this thread with...
Heimhenge said:
Does "two times slower" mean half the speed, or 1/2x2 = 1/4 the speed? Why not just say but it runs at half the speed?
That's whole nother gripe. Even if you take "slower" to mean "inverse of speed", does "two times slower" mean it takes 3 times as long, or is it just another way of saying "twice as slow"? I hear many news reports and ads that use more and as much interchangeably.
I'm more well-versed in math than in language, and I read "more" as "plus", and "as much" as "times". To me, "150% more" means "100% + 150% = 250%", and "150% as much" means* "100% x 150% = 150%".
Bob Bridges said:
[...]
Here's a related question, just for fun. Suppose you have a race track that's half a mile around. A horse runs a lap around this track in a minute, giving him an average speed of 30mph for the first lap. So how fast must the horse do the second lap in order to average 60mph for the two laps taken together? I think my dad first put this question to me, when I was a teenager, to get me thinking about the dangers of averaging figures and especially rates without careful thought; it can be done, but you have to pay attention.
The horse must do the second lap infinitely quickly, resulting in zero time having been spent during the second lap. That is, the derivative of the horse's position with respect to time would have to be undefined (graphically, a vertical line).
Here's another question. The weatherman says today's temperature is 0 ° Fahrenheit. He then says tomorrow is going to be twice as cold as it is today. What temperature is forecast for tomorrow?
telemath said:
...And now I'm thinking that "twice as responsive" may be just as vague and confusing to others as the examples I started this thread with.
No, I think your "responds in half the time" works well, telemath; I like it, and intend to insist on it in future conversations—that is, to insist that "twice as responsive" be taken to mean "responds in half the time".
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My Young Padawan, I can think of several possible meanings of "twice as cold":
1) "Half the heat"; if it's 0 °F yesterday (255 kelvins), then it'll be -230 °F (128 kelvins) tomorrow.
2) "Half the difference above" a given reference point, if the temperature is positive, or "twice the difference below" that point if it's negative. a) If the reference point is 0 °F, then it'll 0 °F tomorrow too (because twice 0 is still 0); b) if the reference point is freezing, then 0 °F is 32 degrees of frost and it'll be 64 °F below freezing tomorrow, or -32 °F.
If I were writing in a scientific periodical, or speaking to my children, I'd probably use the first definition. From a weatherman, I might ask him at least to use 2b. But if he then laughed and said he meant 2a, I'd smile politely and let it go...unless he seemed to think it was actually correct.
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"Parts of a car moving infinitely faster than other parts..."? Hmm. <pause for thought>
Hmm.
Hmm...
Oh, wait! If the car is idling, it can be said that some of its parts (the tires, say) are not moving at all—their velocities are 0—and all the engine parts (well, many of them) are moving, either rotating or reciprocating. The comparative velocities of two objects may be expressed as the vector of one divided by the vector of the other. Mathematicians say that any number divided by zero is not infinity but undefined, and sometimes I believe I have a glimmer of understanding why they insist on this; but if you were to ask me what the difference in speed is between a non-rotating tire and a rotating but disengaged crankshaft (for example), expressed as a percentage, I would probably think of infinity before I remembered to correct it to "undefined". Is that what you meant?
In terms of language as opposed to physics, I consider such statements as twice as cold as being idiomatic rather than literal. Thus I beg the quantification conundrum. I consider it much like millions, a dozen, a thousand, etc. — unless used in a clearly quantitative context, these are not literal. Twice as cold simply means a lot colder.
If forced to take it more literally, I would tend to agree with Bob's approach 2, with a small modification. When discussing weather and ambient temperature, we usually do so with respect to our comfort levels. These perceptions of comfort are typically centered on room temperature of around 70 °F.
Another very common reference point — and more likely in this specific example of twice as cold as 0 °F — is the reference point of the expected temperature. Based on the use of the twice as cold, it is likely that 0 °F is colder than expected. It is impossible, without additional info, such as location and date, to estimate the expected temperature. If it is January in Happy Valley-Goose Bay, then the average January temperature is around 9 °F. Twice as cold in this context could suggest a mere -9 °F.
But this comes from a guy who, when parked in the distant regions of a large parking lot, will say that I am parked way out in Timbuk-four. If it is a mall approaching Christmas, maybe even Timbuk-eight.
Ok, I'll buy that; the reference point is the expected or the comfortable temperature. Actually, that's exactly what I would have meant as a child, before I thought about it. My personal favorite temperature, when I'm outside and moving around, is in the low 60s (18 or 19 C); so if it's 52 today and I say it's going to be twice as cold tomorrow, I might mean it's supposed to be in the low 40s. In other words, it feels twice as cold, that is, twice the distance from the temperature at which I feel perfectly comfortable. Other people, of course, would measure from a different point; my wife, for example, would probably start from about 80. This is all in Fahrenheit, of course; my apologies to the Canadians and other furriners who think in centigrade.
What has parts of itself moving infinitely faster than other parts, and stays in 1 piece?
Answer: the car. But how so?
Bob Bridges said:
… If the car is idling, it can be said that some of its parts (the tires, say) are not moving at all—their velocities are 0—and all the engine parts (well, many of them) are moving, either rotating or reciprocating…the difference in speed is between a non-rotating tire and a rotating but disengaged crankshaft (for example), expressed as a percentage, I would probably think of infinity …
You surely found a way to make the riddle looks too easy. But how about limit it to include only external parts of the car, say visible to pedestrians, and make the car perfectly tight and snug, so no part is shaking or rattling relative to another, and exclude windshield wipers too.
Hint: it's all about instantaneous velocity.
Telemath sounds like he already knows the answer.
Someone around here used that term recently ("instantaneous velocity", I mean), and in context it sounded as if she was referring to the velocity of an accelerating object at an exact moment, as determined using the calculus. If so, I understand that part. But it isn't clear to me what that has to do with infinite relative velocity.
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