Indeed, it's a very good question! Thinking back to my training in mathematics and physics, to how I think about it, and to how I see people think about it, I believe it is something we "know" without having a specific definition - even if people would bring some dictionaries out and write definitions.
We could say "amount of material" [mass?] or use the basic "quanta" element, and so on and so forth. But those would only be "ad hoc" type of definition to me. I used quotes for ad hoc because they are not really ad hoc but I think our notion of the word is inherent in our physical senses and nature. Maybe quantity is a basic building block in our understanding of the world around us?
Food for thought I hope - what's the quantity of food and what's the quantity of thought required to digest that food I do not know though ;-)
--- In email@example.com, "Ralph A. Raimi" <rarm@...> wrote: > > On Sun, 4 Feb 2007, elkashish wrote: > > > I don't assume such knowledge either. If I were to use the word > > quantity I would make sure they know what it means :-) > > 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, > 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 ;-) > > Yes, I recognized that my question was a bit beside the point. > > Ralph A. Raimi Tel. 585 275 4429 or (home) 585 244 9368 > Dept. of Mathematics, Univ.of Rochester, Rochester, NY 14627 > <http://www.math.rochester.edu/people/faculty/rarm> >