In article <gnd4igm08df8@legacy>, email@example.com (Soroban) wrote:
> Hello, Aart! > > That was a great story. Thank you. > > I had similar experiences with my father, an immigrant from Japan > who ran a gift shop in a summer resort. > > When I became a math major, I spent my summers working in the family > store. An invoice had an item at $50 per gross. While I was trying > to estimate its unit price, my father said, "About 35 cents." > > I said something like "Huh? What? How...?" > > He said, "Multiply by 7." > > I did some scribbling (this was in 1962 B.C., before calculators) > and sure enough: 1/144 = 0.006944444 ~ 0.007 > > I said, "So we multiply by 7 and point off 3 places to the left." > > He said, "No, you can SEE where the decimal point goes, can't you? > If it was $50 for a hundred, they'd be 50 cents each. For 144, > it's a bit less." > > I'm retired now, having retired from 38 years of teaching college- > level math. And I still blush over that incident. >
* The sad fact is that students today are not taught the basic skill of estimation. The slide rule, as the poster above says, forced us to come up with a reasonable estimate to put our result within a power of ten.
During the oral exams for PhD in Engineering, my friend was asked by one of the professors: "How many barbers are there in the US?"
"Excuse me, sir, but I am here to take my engineering oral exam."
"Then I will repeat my question: How many barbers are there in the US?"
The puzzled student hemmed and hawed and finally mumbled, "Well there are about 250 million people in the US -- half are men -- and about 80 or 90 percent of them need haircuts. That would be about 100 million men. Let's say they get a haircut on the average of once a month. That would be about 25 million haircuts per week or about 5 or 6 million haircuts per day. If a typical barber can do 20 or 25 haircuts each day, then....."
The professor, interrupting, says, "Fine -- you pass."
What the professor wanted to know is whether the student could come to some reasonable estimate of a solution for a problem with which he was not familiar.
In my youth, we would test each other with such problems. My friend, Peterson and I were in heavy traffic on the Mystic Bridge in Boston, on our way to the airport on a Friday afternoon, and he says to me, Jones, what do you think this bridge weighs?
Well, I said, it's about three quarters of a mile long -- the roadway is about sixty feet wide, and the superstructure underneath must take up about ten feet. Let's assume it is steel, which must have a density of seven or eight, and it is about ten percent dense. Four thousand feet times sixty feet times ten feet divided by seven is about 350,000 cu ft of steel, which would weight about 400 or 500 pounds per cubic foot would be about.....