Michael Barr recently commented on another post about a Dutch student who insisted that the words “long” and “short” in English referred to qualitative differences such as that between “ride” and “rid”, whereas linguists use the words to refer to temporal length, such as the different in the vowels between “hid” and “hit”.
I assume the student acquired the qualitative meaning from English courses in school; that meaning is very still widely used in English classes in the USA and Britain, so that (I’ll bet) nearly any person on the street in the USA would expect the meaning of “long” and “short” to be the difference between “ride” and “rid”.
This is an example of a phenomenon mathematicians have to put up with too. We know that the same word or symbol can have many different meanings in math, but people who know a little math assume that all meanings that they learned in whatever math courses they took are universal and set in granite. They are startled that “pi” can mean anything other that what they think it means. Someone recently started talking to me about “phi” as if I should know what it means, but I recovered fairly quickly, since I had become vaguely aware that it means the so-called golden ratio to laymen. In my experience mathematicians mostly use phi to denote some function.
When I taught, I was constantly in trouble with students who told me that 0 was not a natural number if the textbook said it was, or was a natural number if the textbook said it wasn’t, because that was the definition in some previous course they had taken.
I have written about this phenomenon here and here.
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It should be observed that most fields of science do use fixed symbols. In physics, “m” nearly invariably refers to mass, “c” to the speed (not velocity!) of light, a to acceleration, the various fundamental particles have their own symbols. Chemists have fixed names for the elements, etc. Not only do mathematicians use “pi” for a 1001 different things, but also the same words for different things (“groupoid” has two entirely different meanings, for example) and “exact category” has several (I have to admit to some responsibility for that). Moreover, many a paper will start with “group” means commutative group in this paper. These are conventions the beginner just has to learn.
It is interesting that the natural sciences–most of them–have terminological meetings, settle on terminology and journal editors enforce those decisions. Witness the recent flap over whether or not Pluto is a planet and the recent decision to describe such objects as “plutoids” (one of the uglier scientific neologisms ever created.
The tricky thing is that the two usages are equally well justified historically (although the linguists’ usage is a little simpler and more consistent). Before the Great Vowel Shift, long vowels in English really were lengthened short vowels. During the shift, the pronunciations changed, but people kept calling them long and short vowels, the same way they always had. The net effect is that we ended up with two communities, each of which has a strong historical continuity argument for their preferred usage.