Re: [boost] Re: Dimensional Analysis Interest?

From: Jan Van Dijk (janvandijkinjapan_at_[hidden])
Date: 2003-10-16 23:21:57

On Thursday 16 October 2003 18:23, Deane Yang wrote:
[...]
>
> None of this helps anyone do anything; nobody really needs to know any
> of this. But one way to distinguish between dimensions and units is that
> dimensions corresponds to doing abstract linear algebra and units
> corresponds to doing linear algebra with respect to fixed bases.
> Changing units (like from meters to feet) corresponds to changing the
> basis of the corresponding vector space.

        Hi Deane,

Unfortunately the algebra (the transformation properties) is not linear. Just 
consider conversion from the temperature-'base vector' K (kelvin) to C 
(Celsius), C=K-273.15. 

In technical terms: obviously the K->C base transformation cannot be described 
with a (metric) 00-tensor (or scalar) M via the linear transformation 
relation C=MK.

This is a nasty habit of temperature units, it seems: the seem goes for the 
Fahrenheit and the (less well-known) Rheamur. I don't know of units for any 
other dimension than 'temperature' with this non-linearity property. It shows 
that people quantified the concept of temperature in an era in which they did 
not have a clue about its true meaning :-)

        Bye, Jan.

-- 
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Dr. Jan van Dijk, Room 210
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108 Tokyo, Japan
jan_at_[hidden]
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