Re: speed and velocity

[Phil Parker <PPARKER@TWSUVM.UC.TWSU.EDU>]

> Date:    Wed, 25 Nov 1998 09:03:54 -0700
> From:    "Dewey Dykstra, Jr." <dykstrad@BSUMAIL.IDBSU.EDU>
>
> The problem with the "<" and ">" symbols is that they are mis-named.  The
> names given them are about magnitudes ("less than" and "greater than") but
> the actual function they serve is to indicate direction on a number line.
> The names we give them are only appropriate when both numbers are on the
> positive side of zero.  If you look you will notice that the symbols taken
> as arrow heads (vector heads) they always point toward the number nearer
> negative infinity on the number line.  The names (in English anyway) do a
> real disservice.
The names in English are quite correct for their intended purpose:
comparisons of real numbers as numbers, or scalars in Hamilton's usage.
It is important to keep the distinction between numbers as numbers
(scalars) and numbers as 1-dimensional vectors.  This post thoroughly
confuses the two senses.  It is an unfortunate fact that we use the same
symbols for real numbers as numbers (scalars) and real numbers as vectors.
It gives the false impression that all operations on one can be done on
the other.  Thus -3 < 2 as numbers, but this concept is (mathematically)
*not defined* for vectors. (And I would claim it shouldn't be physically
defined either.)  If you want to compare -3 and 2 as 1-dimensional
vectors, you have to use vector notions, such as length (magnitude), etc.
(It is not accidental that the vector notion of length coincides with the
numerical notion of absolute value.)

---------------------------------------------
Phil Parker        pparker@twsuvm.uc.twsu.edu
Random quote for this second:
  Take heart amid the deepening gloom that your dog is finally
  getting enough cheese.---National Lampoon, "Deteriorada"