linear algebra and others

[glen e. p. ropella]

Chris Landauer writes:
 > orthogonality in general is probably not the right name anyway
 > for the property glen wants -
 > it is much more like a kind of independence,
 > which has been studied in many different guises,
 > perhaps the most general of which is the area of combinatorics called
 > "matroid" theory (more details on request)

Well, first off, "independence" is not really a property *I* want
the systems I study to have.  But, it's certainly a property
we can use to classify systems, even if the interesting systems
don't have that property.

Second, consider this a request for more info on "matroid theory".
[grin]  It sounds familiar; but, I can't recall anything about it.

 > the difficulty with basing a theory of agents on independence
 > is that agents aren't independent -
 > there is some kind of locality of interaction
 > (this is another of the "qualitites" i am looking for),
 > which means that agents further away tend to have a weaker impact
 > (on a given agent) -

Well, just because agents interact doesn't mean those agents aren't
independent *in some behaviour space*.  It's completely reasonable
to think that agent X doesn't give a whit about a given behaviour
of agent Y.  But, what this means is that one should work in behaviour
space and agents will be abstracted from regions of that space.

 > since some messages cause new objects to be created or destroyed,
 > this has remained a difficult problem -
 > so far, the only formal models i have seen do no more than
 > operationalize the definition of the message passing process -
 > this is not very useful because there is no analytical power to it
 > (which is the main point of formalization) -
 > that means you can't learn anything about the system without "running" it -
 > it is for precisely this reason that we believe need some new mathematics -
 > it certainly does not exist now

David Sumpter writes:
 > I find formalisations are of most use when proving that your system
 > makes sense and is consistent. For example checking an environment
 > does not have any strange effects on the behaviour of agents.

Exactly.  Swarm's attempt to become a "thinking tool" is really
a new way of using simulation.  I see the process as having worked this
way:  
  1. Form a minimalist model of some set of observations.
  2. Design experiments that fill the holes in the set of observations.
  3. Generalize a more robust model (which usually posits some ontology).
  4. Repeat 1-3 many times. [grin]
  5. Use the resulting formalism to predict the behaviour of an idealized
     system.
  6. Simulate the system based on a mixture of the formalism (usually
     called the "truth" model) and data taken from the system.
  7. Build the system and see how the simulation differs from the 
     real system.

Swarm is trying to add to the role of simulation in the spirit of game
playing where step 5 and 6 and some of step 4 are not as necessary (if
necessary at all).

So... to the point, if we think of both simulation and formalisms as
equally valid "thinking tools" instead of the more narrow roles of v&v
and provability, respectively, then we can gain ground on hard
problems in leaps and bounds!  Normally, a formalism provides the
bootstrap into the ability to solve a problem, then the simulations
come later.  In the case of ABMs and the systems they jibe with, the
simulations are providing the bootstrap and (I believe) the formalism
will follow.  I think it's time to start batting about ideas for these
formalisms.  And, remember that we need at least a hundred ideas if we
expect any one idea to come to fruition!

glen
p.s. Sorry for the rambliness of this post. [grin]
-- 
{glen e. p. ropella <address@hidden> |                                  }
{Hive Drone, SFI Swarm Project         |            Hail Eris!            }
{http://www.trail.com/~gepr/home.html  |               =><=               }


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