simulation and mathematics

[Nick Thompson]

Dear All,

AllI am trying to keep track, over a VERY slow modem, of all the arguments and counter arguments that have come my way as a result of my attempts to find out from you all what is essentially mathematical, what is essentially computational, and what is essentially just plain good old fashioned LOGIC.  

One point that slipped by in the hail of ">>>>>'s" was a distinction that somebody made between simulation and mathematics.   While I am asking REALLY dumb questions,  I wanted somebody to explain to me how ALGEBRA is not a kind of simulation?  

I promise that these questions arent endless, and that your answers have been  very helpful to me--for what THAT is worth.

n  

Nick

Nick


Nicholas S. Thompson
Research Associate, Redfish Group, Santa Fe, NM (nick at redfish.com)
Professor of Psychology and Ethology, Clark University (nthompson at clarku.edu)
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[glen ep ropella]

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Nicholas Thompson wrote:
> One point that slipped by in the hail of ">>>>>'s" was a distinction
> that somebody made between simulation and mathematics.   While I am
> asking REALLY dumb questions,  I wanted somebody to explain to me how
> ALGEBRA is not a kind of simulation?

Algebra is analogous to source code (and its language).  Where the
source code can describe what a simulation is supposed to do, it is not
the simulation, itself.

Both algebra and source code are [de|pre]scriptions for a machine.  But,
for the [de|pre]scription to be realized, a machine has to actually push
real stuff around (e.g. electrons).  If real stuff isn't being pushed
around, you don't have a simulation.

Now, a calculating machine that assists in (or does by itself) algebraic
transforms can be considered a simulation.  But, there's a remaining
property of simulations in that they must _represent_ some other thing,
a referent.  Unless the symbols being manipulated by the calculating
machine refer to the properties/variables of some referent, then it's
not a simulation... it's just a computation.

And your questions are not tedious at all.

- --
glen e. p. ropella, 971-219-3846, http://tempusdictum.com
A little government and a little luck are necessary in life, but only a
fool trust either of them. -- P. J. O'Rourke

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[Marcus G. Daniels]

Glen E. P. Ropella wrote:
> Algebra is analogous to source code (and its language).
And compilers do algebra by performing operations like common
subexpression elimination and factoring.

Ideally we'd just be able to ask a computer or clever person
"Solve[simulation function,X=x0]" and get a set of functions that
compute each input parameters, i.e. invert the simulation function.  
The models that necessitate simulation usually involve some sort of
recursive function, and are difficult to find analytical solutions for..
so we settle for using simulations to find trend relationships,
sensitivities, level sets, etc.