Moti
Posts:
63
Registered:
11/7/06
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[math-learn] Re: Transforming formulas
Posted:
Feb 5, 2007 9:32 AM
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Don't worry, no offense taken :-)
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 math-learn@yahoogroups.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>
>
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