Wednesday, May 6, 2009

Practical Arithmetic?

While doing research on something completely unrelated to math, I ran into a cute (and tongue-in-cheek) article in an Indiana newspaper of 100 years ago, give or take.

Having trouble with his homework (sound familiar?), young John, a seventh grader, seeks out his father for help (sound familiar again?). It's a word problem, of course. "Asked how much money he has in the bank," the problem reads, "[a man] replies, 'If I had $10 more I would have $1,000 more than half what I now have." John is supposed to find out how much the man has in his account.

Dad is no help. That's because he's a card-carrying curmudgeon. Anyone who wants to know the actual amount, he snarls, should simply ask the teller. "In my day," he announces, unable to resist a dig at "modern" methods of teaching math, "we had practical problems in our arithmetic." [Kids, get off my lawn.]

Curious, John now repairs to the library to examine arithmetic books from the previous century. Each of them, it turns out, is chock-full of the sorts of problems his father is enthusiastically disparaging. John eventually tracks down an 1805 text, where he finds the following gem:

"A good man driving his [geese] to market was met by another, who said, 'Good morrow, master, with your 100 geese.' Says he in reply, 'I have not 100 geese, but if I had half as many as I now have and two and a half geese besides the number I now have already I should have 100.' How many geese had the man?"

At which point the writer of the article temporarily abandons both John and his father and addresses the reader directly. "How long," he demands, "would you permit a man to live if he made such an answer to you?"

[Well, let me think. What's the best way to express the answer, I wonder? Ah--got it. If the time interval were increased by seventeen seconds, it would be precisely four times one third the actual number of seconds diminished by the cube root of...]

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