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Thursday, March 15, 2007

Can we have archaic and read it too?

If you are translating an archaic language into English, should your writing sound archaic? Or should it be readable? Altogether too many amateur translators think the former.

One of my colleagues inadvertently provided a lovely example yesterday. In precalculus class we have been studying cubic functions and other polynomials of lower and higher degree, so the subject of solving quadratic and cubic equations naturally arises. We all know the quadratic formula, and nobody in his right mind would want to memorize the cubic formula — you especially don’t want to memorize the quartic formula — but it would be helpful to gain an historical perspective on all this. (I, for one, firmly believe that mathematical understanding is almost always enhanced by learning the historical context.) So we looked at an excerpt from an ancient Egyptian papyrus:
Find a value eight of which does exceed two of its squares by six. Do apply as a factor the number of squares to the desired excess obtaining twelve.
Decrease by this amount the square formed from half the factor of the number sought. This square has a side of two which should by increased by half the factor of the number sought. Remove from this as a factor the number of squares sought thus obtaining the desired value.
The unknown translator clearly wanted to make his English sound archaic. But he did this at the expense of readability! No actual spoken language ever sounded like this, and Middle Egyptian really was an actual spoken language.

So I took on the task of trying to find the original problem. (I always knew that my two semesters of Middle Egyptian in college would turn out to be useful some day.) Unfortunately I have not yet been able to locate the original, so I can’t honestly offer a more accurate translation. Even a very rough and very free paraphrase is impossible without the original Egyptian text (and, in any case, “traditore tradutore,” as they say). But here it is in algebraic language:
I’m looking for a certain quantity, x, such that 8x is 6 more than twice the square of x. Multiply the number of squares, 2, by the excess, 6, giving 12. Subtract this from the square of half of the multiplier of x. Add the square root of this number to half of the original multiplier of x. Then divide that sum by the original number of squares.
Note how awkward it is to express algebra in words rather than symbols, and even the mixture of words and symbols doesn’t help much. A modern translation is more readable, but still pretty opaque. Converting this text into plain algebra is a good exercise that helps to teach the value of a symbolic notation; see if you can derive the quadratic formula from it! This is, of course, left as an exercise for the reader.

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