In article <wmGcAGAUZ6+yEwEK at fssc.demon.co.uk>, HSauro at fssc.demon.co.uk says...
>[...]
>Interestingly, both Henirk and Jim Burns did quite a bit of simulation
>early on in the development of MCA and in fact the summation theorem was
>'discovered' through a computer simulation. They reasoned that if there
>was one relationship there might be more, and with more searching they
>came across the connectivity theorem. At first they thought that these
>theorems might have been specific to the model they were running, so
>they tried, and successfully showed that both the summation and
>connectivity theorems were completely general.
Herbert,
This is actually one of the most powerful arguments in favour of simulation. In
the field of nonlinear dynamics this usage of simulation is called
"experimental mathematics". The following review (dedicated to the memory of
Stanilaw Ulam, of soliton fame) rehearses the the arguments:
D. Campbell, J. Crutchfield, D. Farmer & E. Jen. 1985. Experimental
mathematics: the role of computation in nonlinear science. Commun. ACM. 28,
374-384.
On a different note, the only thing that bothers me about steady state
analyses is that steady states are mostly inexistent in the wild. I know that
the steady state is used as it is easier to deal with. Maybe it is time we
depart from this to the more complicated (but more interesting) analysis of
non-steady states. The late 1980's work you did with Acerenza and Kacser was a
good starting point, more recently Hans Westerhoff's group has developed MCA
for oscillating states but we still have a lot to do in this area. Maybe the
use of simulation will be a great help to let us explore behaviours and find
regularities (and ultimatly some laws)
--
Pedro Mendes
home: pedro at enzyme.demon.co.uk , work: prm at aber.ac.ukhttp://gepasi.dbs.aber.ac.uk/pedro/prmhome.htmhttp://gepasi.dbs.aber.ac.uk/softw/gepasi.html
