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i,j,k things, Math & Physics

At 3:50 PM +0800 9/23/99, Darwin Z. Palima wrote:
When I was teaching introductory physics laboratory, I would tell my
students that there is a difference between _vector_quantities and
_vectors_. Vectors are mathematical entities with a definite "rules" of
combination while vector quantities are physical quantities.

It amazes me that these mathematical entities (vectors) can be used to
represent certain physical quantities (vector quantities) and such that
the mathematics of vectors can also be applied in the analysis of these
physical quantities!

I often tell my alg/trig intro HS physics students (many of whom are
Draftees!) to NOT confuse the math with the physics!

example, we calculate the AREA under the velocity vs. time graph and
find that this AREA has the units of meters (heretofore every area
has had units of meters SQUARED). Trust me, this IS a novel concept
to those who have not 'grown up' knowing this!)

THEN we calculate the area to be NEGATIVE for a time interval during
which the velocity is negative!

It is ONLY by seeing the pragmatic usefulness of these TOTALLY BOGUS
ideas that anyone is able to 'accept' them.

NEGATIVE areas? With units of METERS?? yeah, RIGHT!

(Don't confuse math with reality!
Math is PURELY a 'mindgame' based on, often overlooked, assumptions
and CAN lead to clearly unrealistic results.)


But is also an extremely useful TOOL when used with skill.

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