analytic power -

[Chris Landauer]

i (address@hidden) wrote
>>for my purposes, if a question is easier to answer by "running" the 
>>simulation,
>>then the formalism is lacking in analytic power,
>>and if it is easier to answer by some kind of mathematical analysis,
>>then it (the formalism) is strong enough (for some questions)

David Sumpter said
>I realise you said `for your purposes' but I'm a bit surprised at this 
>statement. When we make a formalistation of Swarm systems it is surely not 
>essential that we create something to answer all the queations we wanted to 
>answer with the simulation? Whats the point in having a simulation (or Swarm) 
>if 
>we have that formalism then?

i didn't _really_ intend to imply that i wanted to answer ALL questions,
since i know that the mathematics that exists is not sufficient
for all interesting questions -
on the other hand, i _want_ the math to be sufficient eventually

i would be _glad_ to have formalisms powerful enough not to need the 
simulations,
but i think that will never happen 
we will always be able to construct systems using sets of rules
from which we cannot easily derive results -
a simple case in point is finite group theory -
we have had a simple axiom set for almost 100 years,
and there are still new results and simplifications being discovered these days

also, every time we can do some part of a difficult problem analytically,
we discover new questions that we cannot yet do -
that is the reason i push so hard for formal analytic methods:
_after_ you have those analytic methods,
then you can start to look for answers to other (more) interesting questions

more later,
cal


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