# Math textbook stupidity **URL:** \ **Category:** Factual Questions\ **Created:** [December 16, 2004, 5:29pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179 "2004-12-16T17:29:03Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Scarlett67](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/scarlett67/32/7387_2.png) [@Scarlett67](https://boards.straightdope.com/u/Scarlett67)\ **Post date:** [December 16, 2004, 10:02pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/21 "2004-12-16T22:02:51Z")
Occasional math textbook copyeditor checking in. I wish I had a buck for every time I’ve asked authors to correct this error. Bill Walsh ([http://www.theslot.com](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. Innumeracy thrives. ---
**Author:** ![easy\_e](https://avatars.discourse-cdn.com/v4/letter/e/eb8c5e/32.png) [@easy\_e](https://boards.straightdope.com/u/easy_e)\ **Post date:** [December 17, 2004, 1:33pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/22 "2004-12-17T13:33:03Z")
> [@yabob](#): > > I’m curious about something else - it’s a word problem to motivate an exercise in simple arithmetic, making sure the student knows how to handle negative numbers. 7th grade? It’s seems more like an elementary school level problem, doesn’t it? 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. ---
**Author:** ![Eonwe](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eonwe/32/240_2.png) [@Eonwe](https://boards.straightdope.com/u/Eonwe)\ **Post date:** [December 17, 2004, 6:20pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/23 "2004-12-17T18:20:11Z")
> [@Scarlett67](#): > > Innumeracy thrives. There’s a bumper sticker for ya. ---
**Author:** ![Nightime](https://avatars.discourse-cdn.com/v4/letter/n/e9c0ed/32.png) [@Nightime](https://boards.straightdope.com/u/Nightime)\ **Post date:** [December 17, 2004, 6:48pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/24 "2004-12-17T18:48:53Z")
> [@](#): > > How many times colder is it today than it was yesterday? Maybe it is a typo. It was supposed to say “how many times is it colder today than it was yesterday.” Your initial guess might be “50% of the time”, but think again. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [December 17, 2004, 8:31pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/25 "2004-12-17T20:31:21Z")
> [@Mathochist](#): > > For those who care about this sort of thing, it’s a distinction between the _vector_ space **R** and the _affine_ space **R** , which most calculus books also screw up. The distinction is only clearly drawn post-calculus in most people’s experience. Well, if it’s such affine distinction, maybe an elementary text can be given a pass. Punning is the worst vice: There’s no vice versa. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [December 17, 2004, 8:50pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/26 "2004-12-17T20:50:37Z")
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! - Jinx ---
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [December 17, 2004, 9:01pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/27 "2004-12-17T21:01:19Z")
> [@Nametag](#): > > Richard Feynman had the same reaction while reviewing textbooks – his example was asking students to calculate the average temperature of a bunch of stars. Math textbooks are written under pressure to include word problems from which students have to extract the necessary information. They don’t seem to mind if the situation is impossible, or the problem makes no physical sense. I don’t get why it’s meaningless to calculate the average temperature of a bunch of stars. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [December 17, 2004, 9:05pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/28 "2004-12-17T21:05:54Z")
> [@Jinx](#): > > Hey, but my college circuits book showed a graph with time on the y-axis! Yow! > > - Jinx 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 _sin_ful, sometimes hyperbolically so. ;)) ---
**Author:** ![Giles](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/giles/32/60_2.png) [@Giles](https://boards.straightdope.com/u/Giles)\ **Post date:** [December 17, 2004, 9:18pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/29 "2004-12-17T21:18:09Z")
> [@Nametag](#): > > Richard Feynman had the same reaction while reviewing textbooks – his example was asking students to calculate the average temperature of a bunch of stars. 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](http://www.textbookleague.org/103feyn.htm) the problem is with total temperatures of stars: > [@Richard Feynman](#): > > Then comes the list of problems. It says, “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?” – and I would explode in horror. > > My wife would talk about the volcano downstairs. That’s only an example: it was perpetually like that. Perpetual absurdity! There’s no purpose whatsoever in adding the temperature of two stars. Nobody ever does that except, maybe, to then take the average temperature of the stars, but not to find out the total temperature of all the stars! ---
**Author:** ![Tierce](https://avatars.discourse-cdn.com/v4/letter/t/ea5d25/32.png) [@Tierce](https://boards.straightdope.com/u/Tierce)\ **Post date:** [December 17, 2004, 9:19pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/30 "2004-12-17T21:19:08Z")
> [@bup](#): > > I don’t get why it’s meaningless to calculate the average temperature of a bunch 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!](http://www.amazon.com/exec/obidos/ASIN/0393316041/qid=1103318397/sr=2-1/ref=pd_ka_b_2_1/102-0197777-6443365), last chapter I believe. ---
**Author:** ![keeper0](https://avatars.discourse-cdn.com/v4/letter/k/b19c9b/32.png) [@keeper0](https://boards.straightdope.com/u/keeper0)\ **Post date:** [December 17, 2004, 9:26pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/31 "2004-12-17T21:26:08Z")
> [@bup](#): > > I don’t get why it’s meaningless to calculate the average temperature of a bunch of stars. 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. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [December 17, 2004, 9:44pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/32 "2004-12-17T21:44:34Z")
> [@Derleth](#): > > Punning is the worst vice: There’s no vice versa. Agreed. I, myself, am an invertebrate punster. Absolutely spineless. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [December 17, 2004, 10:26pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/33 "2004-12-17T22:26:21Z")
_“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. ---
**Author:** ![Yeticus\_Rex](https://avatars.discourse-cdn.com/v4/letter/y/a698b9/32.png) [@Yeticus\_Rex](https://boards.straightdope.com/u/Yeticus_Rex)\ **Post date:** [December 17, 2004, 10:44pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/34 "2004-12-17T22:44:44Z")
> [@Derleth](#): > > \*(Trigonometry buffs are the worst people. They’re downright _sin_ful, sometimes hyperbolically so. ;)) Especially, when they refuse to cosine on a loan and then go off on some tangent to rant about it. ---
**Author:** ![Polycarp](https://avatars.discourse-cdn.com/v4/letter/p/82dd89/32.png) [@Polycarp](https://boards.straightdope.com/u/Polycarp)\ **Post date:** [December 17, 2004, 11:29pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/35 "2004-12-17T23:29:07Z")
> [@Yeticus Rex](#): > > Especially, when they refuse to cosine on a loan and then go off on some tangent to rant about it. You can see, can’t you, why they might do that! 😉 ---
**Author:** ![Nametag](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nametag/32/406_2.png) [@Nametag](https://boards.straightdope.com/u/Nametag)\ **Post date:** [January 1, 2005, 7:14pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/36 "2005-01-01T19:14:43Z")
> [@Giles](#): > > 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](http://www.textbookleague.org/103feyn.htm) the problem is with total temperatures of stars: :smack: ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [January 1, 2005, 7:37pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/37 "2005-01-01T19:37:42Z")
This makes about as much sense as asking… "Here is a table showing the temperature each day for a week: ```auto Day Temperature (ºC) ----------------------------------- Monday 4 Tuesday 6 Wednesday 11 Thursday 7 Friday 3 Saturday 0 Sunday –2 ``` What was the total temperature for the week?" ---
**Author:** ![bluecanary](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bluecanary/32/3614_2.png) [@bluecanary](https://boards.straightdope.com/u/bluecanary)\ **Post date:** [January 1, 2005, 7:49pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/38 "2005-01-01T19:49:20Z")
/me is pleased he’s not the only one to immediately recall _Surely You’re Joking, Mr Feynman_ upon reading the OP. ---
**Author:** ![Hoodoo\_Ulove](https://avatars.discourse-cdn.com/v4/letter/h/58956e/32.png) [@Hoodoo\_Ulove](https://boards.straightdope.com/u/Hoodoo_Ulove)\ **Post date:** [January 1, 2005, 8:21pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/39 "2005-01-01T20:21:12Z")
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. ---
**Author:** ![Spectre\_of\_Pithecanthropus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spectre_of_pithecanthropus/32/12343_2.png) [@Spectre\_of\_Pithecanthropus](https://boards.straightdope.com/u/Spectre_of_Pithecanthropus)\ **Post date:** [January 1, 2005, 9:01pm UTC](https://boards.straightdope.com/t/math-textbook-stupidity/280179/40 "2005-01-01T21:01:02Z")
> [@vetbridge](#): > > It’s not the heat, it’s the humidity. 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. [Previous page](https://boards.straightdope.com/t/math-textbook-stupidity/280179.md?page=1) [Next page](https://boards.straightdope.com/t/math-textbook-stupidity/280179.md?page=3)