All pretty silly, really. Before one can pontificate about "measures of complexity", one must have a few starting points, such as: which complex system is of interest; what behaviors wish to be studied, and so on. They're all different, you know...
On 7/23/06, Robert Holmes <[EMAIL PROTECTED]> wrote:
Errrr.... not quite what I was asking. Try applying the equation below to an ant algorithm. What's the ants' viscosity?
RobertOn 7/23/06, Douglas Roberts <[EMAIL PROTECTED] > wrote:First off, the Reynolds number is used in fluid dynamics, not just physics.
Secondly, it is defined (courtesy of Wikipedia, and validated by my Chem E. background) as:Osborne Reynolds ( 1842�C 1912), who proposed it in 1883. Typically it is given as follows for flow through a pipe:
or
where:
Thirdly, it *is* an interesting measure of system complexity, by nature of the fact that it is
- vs - mean fluid velocity,
- L - characteristic length (equal to diameter 2r if a cross-section is circular),
- μ - (absolute) dynamic fluid viscosity,
- ν - kinematic fluid viscosity: ν = μ / ρ,
- ρ - fluid density.
Fourthly, no physics envy involved at all: I'm not even sure I *like* physicists, in general.
- it is a dimensionless number, and dimensionless analysis can provide intriguing information about systems behavior, and
- it is quite accurate at producing information about a specific, yet very complex system, i.e. when flow will transition from laminar to turbulent flow in fluids flowing in a pipe.
;-|
--DougOn 7/23/06, Robert Holmes < [EMAIL PROTECTED]> wrote:OK, I'll bite. Could you just give some details of how I calculate the Reynold's number for (say) an ant algorithm? I can see how I might ascribe a density, a characteristic length and a mean velocity but viscosity?? What's the analogue there?
Why don't we all just get over our physics envy and develop our own equations and laws...
RobertOn 7/22/06, Stephen Guerin < [EMAIL PROTECTED]> wrote:Owen writes:
> A similar measure, as far as I know, is not available for
> description of Complex systems .. one that offers a solution
> to the inclusion principal for Complex processes.
There are a couple of useful measures that come to mind:
A measure to characterize the onset of complexity (ie when an applied external
gradient is greater than the internal degrees of freedom of a system) is the
dimensionless Reynolds number:
http://en.wikipedia.org/wiki/Reynolds_number
Correlation length is often a useful statistic to collect in describing phase
transitions in complex systems:
http://en.wikipedia.org/wiki/Correlation_length
Further borrowing from statistical mechanics, mean free path and mean relaxation
time are sometimes useful measures for phase transitions in complex systems:
http://en.wikipedia.org/wiki/Mean_free_path
We showed phase transitions with these parameters in the ant foraging model in:
Gambhir, M., Guerin, S., Kauffman, S., Kunkle, D. (2004) Steps toward a possible
theory of organization. In: Proceedings of International Conference on Complex
Systems 2004. Boston, MA.
http://www.redfish.com/research/NECSI_StepsTowardPossibleOrganization_v0_8.pdf
and
Guerin, S. and Kunkle, D. (2004) Emergence of constraint in self-organizing
systems. Journal of Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 8,
No. 2, April, 2004.
http://www.redfish.com/research/art0801-2_NDPLS_Article.pdf
============================================================
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
--
Doug Roberts, RTI International
[EMAIL PROTECTED]
[EMAIL PROTECTED]
505-455-7333 - Office
505-670-8195 - Cell
============================================================
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
--
Doug Roberts, RTI International
[EMAIL PROTECTED]
[EMAIL PROTECTED]
505-455-7333 - Office
505-670-8195 - Cell
============================================================ 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
