I wish I had a buck for every time I’ve asked authors to correct this error. Bill Walsh (http://www.theslot.com) has an excellent explanation of why “X times less/shorter/smaller” is a meaningless entity. “One time smaller” than anything is zero; any larger numbers are meaningless in this context. I always ask the author to change it to “one-fifth as large” or whatever it is that they REALLY mean.
As for the “times colder” issue; as others have said, cold is an absence of heat. There is no such thing as an amount of cold. Even in Kelvin.
And while I’m ranting, here’s one I corrected a few times just today: “Four times larger” is actually FIVE times AS MUCH. Think about it. “One time larger” would be double, no? And things progress from there.
You know, know that I think about it, I don’t think I “officially” learned about negative numbers until 7th grade, in pre-algebra. Sure, I had seen them with regard to temperature, but I didn’t learn how to manipulate them (subtracting a negative is like adding a positive, multiplying 2 negatives gives you a positive) until that class.
That is a meaningless question. People fail to understand that temperature is a result of heat energy, not a measurement of heat energy. You cannot flat-out equate a temp to an amount of energy (i.e. dgrs = BTUs). So, you’re correct, that factor of 4 is absolutely meaningless!
Hey, but my college circuits book showed a graph with time on the y-axis! Yow!
Why is this such a sin*? I understand that time’s arrow is usually shown flying left to right (x-axis), but what’s so bad about letting it vary vertically?
*(Trigonometry buffs are the worst people. They’re downright sinful, sometimes hyperbolically so. ;))
In fact, it is moderately meaningful to calculate the average temperature of stars, though there may be several different ways of doing this which would be beyond elementary school mathematics. According to this article by Feynman the problem is with total temperatures of stars:
Actually it was worse. The students were supposed to calculate the total temperature of several stars. Feynman’s comment was that the only remotely meaningful reason to add temperatures together was if you were immediately going to divide by the number of stars to get the average. And even that is not terribly useful. Surely You’re Joking, Mr. Feynman!, last chapter I believe.
If I recall correctly, there were two problems with this.
First, from a scientific standpoint, it really doesn’t make much sense to talk about average temperature of stars. No astronomer/cosmologist etc. is likely to want that information. But I think that is the kind of quibble that we scientists would make that really doesn’t matter much for a grade school textbook.
Second, and more importantly, the list of stars and temperatures were completely bogus. They listed the stars by color, including colors like blue or purple. There are NO purple stars. And then their temperatures for onces that sort of exist (like interpreting a brown star as a brown dwarf star) were way off.
His point was, if you are going to put a word problem in a book to show students the practical value of mathematics, you should make it a real problem. For example, these are the stars in our region of space (Sol, Alpha Proxima,…) and their temperatures. What is the average temperature of stars in this region?
Not the most useful information, but at least a real question.
Ahhh, preview shows gregj correcting the calculation to total temperature. That does match better with my recollection of him saying that it was a useless calculation. I stand by the purported existence of purple stars.
“John and his father go out to look at the stars. John sees two blue stars and a red star. His father sees a green star, a violet star, and two yellow stars. What is the total temperature of the stars seen by John and his father?”
Maybe the class was Zen and the Art of Astronomy. Just a thought.
To return to the OP, it makes perfect sense as written if it is assumed that zero Celsius is that temperature below which cold begins. Thus, the writer of that question should have no objections to being sent outside in his or her shorts at said temperature.
It’s not just the temperature, it’s also the windchill!
I can’t fathom why they would put a question like that in a math book. IMO the goal of teaching math should be to get students to think in precise terms, and that question certainly doesn’t do that.
