The unreasonable Effectiveness of ABMs in Complex Systems

[Jochen Fromm-4]

If physics is so successfully described by mathematics
because the physical world is mathematical, and nearly
isomorphic to a mathematical structure, then maybe
complex systems are so successfully described by ABMs
because their are isomorphic to them, too. Complex systems,
especially social ones, are "agent-oriented".
What do you think ?

-J.

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[John Kennison]

Thanks Robert for your reply

I want to move on to the question of where math is effective. Previously, I wondered about the existence of domains where short logical implications were reliable but long chains of logical implications may start to be ineffective. In a sense this is true of any chaotic system, such as weather. We can now predict weather fairly well for the short term but not for the long term because we cannot measure the initial conditions to the required degree of precision (as even arbitrarily small changes now can cause big changes in future states). It is posible that weather is mathematically determined, say perfectly described by some chaotic system and yet math itself would be only of limited use in predicting weather?

Perhaps Physics has (so far, mainly) only analyzed non-chaotic phenomena.

This raises the question of whether some other mathematical system, say one not involving numbers, could tell us somethging useful about chaotic phenomena. Maybe the use of ABMs would work, as suggested by Jochen.
________________________________________
From: [hidden email] [[hidden email]] On Behalf Of Jochen Fromm [[hidden email]]
Sent: Tuesday, April 28, 2009 2:27 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: [FRIAM] The unreasonable Effectiveness of ABMs in Complex Systems

If physics is so successfully described by mathematics
because the physical world is mathematical, and nearly
isomorphic to a mathematical structure, then maybe
complex systems are so successfully described by ABMs
because their are isomorphic to them, too. Complex systems,
especially social ones, are "agent-oriented".
What do you think ?

-J.

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[Russell Standish]

On Tue, Apr 28, 2009 at 08:27:27PM +0200, Jochen Fromm wrote:
> If physics is so successfully described by mathematics because the physical
> world is mathematical, and nearly
> isomorphic to a mathematical structure, then maybe complex systems are so
> successfully described by ABMs because their are isomorphic to them, too.
> Complex systems, especially social ones, are "agent-oriented". What do you
> think ?
>
> -J.
>

All multi-component systems can be modelled using ABM. Eg, you can
model an ideal gas as a collection of simple agents, each agent being
a molecule.

Its just that when the agents are simple enough, other techniques (eg
partial differential equations in CFD, or dynamical systems equations
in Molecular Dynamics) are more effective than ABM. At some point, the
structure of the individual agents become important as well as their
interactions, these other techniques lose their power, and then ABM
remains the only possibility.

If one defines Complex Systems as those exhibiting Emergence, and
further note that emergence necessarily involves multiple interacting
components (I'm not 100% convinced this is the case, but certainly all
compelling examples of emergence do), then it is hardly
surprising that a complex system will always be modelled by an ABM (a
sort of lowest common denominator of modelling techniques).

Cheers

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