Re: Radians, dimensions, & explanations

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

James Mclean wrote:

> Now that sounds like you are talking about *units* again, rather than
> dimensions.  Come to think of it, I'm not sure how I would define
> 'dimension'.  Jack (I think?) gave a fine description of how one might
> decide on different base dimensions, but I don't think we've seen a
> definition of 'dimension' itself.  Any takers?

I am not sure if this is correct but in my mind inches, meters, and miles
are units of length while the concept behind the symbol L (a variable, if
you wish) which we use to perform the analysis of units, is the dimension.
Likewise M*L/T^2 is the dimension of force while  kg*m/s^2, named
after Newton, is one of many possible units. Another possible unit of
force could be g*mi/year^2, etc.

In the same spirit, [A] would be the angular dimension, while degree
or zod (after zodiac which could be subdivided into 10 equal parts to
define a decimal angular reference) would be units. We do not need to
know how far each star is from us, or from each other, to define a unit of
angle. The concept of the angle can come before the concept of the circle.
Once again let me say, I am happy with radians  as they are.
Ludwik Kowalski