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