From owner-metabolic-reg@net.bio.net Mon Jan 06 22:00:00 1997
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From: daf@bms.brookes.ac.uk (David Fell)
Newsgroups: bionet.metabolic-reg
Subject: Re: Logarithmic definitions of control coefficients
Date: 7 Jan 1997 14:07:54 -0000
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Athel wrote:


I recently made an informal poll of several colleagues about whether
they preferred to write control coefficients and elasticities in the
logarithmic form, i.e.   ...........etc

My response when Athel asked me was:

There is definitely a problem in the UK at the moment, where roughly about 
50% of Biology undergraduates arrive at university unfamiliar with 
logarithms as a concept.  Even those that are aware of them are not 
necessarily well versed in their properties.  Having said that, dlny/dlnx 
behaves itself quite well once you've accepted the transformation onto a 
logarithmic scale.  (x/y)(dy/dx) may look simple and benign, but you have to 
keep your wits about you to appreciate why it is not constant for a straight 
line (in x y space) that doesn't go through the origin, whereas it is for a 
line that does.


>The other thinks that any student who can cope with matrix algebra should
>have no trouble with logarithms, and that as things like delta ln x (where
>delta is a symbol, of course) is easier to print than (1/x) delta x,
>especially in complex equations with lots of such things in a fraction in
>which both numerator and denominator are themselves fractions, one ought to
>prefer the log form.
>

This is where I have a more serious problem with the x-y space 
representation.  As soon as you consider finite, i.e. delta, changes, then 
(x/y)(delta y/delta x) is a can of worms because you parameterise the (x/y) 
component.  This leads to the familiar problem of getting different answers 
according to which end of the interval you choose to take the x and y 
values.  In my view, this is clearly an error.  The valid finite 
representation is delta ln y/delta ln x, which is the only answer to the 
definite integral for BOTH differential forms.  This is the reasoning behind 
the statements in my book on pp. 107-8 and pp. 171-172.  I regret that I've 
not been successful at persuading some of our experimental colleagues (e.g. 
[names suppressed in this public version]) of this.

In conclusion, I'm not very optimistic about the extent to which logs are 
understood, but I think it's unavoidable using them.

David

=========================================================

David Fell,
School of Biological & Molecular Sciences,
Oxford Brookes University,
Oxford OX3 0BP,           Tel. +44 (0)1865 483247
UK                        FAX  +44 (0)1865 484017

daf@bms.brookes.ac.uk

See my book at:  http://www.portlandpress.co.uk/books/isbn/185578047X.htm


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