Academic journal article ETC.: A Review of General Semantics

Three Voices. (Refereed Paper)

Academic journal article ETC.: A Review of General Semantics

Three Voices. (Refereed Paper)

Article excerpt

The Mathsemantic Monitor *

TO THE BEST of our knowledge, what follows constitutes the first time that an English professor and a mathematics professor, let alone a business consultant, have publicly pooled their talents in an effort to bridge the gap between our two most important languages, English and mathematics.

One of us, Ed MacNeal, works as an aviation consultant. His work uses a lot of math and a lot of English, although neither on a very complex level. He also has long-standing interests in semantics. As a result, he became curious about the interplay of the meanings of ordinary language and ordinary mathematical expressions, particularly as they affect job performance. So, when his firm ran want ads for people who were "good at numbers," and gave the applicants a quiz, he couldn't help but wonder what kinds of meanings or lack thereof influenced their answers. He ended up writing a book and more than two dozen articles on the subject.

The book led another of us, mathematics professor Kurt Lemmert at Frostburg State [Maryland] University (FSU), to volunteer his efforts in joining the author to further the field of mathsemantics. To this association was soon joined the third one of us, FSU's English professor emeritus Glynn Baugher, whose earlier interest had been in mathematics.

Since coming together we have engaged in five joint mathsemantic endeavors. Our first was a survey designed to find out whether students and teachers felt they had been exposed to mathsemantics instruction. Second, we made a well-attended joint presentation at the May 2001 Annual Mathematics Symposium at FSU. Third, we gave a few in-service training sessions for teachers in the Frostburg area. Fourth, we formed the Mathsemantics Institute of Frostburg. Fifth, at the April 2002 Annual Mathematics Symposium at FSU, to a larger audience than the year before, we made the presentation on which this paper is based. You can look up much of this on the web, starting with the address,, so we quickly proceed to more substantive matters.

One really basic tenet all three of us hold--and we reasonably suspect you already know--is that ordinary English and mathematics march to different drummers. They have different internal logics, not completely different, of course, but still very different. Math emphasizes concision, precision, and non-contradiction. English, you might say, emphasizes poetry, empathy, and the avoidance of monotony. Nothing startling here that should take up your time, right? In our opinion, wrong.

The Business Voice (Edward MacNeal)

What makes it wrong is that neither English nor mathematics takes the time to explain the similarities and differences between ordinary English and mathematics. I suspect this leads to unnecessary problems in teaching both subjects. Whatever the effect in school, it's compounded in business, where one has to combine the two disciplines.

For example, some people come into business without understanding that "addition" involves putting things together. They think it's an algorithm, usually the algorithm that goes, "add the right hand column, carry the tens, and repeat to the left." I say this, because when an addition problem on the aforementioned quiz for job applicants didn't line numbers up on their decimal points many of the applicants just added the columns where they stood, regardless of the absurdity of the answer generated by the procedure. (1)

Further, when they were asked to "solve the problem" in adding two apples to five oranges, only a quarter of the job applicants answered "seven fruit." (2) The addition problem here, of course, is the one identified by the eminent French mathematician Henri Poincare when he said, "Mathematics is the art of giving the same name to different things." (3)

The problem confused three-quarters of the applicants. …

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