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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.

Keio-Tsuushin Residence
Dr. Jan van Dijk, Room 210
2 Chome 19-30, Mita Minato-ku
108 Tokyo, Japan
tel: +81 3 5476 9461 (home)

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