Math CentralQuandaries & Queries


Question from Brian, a parent:

My 14 year old is confused about indirectly proportional and inversely proportional. On searching on the internet we were directed to: Here leanne starts explaining indirectly proportional and ends up describing inversely proportional. Has Leanne got it wrong ?
What is indirectly proportional.




My guess is that Leanne was just being polite to her questioner. When discussing how quantities vary with respect to one another, the opposite of DIRECTLY is INVERSELY. I do not recall ever having seen the word INDIRECTLY used instead of INVERSELY. A reliable source is the OXFORD ENGLISH DICTIONARY, which uses "inversely proportional" and "vary inversely" in many places throughout the dictionary (for example, under the word INVERSE), but not once do they suggest that the word "indirectly" would be an option. I also checked the reliable reference books that happen to be handy, and none refer to "indirect" proportionality. I can imagine a non-expert reasoning that the opposite of "direct" should be "indirect", but I have never seen that terminology used anywhere except on the internet. (The meaning of indirect when applied to proportional quantities sounds ambiguous to me -- it sounds as if the proportional quantities are related in an undetermined way, through some further variables, perhaps like a brother-in-law is indirectly related to a person.) However, Leanne's answer seems correct to me; note that she does not say explicitly that the word "indirect" is not used in with proportion, but she does suggest that she prefers the word "inverse".
My advice: avoid "indirectly proportional", using instead the terminology "inversely proportional" to describe the relationship between two quantities that vary so that their product remains constant. The OED does say that the terminology "inverse proportion" is often loosely extended in informal (nonmathematical) language to describe a relationship in which one quantity increases while the other decreases (without the mathematical requirement that their product remains fixed) -- by way of example they offer a quotation from Edmund Burke (1790): "The operation of opinion being in the inverse ratio to the number of those who abuse power." That sounds as if he had anticipated the current economic crisis in the U.S.


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