Re: domain questionnaire

From: Vadim Tropashko <Vadim_member_at_newsranger.com>
Date: Sat, 24 Feb 2001 21:31:28 GMT
Message-ID: <QKVl6.833$aw5.1114_at_www.newsranger.com>

In article <zxTl6.817$Wk3.193859732_at_radon.golden.net>, Bob Badour says...
>
>The domains are still distance, mass and time regardless of representation.

Let's focus on CGS, which is arguably more advanced that SI. Then, every combination (x,y,z) where x,y, and z are powers from

<cm> power x
<g> power y
<sec> power z

is a distinct domain. For example, weight would be x=1, y=1, z=-2. Your preference might be to interpret those numbers as powers against (length, mass, time), but it wouldn't change characteristic tuple (1,1,-2) for weigth, for example.

Now, if we switch to a single unit system (which is even more advanced:-) and classify domains by a single power, do we still have the same set of domains? Wouldn't some distinct CGS domains collapse into one? It is easy to see that it is.

In a single unit system both Plank's constant and the speed of light are equal to 1. Then, distance and time are mesured in the same units, while mass is measured in <cm>**(-1). Energy is measured in mass units as well.

If I'm not certain (is it only me?) about domains in work-of-god arena (physics:-), how can I hope to successfully identify domains in down-to-earth mess that is created by man?

>
>><60|kg> = <135|lb>
>>
>>which is too similar to scalar product to ignore it.
>
>
>You assume that the scalar is constant, and it is not. The equation you
>present holds true at certain points on the face of the earth, but certainly
>does not hold true anywhere on the surface of the moon.

Let's not stretch this example beyond the point where one can see the difference between weight and mass. There are still big problems with the equation. For example, what does vector <60| mean?

Still, for conversion between units I could write something like:

|kg> = A * |lb>

Then,

<60|kg> = <60|A lb> = <60 A*|lb> = <136|lb>

where A* is an operator, adjoint to A.

BTW, if you look into archives, you might notice that I was exactly at this position a year ago. The fact of not making any progress really bothers me.

>Nothing prevents an operator from converting among domains. One can define a
>WeightOnEarth operator to calculate the weight on earth of a known mass.
>Additionally, one can define a WeightOnMoon operator to calculate the weight
>on the moon of a known mass.

I fail to understand what the weight domain is, providing that we don't know the location of the mass. Shouldnt't an intersection of domain with a row give an unambiguous value in a table cell? Or would you rather specialize the weight domain as a column "Weight on Earth" to achieve this?

>More generally, one can define a GravitationalForce operator on any two
>masses and a known distance between them. To achieve physical independence,
>the database should manipulate the resulting force values with equivalent
>results regardless of representation in pounds or newtons or any other
>measure of force.

I'm OK with this solution, but again, let's not be tempted stretching it too far:-) Received on Sat Feb 24 2001 - 22:31:28 CET