Interesting. I just checked Google. First hit: "Coefficient of Friction: 0.3 to 1.0 (a unitless quantity). Actually, I can easily imagine someone saying "the coefficient of friction is that quantity which ...." On the other hand, how about this one: "There is no measure to the quantity of love we are able to give to others and to ourselves."
Anyway, I was going to say that Patrick Suppes sometimes ago (and perhaps still) did, if I remember correctly, some work on quantity (I think most of this fell in that area termed measurement theory, but it has been sometime). However, any answers were far from short and pithy.
> Quite so; but my message didn't intend to accuse you of anything >> at all, for you were clearly quoting a hypothetical teacher and not >> (necessarily) yourself. I had hoped *someone* would be able to explain >> 'quantity' to me; indeed, my message was explicitly addressed to >> "math-learn" and not to "elkashish". I have been puzzled by the word >> "quantity" a long time, going back to a graduate-level course I once took >> called "tensor analysis", in which on Day 1 the professor began with a >> definition of "tensor" as a matrix (n-dimensional array, actually) of >> "quantities" that did this or that very complicated thing. I never got a >> definition of "quantity" from him, though later, a couple of years later, >There are many ways to define things. As has already been pointed out a >quantity is something that can be measured or calculated. But that >definition is not really correct. The calculable coefficient of friction is >never called a quantity, and one does not use the phrase the quantity of >distance. > >Physics is full of words for which there are no satisfactory definitions. >So each author may start at a different place. In the equation a=F/m the >acceleration is defined as the slope of a velocity time graph, but force and >mass are often defined operationally. > >A better definition of quantity is something you measure or calculate that >you think of as being accumulated. A speed would not be a quantity, but >momentum would because it is conserved. Energy is treated as a quantity, >and mass, charge... would all be quantities. I suspect that the term >quantity was probably being used as a synonym for value. Tensors would be >used for force, but one seldom talks about the quantity of force. Intensity >or amount would more often be used, as force is not conserved. I have never >heard of distance as being called a quantity, but the volume of something is >often called a quantity. Quantities do not have to be conserved, but most >conserved things are called quantities. Charge is a strictly conserved >quantity, but mass is not yet it can still be called a quantity. > >An example here is that momentum was originally called the quantity of >motion, but velocity was not, because momentum is conserved. So I would say >the term quantity is not well defined, and varies a lot from one person to >the next. > >Even the word variable does not have a strictly true definition. One says >that a variable is something that changes and when X appears in an equation >it is called a variable, but in the equation X-3=5, X does not change, and >has only one value. In an experiment you may have several variables, but >when you keep one of them constant, it is not called a constant. Similarly >parameter is also very slippery. > >The big problem comes in when two people use the same word, but have >different meanings for it. This is precisely one of the big problems that >happens in teaching. The teacher has one meaning, and the student has a >different one, but often neither is aware that this is going on. > >John M. Clement >Houston, TX > >> I did come to understand what he (or the sage he was quoting from) >> probably meant. >> >> As a teacher, if I were asked such a question and didn't have a >> precise answer, I would rephrase my statement in such a way as to use >> language I was sure had already been made plain -- though if that were not > > possible I might give enough examples (and use them) to convey the idea >> even if not given in full and correct abstraction. But rushing past a >> word that students don't understand is bad policy. >> >> Again, I'm sorry to have given "elkhasish" the idea that I was >> demanding an answer from *him*. (though in fact I thought, or hoped, he >> might have one) >> >> > Again, the point of this conversation was not to show how it should be >> > taught but rather to illustrate a point in a bit more interesting way >> > than we usually would ;-) >> > >