More Multiplication:

A comment to the follow-up to my "A Little Multiplication Could Have Gone a Long Way" post says:

What? You mean not everyone memorizes useless conversions like that there are 1440 minutes (or 86400 seconds) per day? What is this country coming to?

I'd have let this slip, but given that the whole thread was about multiplication -- and that I'm a math geek -- I just couldn't resist. First, knowing how many minutes there are in a day, it turns out, is not useless: Among other things, it would help journalists and press release authors avoid errors like the one I was blogging about.

But second, here's a secret -- you don't have to memorize the conversions. Even if you don't remember the conversion, you can still figure out how many minutes there are in a day, whenever you need to (for instance, if you want to check whether the item you're about to publish is accurate). How, you might ask? What occult science will give me this magical power? Why . . . multiplication!

In fact, you don't even know how to do multiplication, since there are, I'm told, electronic devices that can do it for you. All you need to know is that such an operation exists, and that it can be deployed to solve immensely difficult problems like the "how many 5-minute increments in a day" one? (To be fair, it also helps knowing about multiplication's partner in crime, division.)

As it happens, I do remember a rough estimate of the number of seconds in a year, partly because one runs into these "every X seconds/minutes Y happens" -- 30 million, or (for a better approximation) 10 million pi for math geeks. I don't remember the number of minutes or seconds in a day. But I am so learned that the numbers are nonetheless available to me whenever I please. And you too can have this fearsome power . . . .

Gene Vilensky (mail) (www):
Ha! This post just made my day. But then again, like you, I'm both Russian and a math geek (and named Zhenya).
2.4.2006 12:54pm
Jim Hammerand (www):
I didn't find a handy seconds-minutes-hours-etc. conversion chart in the A.P. Stylebook, but I'd be more concerned if I did.
2.4.2006 1:02pm
Eugene Volokh (www):
That's the beauty of blogging -- you can post something knowing that the only people it will really amuse are you and a handful of readers, and still feel just fine about it.
2.4.2006 1:03pm
Robert Cote (mail) (www):
If I had a nickel for the ten thousand times I've heard this complaint I'd be a millionare. Good job fellow math geek and remember; pi are not square, pi are round, cake are square.
2.4.2006 1:15pm
John Jenkins (mail):
There is another fersome power that Prof. Volokh seems to be exhibiting here: that of sarcasm...
2.4.2006 1:17pm
The Franchise (mail):
My favorite is ".08 BAC". You bet they're drunk at 8%. Probably long dead also.
2.4.2006 1:53pm
Proof once again that Issac Asimov was ahead of his time - go find a collection of his short stories and read "A Feeling of Power" for another take on the consequences of innumerancy.
2.4.2006 1:56pm
A. Zarkov (mail):
Many educated people don't know even the most basic numeric facts. For example, I knew an American public school teacher (with an MA degree) who didn't know we have 26 letters in the modern basic Latin alphabet. She said: "Why should I know that?" and "What good does it do me to know that?" For that matter try ordering 3/8 lb of deli meat in your local supermarket. Usually I find that they can't make the conversion to their decimal read-out scales. I had one clerk tell me "we can't sell you that amount."
2.4.2006 2:21pm
Henry Schaffer (mail):
An editor at my local newspaper wrote a column comparing murder rates in cities in the state. He said that the 2005 murder rate in Charlotte was 12.7%.

I wrote to him and noted that such a figure would indeed make for a major headline - and that he probably meant to express this in the standard format of events per 100,000 population.

"Oops! Good catch." he replied.
2.4.2006 2:21pm
Ryan Waxx (mail):
I wonder how much of 'failure of skepticism' plays into this.

After all, it stands to reason that you are less skeptical towards positions or issues you agree with. Which would mean more instances where you don't even stop to think at all.
2.4.2006 2:28pm
Anonymous coward:
Priceless. It's not often that you come across someone that can set themselves up so nicely.
2.4.2006 2:33pm
Fishbane (mail):
I suppose not remembering 86400, 5280, 28.349, are one of the joys of not being a professional software engineer. Me, I wish I could purge constants from time to time - I notice that I get false hits occasionally, a sort of mental misfire, where something looks like, for instance, Avogadro's number, but in reality has nothing to do with it. True story, happened two days ago, while cooking. 6.02 was a guess at the ratio intended by the instructions (Thai shrimp paste, don't make it without ventilation). Lucky for me, my partner tends to enjoy^H^H^H^H^Htolerate non sequitur math and physics.

It is said that math geeks tend to have a rich inner life, in the pejorative sense. I won't speak for others, but it is true of me.
2.4.2006 2:40pm
J. Giaime:
Just go to google and submit the following:

1 day / 5 minutes =
2.4.2006 2:53pm
Ross Levatter (mail):
Professor Volokh's point is very important. Math is crucial to modern life, like it or not.

For instance, I heard a story the other day that the Republican caucus, on voting for a new whip to replace someone removed because of claims of ethical impropriety, had to re-do the first round of voting when they ended up with more votes than there were members of the caucus (true story.) I submit that this sort of thing wouldn't happen if they were better at math... :->
2.4.2006 3:16pm
lee (mail):
Perhaps the Women's Center is a follower of the late Andrea Dworkin and believes every sexual encounter between a man and a women is rape. Then the estimate of 200 million rapes is perhaps a bit low.
2.4.2006 3:23pm
Mary Katherine Day-Petrano (mail):
"I'm a math geek -- I just couldn't resist."

And that is what is most amazing about Mr. Volokh, a prodigy at age 15, an amazing accomplishment he rarely talks about. A feat a math-impaired autistic really admires. My mother was a math geek, but not by age 15, although she topped her classes in then-called atomic physics. All of it completely beyond the comprehension of myself, sad to say.

"In fact, you don't even know how to do multiplication, since there are, I'm told, electronic devices that can do it for you. All you need to know is that such an operation exists, and that it can be deployed to solve immensely difficult problems like the "how many 5-minute increments in a day" one?"

Even the prodigy's who really have the know how will never convince those standardized test designers, this time I am referring to No Child Left Behind (but by analogy to others), who have implemented a policy to prohibit those electronic devices and the idea a peson can be very competent by simply utilizing one while knowing about the issue.

But then, who ever agrees with anything I have to say.
2.4.2006 3:24pm
Alan Gunn (mail):
I think the low point of my teaching career occurred when, in working through a simple tax calculation with a student after class, I asked her to calculate 2 percent of 100. She said she couldn't do it without a calculator. We give them a degree with the word "doctor" in it.
2.4.2006 3:30pm
Fishbane (mail):
I heard a story the other day that the Republican caucus, on voting for a new whip to replace someone removed because of claims of ethical impropriety, had to re-do the first round of voting when they ended up with more votes than there were members of the caucus (true story.) I submit that this sort of thing wouldn't happen if they were better at math...

How to put this delicately... do you think that's a failure of math skills, or, perhaps, um, ethics? "One person, one vote" isn't something that requires precalc, afterall. I suppose procedure could be at fault, but they have been doing this for a rather long time, and if process is at fault, that's more damning than cheating.
2.4.2006 3:45pm
Andy (mail) (www):
Of course, if you want to make some figure memorable (such as 86,400 seconds in a day), all you have to do is set it to music and put it in a Broadway show.
2.4.2006 3:54pm
Frank Drackmann (mail):
I had an attending in medical school who demanded we use the Celsius scale when giving reports of a patients vital signs. One day we used the Kelvin scale just to be assholes.
2.4.2006 4:04pm
Jared K.:

I don't intend to put words in Ross's mouth, but I think the smiley that you omitted in your quotation of his post implied that he too believed it was actually more a problem of ethics than of calculation.
2.4.2006 4:05pm
LTEC (mail) (www):
My guess is that Prof. Volokh knows about the Asimov story, and consciously intended this post as an homage to it (and him).

I think students should understand how to do arithmetic calculations before being allowed to use calculators. Otherwise, their sense of numbers will be so poor that they will not even be able to multiply by 1 in their heads (true story).
2.4.2006 4:08pm
Fishbane (mail):
I don't intend to put words in Ross's mouth, but I think the smiley that you omitted in your quotation of his post implied that he too believed it was actually more a problem of ethics than of calculation.

Erm, color me embarrassed. I completely missed the smiley, not just in copy-paste, but in reading. Back to school for reading comprehension for me, and Sorry, Ross.
2.4.2006 4:43pm
Duncan Frissell (mail):

had to re-do the first round of voting when they ended up with more votes than there were members of the caucus (true story.)

They didn't do the math wrong. They wondered why they had an extra vote and were considering a redo when someone remembered that the Puerto Rican Delegate (Luis Fortuno) who is a Republican could vote in the caucus though not on the floor. See here:

The count was deemed valid despite confusion when the number of votes cast exceeded the number of Republicans thought to be present. Vote-counters had forgotten about the Puerto Rican delegate, who is not allowed to vote on the House floor but who does receive a vote in conference.

"We were pleased to learn we're not corrupt, just stupid," one congressman said after the caucusing.

2.4.2006 5:06pm
Ross Levatter (mail):
Modern American politics summed up in one sentence:

"We were pleased to learn we're not corrupt, just stupid," one congressman said after the caucusing.

And they should be pleased, since OTOH more and more politicans ARE corrupt, while OTOH, stupid Americans, a growing constituency, need representation too...

Fishbane: Glad to see you saw the Smiley in the end...
2.4.2006 6:44pm
JGR (mail):
Like the commentator above, I was also struck by the similarity to Asimov's short story "The Feeling of Power". For readers unfamiliar with the story, it's a funny story about a future age when everything is run by computers, and a sudden excitement occurs in the halls of power when a citizen discovers what they call "computing on paper".
" 'Aub, How much is nine times seven?'"
" Aub hesitated a moment. His pale eyes glimmered with a feeble anxiety. 'Sixty-three,' he said."
"Congressman Brant lifted his eye-brows. 'Is that right?'"
"Check it for yourself, Congressman."
After explaining that he simply memorized the simple, single-digit multiplications, he goes on to show how he can multiply any length of numbers through a simple process, which leads to consternation ("'Computing without a computer', said the president, 'is a contradiction in terms'"). And of course he explains that once upon a time, computers had to be programmed by people, and these rules are the basis of how computers themselves operate.
On the one hand, Volokh might be read to making a different point since he is arguing that journalists can use a calculator, but what I think is the real point is that figuring how many minutes are in a day and similar operations is actually not very difficult. Any half-educated journalist should be able to write on paper 60 x 24, or even get a very close approximation in his head (24 x 6 and add a zero). And given the frequency with which these statistics are wildly off-base, any halfway decent reporter will run through a several second calculation in his mind to see what the actual figures per year are. The fact that journalists repeatedly print these off-the-wall ridiculous statistics does not speak well for them, when it only takes a few seconds to run the numbers even if one runs them approximately in their head. (i.e., if one can't figure out 24 x 6, just take 25x6= 150, take 1500 x 365, and see if that seems at least about right. Clearly, many journalists don't even do a rough calculation).
2.4.2006 7:37pm
Steven Jens (mail) (www):
pi times 10^7 isn't bad for the number of seconds in a year, but 10^7.5 is a little closer, and I generally find it more usable. For one thing, when I'm using it, I'm usually doing multiplication and division of the sort that I find easier as addition and subtraction of logarithms.
2.4.2006 9:49pm
Tony (mail):
I'm inclined to recast statistics in personal terms. For example, if the government spends 100 billion dollars on something, I think of it as (roughly) five hundred dollars for each working American. Or, if a crime occurs every five seconds, I think of it as happening to the typical American once every fifty years.

What bothers me is not that Americans are innumerate. What bothers me is that numbers are cast into different units for purely political reasons, when their actual relevance to an individual could be either very high or very low. And as you point out, the actual number is not nearly so important as the sense of panic it generates, so nobody bothers to check the figures or think about them in any depth. It's just empty blather, like so much in American politics.
2.4.2006 10:11pm
R Gould-Saltman (mail):
So, Doc, are we going to take a run at the "significant digits" concept next week?
It's more of an issue for the fundamentally innumerate since the wide availability of calculators (in cell phones, pens, etc.) has convinced supposedly educated people that they really don't need to have any feel for how numbers work. Last week, I yet again found myself explaining to yet another attorney that if you're doing a "pro tanto community property share" calculation on a piece of real estate in Southern California, and one of the numbers that goes into the multi-step calculation is an appraiser's estimate of the value ten years ago, the fact that your calculator yields "$XXX,X66.66" doesn't mean that you really can calculate it that precisely...

BTW, Fishbane, if you didn't remember your chem constant trivia, your enjoyment of dumb puns like Trader Joe's "Avocado's Number GuacaMOLE" would be lessened... (they did start out, IIRC, just west from Caltech....)

2.4.2006 10:59pm
One of the major problems is that students now-a-days are taught hw to use calculators and computer programs...not how to actually do the calculations or even to understand them.

I once taught an analytical chemistry lab. Two students turned in their report (% K2CO3 out of a mixture of K2CO3 and Na2O3). They reported over 100% and asked what was wrong with the computer program they used! When they asked me I checked their data (at a glace I could tell that they messed up the experiment and that that is what the data actually said).

It turns out that they didn't even know why they were doing what they were doing. I told them to figure it out on the whiteboard. They protested that they couldn't do so because they didn't have the computer with them! I forced them to do it by hand, even going to far as to stop them from using the calculator. When they protested that they couldn't do basic arithmetic with "big numbers" I just made them do some basic rounding (a concept that was completely alien to them).

I finally gave up and forced them to watch me do it by hand and explain why I was doing what I was doing.

Scary, that these were students who were going to graduate in the spring from college with degrees in chemistry.

2.4.2006 11:03pm
Chris S.:
But BAC is explicitly a percentage, and so ".08 BAC" assumes the lack of necessity for conversion.
2.4.2006 11:50pm
I regret the focus of my sarcasm wasn't obvious. It was the former part intended to be sarcastic, not the latter. For what little it's worth at this point, I don't consider those conversions useless; and yes, wrote fully aware that knowing a few of these conversions would help reduce such errors (albeit not prevent them -- never underestimate the hazards of an empty coffee pot).

Perhaps my knowing c in furlongs per fortnight is useless... but I know that one (about 1.8 trillion) without need of further reference, just as well as 86400, 1440, 5280, 2.54, 2.205, 6.022E23, and 0.6931, and 0.47712... and feel those others should be easily recognized by anyone. (Yes, I am a math geek, too.)

Mathematics is fundamental to the nature of the world, even in politics. (For any not already familiar, look up "Arrow's Impossibility Theorem".) But if people don't even bother to become comfortable and familiar with something as basic as conversions, what happens when anything harder needs to be decided? I swear, modern technological civilization is starting to look to me more and more like a statistical fluke by the day.
2.5.2006 12:27am
Mary Katherine Day-Petrano (mail):
LTEC -- "Day-Petrano:
I think students should understand how to do arithmetic calculations before being allowed to use calculators. Otherwise, their sense of numbers will be so poor that they will not even be able to multiply by 1 in their heads (true story)."

I agree with you -- if they are capable. But between a rock and a hard spot of either (A) the person just does not have that capability, and can never do it unassisted by electronics, and (B) the person is able to do it with assistance of electronics, wouldn't it be preferable in that circumstance to opt for B?

I was unable to manually do statistics at all, but got an A+ both semesters via computers. It was a required course. Either it would have prevented my degree, or I had to utilize electronics.

If I had the capability, I would not have hesitated to go your preferred course. I cannot do word problems in mathematics, either. No capability to think that way. Some autisics are very numbers oriented, I am not and no amount of effort to achieve this is possible. Both of my parents were mathematics and physics geniuses. What can one do?

I went to law school.
2.5.2006 1:18am
Sarah (mail) (www):
Now that my job involves explaining money and basic calculations (i.e. subtraction) to members of the general public, I find myself paradoxically far less concerned about serious math errors in newspapers. I don't think that the majority of readers will understand the incorrect calculations or how they might apply, nor that there was an error, nor the corrected information. I doubt very much they'd do much more than register an "ah, there's a number there, that's nice, makes me think they looked something up," and move on with their scan of the article.

The first day of training, I was concerned about how my employer wanted me to explain what the APR on a tax refund anticipation loan meant (since I suspected an explanation of "if we were charging you interest over time for an entire year, at this pace..." would just confuse and upset the customers) and I was assured, with shocking self-confidence on the part of my trainer, that there was no chance of any customer ever asking. Most of them are surprised to see that we include a list of each charge included in the loan amount when I tell them. And nearly all of them decline any offer for me to read them that list when they can't find the check stub, trusting that I'll do the subtraction for them -- even though they'd been yelling about some small sum of money they thought was missing from their check, a minute earlier.

On the other hand, it's quite nice to let the power of subtraction calm upset customers; if only I didn't have to walk them through calculations like $3565 minus $2500, I'd still have faith in humanity.
2.5.2006 1:20am
Frank Drackmann (mail):
As a former physics nut, I love the European car magazines where power and torque are expressed as Kilowatts and Newton-Meters. Nothing beats a 70' Hemi Challenger pumping out 700 Kilowatts and 1000 N-M.
2.5.2006 8:15am
Sasha (mail):
On Asimov's "The Feeling of Power," see this May 2002 post of mine.
2.5.2006 9:37am
lee (mail):
I purchased a few hardware items at H&J one day. Included was 1 light bulb marked 2/$1.00. I watched in amazement as the clerk reached for a piece of paper and a pencil and carried out long division. When she got a zero after subtracting the ten(5X2)(hundreds and tens column) from 100 I thought I might get it for a nickel but she recovered and charged me $.50.
2.5.2006 10:59am
Cornellian (mail):
There really needs to be more emphasis on math in schools. "Innumeracy" ought to be required reading. Why do politicians think it's hilarious to brag about how bad at math they were in school? They'd never brag about their poor reading comprehension skills.
2.5.2006 11:13am
strategichamlet (mail):
Even science people frequently misremember constants in my experience. They all know that the charge on the electron starts 1.602 but then they frown and have to think to remember the power of ten (it's -19), even though if you don't remember that the rest of it means alsolutely nothing. With students my biggest problem has always been that they refuse to think about the answers they get in real world terms. I had a student measure the density of aluminum as something like 3.06E-5 g/cm^3 and didn't even seem to understand the connection when I asked him whether aluminum generally floats in water or air.
2.5.2006 11:52am
David Matthews (mail):
"But second, here's a secret -- you don't have to memorize the conversions."

As a math teacher, I find that point the most important, and the most often missed. To relate the metric lengths to the American ones, all I need to remember is that the 440 yard "dash" I ran in high school (I could never "dash" the whole distance, but the good ones can) is now the 400 meters. Everything else proceeds from that fact. To relate the metric weights to the American ones, I remember 2.2 lbs per kilogram. As far as the strange American area units, I grew up knowing that there are 640 acres in a "section" (a square mile.) I still use that one to convert some "square feet" measurement into fractions of an acre.

An easy skill for students to learn is to cancel units, so they don't even have to puzzle out whether to multiply or divide.

Trigonometry is another great example. I always tell my students, "Where else can you take a 3-credit class where the only things you need to memorize are one formula you already know (the Pythagorean Theorem) and six simple definitions?" Everything else we just build from scratch. (OK, that's a bit of an exaggeration. It also helps to know that C=2*pi*r and A = pi*r*r, but that's about it.)

With the BAC measurements, the one that kills me (and would kill the drinker) is that students frequently report that their buddy "blew a 1.2" (instead of a .12); even if we assume the "percent" we still have a problem.
2.5.2006 1:06pm
Nathan Hall (mail):
Those two are partners in crime the way your twin is your doppelganger. Division is multiplication.
2.5.2006 1:07pm
Sorry to bring this post away from multiplication, but I have to correct a poster's comment above claiming that Andrea Dworkin said all male-female sex is rape. Dworkin never said any such thing and explicitly disavowed any such claim.
2.5.2006 4:39pm
And there you go, just posting this on the internet. If this power falls into the hands of the terrorists, who knows what might happen?!?!
2.5.2006 4:51pm
Frank Drackmann (mail):
Why can't you divide by 0? And don't say cause its against the rules, its ok to multiply by 0, so why is division verboten?
2.5.2006 8:02pm
Richard Gould-Saltman (mail):
goin' WAY off-tpoic here...

SLS 1L: While Dworkin "explicitly disavowed" that formulation of her view, her "Intercourse" is full of statements that can reasonably be parsed as such, e.g., "Intercourse is the pure, sterile, formal expression of men's contempt for women. . ."

2.5.2006 10:22pm
Bob Loblaw (www):

"Intercourse" is full of statements that can reasonably be parsed as such, e.g., "Intercourse is the pure, sterile, formal expression of men's contempt for women. . ."
How in the world can this statement be deemed to be the equivalent of saying "all male-female sex is rape"? Rape by definition requires a lack of consent. Even if one were to accept the (ridiculous) assertion that all m/f sex was the expression of men's contempt, that wouldn't make consensual sex rape. It would just make it creepy.
2.6.2006 12:05am
R Gould-Saltman:
Continuing with the wildly off-topic digression: I didn't say that Dworkin made the assertion; I said she wrote a bunch of things, which might reasonably be read to make that assertion. The rest of Chapter 7 of "Intercourse" contains more stuff like it; try:

A human being has a body that is inviolate; and when it is violated, it is abused. A woman has a body that is penetrated in intercourse: permeable, its corporeal solidness a lie. The discourse of male truth--literature, science, philosophy, pornography--calls that penetration violation. This it does with some consistency and some confidence. Violation is a synonym for intercourse. At the same time, the penetration is taken to be a use, not an abuse; a normal use; it is appropriate to enter her, to push into ("violate") the boundaries of her body.
She is human, of course, but by a standard that does not include physical privacy. She is, in fact, human by a standard that precludes physical privacy, since to keep a man out altogether and for a lifetime is deviant in the extreme, a psychopathology, a repudiation of the way in which she is expected to manifest her humanity.

There is a deep recognition in culture and in experience that intercourse is both the normal use of a woman, her human potentiality affirmed by it, and a violative abuse, her privacy irredeemably compromised, her selfhood changed in a way that is irrevocable, unrecoverable. And it is recognized that the use and abuse are not distinct phenomena but somehow a synthesized reality: both are true at the same time as if they were one harmonious truth instead of mutually exclusive contradictions. Intercourse in reality is a use and an abuse simultaneously, experienced and described as such, the act parlayed into the illuminated heights of religious duty and the dark recesses of morbid and dirty brutality. She, a human being, is supposed to have a privacy that is absolute; except that she, a woman, has a hole between her legs that men can, must, do enter. This hole, her hole, is synonymous with entry

This is admittedly, pretty obscure stuff; I've read it repeatedly and am still not entirely clear on what Dworkin really MEANT. The reading of it as "intercourse= rape", while it may be wrong, isn't particularly farfetched...
2.6.2006 12:55am
Bob Loblaw (www):
Look, I agree Dworkin's writings are pretty bizarre, but she's not saying "intercourse=rape", because she's not suggesting there's a lack of consent. If that's what she were trying to say, it would have been pretty easy to say it.
2.6.2006 2:07am

Frank Drackmann: "Why can't you divide by 0? And don't say cause its against the rules, its ok to multiply by 0, so why is division verboten?"

Some good (and a couple of OK but not-as-good) explanations are at:

I would suggest that division isn't really forbidden, just that since the answer is "undefined", it makes that operation kind of pointless - "illegal" is just good shorthand to keep folks from doing it and thinking it means something.

As for numbers and "calculating machines" in general, the late SF author Hal Clement (aka Harry Stubbs) was a chemistry teacher who, when this subject came up, liked to recount an anecdote where one of his students multiplied instead of divided by Avogadro's number (a big number that defines the number of particles in a mole). The student was calculator-dependent, and could not figure out by just looking at the number that he had calculated enough of a substance to more than fill a galaxy rather than a test tube.
2.6.2006 6:47am
Oris (mail) (www):
During Rent (long before it was a movie), my sister leaned over and whispered to me, "Is that a year?" (The number is the first line of the song.) I told her it was, and then asked why she expected me to know that off the top of my head. She shrugged, and said, "That's just the kind of thing you know." *sigh* I did the calculation in fifth grade. Hadn't had cause to see it since. Prior to seeing Rent, I didn't have the number readily available in my brain, but I did recognize it when I heard it.
2.6.2006 8:36am
One time the husband was at a national lab (name withheld to protect the guilty) whose library was full of warning signs that weight limit on the floor was only 100 lbs per square foot. Virtually everybody who works at a physics lab is a math geek -- I imagine the signs must drive them insane.

Since the husband has been teaching physics to pre-meds for the better part of a quarter century, he has many terrifying stories of student innumeracy. The most memorable one was for a homework problem to calculate how long it takes the space shuttle to orbit the earth. The student wrote down something times ten-to-the-minus-thirty-six seconds. She was a pre-pharmacy major -- now there's a comforting thought: a pharmacist who has no intuition about a dose being so tiny as to be ineffective, or so large as to kill every living thing on the planet. They had a measurement lab at the beginning of physics I where the students took a meter stick and measured the doorway three times and calculated the mean and standard deviation. They would write down their data -- 1.0115m, 1.0114m, 1,011.6m, add them up, divide by three to get 337.8743m, calculate a standard deviation, turn in the lab with nary a thought about the absurdity of a 300 meter wide doorway.

cathy :-)
2.6.2006 11:06am
lee (mail):
Thanks rfgs for backing my assertion(without quotations)that for Dworking rape=sex(or almost so). Let's see if SLS1 will show us some of Dworkin's "explicit disavowal."
2.6.2006 11:43am
cathyf: no problem. Just keep your weight below 200 lbs. and make sure, when you stand, that your feet are on separate floor tiles.
2.6.2006 12:19pm
Bruce Hayden (mail) (www):
One of the things that I am trying to teach my high school aged daughter is doing reasonability testing of her results. Like many of her generation, she doesn't, without prodding, and on occasion, ends up with results that are orders of magnitude out of line. She is starting to come around, having lost points on occasion for doing just that.

My favorite personal story is when I took a real estate broker's test. One of the questions was how many square feet in an acre. Some, of course, memorized that number. But it is one of those numbers that I still don't see much need for, so I did the opposite, squared 5,280 (sq. feet per section) and divided by 640 (acres per section) for 43,560 sq. feet per acre. And I didn't even have to do it by hand, since they let us use our trusty HP-12Cs to compute who owed whom what on the closing statements.

Let me also concur about trig. I took a trig test a couple years after graduation from college, and couldn't remember any of the trig equations. But it was fairly easy to derive them on the fly, given that I had a math degree by then. I got a 100% on the test, while completing before the time limit. At least a math degree is useful for something.
2.6.2006 12:26pm
Timothy (mail) (www):
Avagadro's number: 6.022x10^23, why I remember that from high school chemistry is beyond me. IIRC it is spelled "mol" not "mole".

As for Eugene's post, hilarious. Although I'd argue that multiplication isn't math, it's arithmetic. The difference being that it's not math until there aren't numbers involved anymore.
2.6.2006 1:10pm

Bruce Hayden : "squared 5,280 (sq. feet per section) and divided by 640 (acres per section)"

Now there's some strong evidence you probably come from flyover country. "Section" is a term that will get you blank stares from 99+% of the population within a few hundred miles of either coast...

(A Minnesota native in New England who would have computed ft/acre exactly the same way…)

And "mole" is correct.
2.6.2006 1:56pm
Oris (mail) (www):
Mol, bizarrely, is an abbreviation for mole, it being such a very long word and all. So what Timothy is remembering (correctly) is that most equations say "mol" rather than "mole."
2.6.2006 2:20pm
Allan (mail):
2.6.2006 2:43pm
SeaDrive (mail):
True story. A new man became head of a division of a major chemical corporation. One of the matters on his plate was a suit from a customer for whom the company had built a chemical manufacturing plant. The suit held that the plant did not meet the yields guaranteed in the contract. He called in his top engineer, handed him the contact and asked "Can we meet these yields?" The engineer studied the contract for bit, made a few quick calculations and said, "These yields are better than stoichiometric!"

The new boss asked, "What's stoichiometric?"

My opinion, based working with a fair sampling of each, is that lawyers as a group are much better at math than MBA's. In particular, many marketing types have very little number sense.
2.6.2006 3:01pm
M.E.Butler (mail):
Calculating the number of square feet in an acre by figuring the number in a section and dividing by four is a little like arriving at the number of cows in a herd by counting the teats and dividing by four. It'll get you there, but you have to run through some big numbers on the way.

But, for something completely different, I'd like someone to tell me that the ice cream makers' estimate that Americans eat 1.5 billion gallons of ice cream a year, "enough to fill the Grand Canyon," is wrong. It's only a math problem in the way that Archimedes' challenge was--and I don't think we can fill the whole canyon and measure the water on the way out.
2.6.2006 4:59pm
"Calculating the number of square feet in an acre by figuring the number in a section and dividing by four is a little like arriving at the number of cows in a herd by counting the teats and dividing by four...."

Umm, no not really.
I know the number of feet in a mile (easy).
I know the number of square feet in a "builder's acre" (40,000), and that a "real" acre is a bit more, but not the exact number.
I know that a square mile (a section) is 640 acres.
Kindly explain how I can get to sq ft/acre with an easier calculation.

The Grand Canyon is around 52 billion cubic yards in volume according to an estimate of the U.S. Geological Survey I found. That is 10,502,649,350,649 liquid gallons (10.5 trillion gallons) according to an online conversion tool.

At 1.5 billion gallons a year, it would take only a bit less than 7,002 years to fill the Grand Canyon, according to my calculation. They are not even close.
2.6.2006 7:54pm
lee (mail):
Oris, you've gotten to used to the word. Both mol and mole are abbreviations for(a really long phrase)--gram molecular weight.
2.6.2006 9:10pm
lee (mail):
is "to"
S/B "too"
2.6.2006 9:12pm
M.E.Butler (mail):
Thanks, Dew, for the estimate on the volume of the Grand Canyon. That confirms what I suspected when I heard the figure, which has been spread all over by the ice cream companies.
2.6.2006 10:05pm

No problem. Some coworkers were recently discussing random dishonesty like this in many advertisements -- annoying, but not quite worth a complaint -- and it piqued my curiosity.
2.6.2006 10:31pm