Lyapunov Exponent

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Lyapunov Exponent

Owen Densmore
Administrator
At yesterday's FRIAM, I mentioned the Chaos has the luxury of  
reasonably formal techniques, much lacking in Complexity.  My point  
was that there was an "inclusion principal" for chaos .. a way to  
partition processes into those that are chaotic and those that are  
not.  And naturally, neither set is null.

The technique used in Chaos is the Lyapunov exponent:
   http://hypertextbook.com/chaos/43.shtml
   http://en.wikipedia.org/wiki/Lyapunov_exponent

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.

BTW: We were having difficulty remembering the name of the author of  
one of the more popular books.  I believe we were searching for  
Robert Devaney.  He is editor of the Studies in Nonlinearity series  
of books, which includes a rather interesting one by Brian Davies  
which has a wonderful set of Java applications/applets for exploring  
chaos .. a sort of lab if you will.

     -- Owen

Owen Densmore
http://backspaces.net - http://redfish.com - http://friam.org




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Lyapunov Exponent

Stephen Guerin
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
       




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Lyapunov Exponent

Michael Agar
In reply to this post by Owen Densmore
I'm just back from a week's work in Baltimore on a project to  
research and improve treatment entry and engagement among narcotics  
addicts. Reason they invite me is because the characteristics of  
complex co-evolutionary systems help them see, understand and act on  
the problem in new and more effective (we all hope, evaluation to  
come) ways. It's less a measure of complexity and more a phase  
transition in perception and action on the part of human actors who  
are part of the system.

What about algorithmic complexity, the measure suggested by Gell-
Mann, I  think it was? It won't offer an in or out, necessary and  
sufficient condition measure, but rather a "more or less" evaluation  
that allows translation between system patterns and computer code.  
The code is then the measure.

Mike


On Jul 22, 2006, at 11:36 AM, Owen Densmore wrote:

> At yesterday's FRIAM, I mentioned the Chaos has the luxury of
> reasonably formal techniques, much lacking in Complexity.  My point
> was that there was an "inclusion principal" for chaos .. a way to
> partition processes into those that are chaotic and those that are
> not.  And naturally, neither set is null.
>
> The technique used in Chaos is the Lyapunov exponent:
>    http://hypertextbook.com/chaos/43.shtml
>    http://en.wikipedia.org/wiki/Lyapunov_exponent
>
> 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.
>
> BTW: We were having difficulty remembering the name of the author of
> one of the more popular books.  I believe we were searching for
> Robert Devaney.  He is editor of the Studies in Nonlinearity series
> of books, which includes a rather interesting one by Brian Davies
> which has a wonderful set of Java applications/applets for exploring
> chaos .. a sort of lab if you will.
>
>      -- Owen
>
> Owen Densmore
> http://backspaces.net - http://redfish.com - http://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



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Lyapunov Exponent

Russell Standish
Gell-Mann's proposal was a little vague. I have a more detailed
explication in "On Complexity and Emergence", (available from my web
page and other select internet outlets) and indeed I consider
the property of emergence to be the crucial characteristic of
complex systems. Without emergence, algorithmic complexity doesn't
really measure anything useful from a systemic point of view.

Cheers

On Sat, Jul 22, 2006 at 12:09:10PM -0600, Michael Agar wrote:

> I'm just back from a week's work in Baltimore on a project to  
> research and improve treatment entry and engagement among narcotics  
> addicts. Reason they invite me is because the characteristics of  
> complex co-evolutionary systems help them see, understand and act on  
> the problem in new and more effective (we all hope, evaluation to  
> come) ways. It's less a measure of complexity and more a phase  
> transition in perception and action on the part of human actors who  
> are part of the system.
>
> What about algorithmic complexity, the measure suggested by Gell-
> Mann, I  think it was? It won't offer an in or out, necessary and  
> sufficient condition measure, but rather a "more or less" evaluation  
> that allows translation between system patterns and computer code.  
> The code is then the measure.
>
> Mike
>
>
> On Jul 22, 2006, at 11:36 AM, Owen Densmore wrote:
>
> > At yesterday's FRIAM, I mentioned the Chaos has the luxury of
> > reasonably formal techniques, much lacking in Complexity.  My point
> > was that there was an "inclusion principal" for chaos .. a way to
> > partition processes into those that are chaotic and those that are
> > not.  And naturally, neither set is null.
> >
> > The technique used in Chaos is the Lyapunov exponent:
> >    http://hypertextbook.com/chaos/43.shtml
> >    http://en.wikipedia.org/wiki/Lyapunov_exponent
> >
> > 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.
> >
> > BTW: We were having difficulty remembering the name of the author of
> > one of the more popular books.  I believe we were searching for
> > Robert Devaney.  He is editor of the Studies in Nonlinearity series
> > of books, which includes a rather interesting one by Brian Davies
> > which has a wonderful set of Java applications/applets for exploring
> > chaos .. a sort of lab if you will.
> >
> >      -- Owen
> >
> > Owen Densmore
> > http://backspaces.net - http://redfish.com - http://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
>
>
> ============================================================
> 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

--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

----------------------------------------------------------------------------
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Mathematics                               0425 253119 (")
UNSW SYDNEY 2052                 R.Standish at unsw.edu.au            
Australia                                http://parallel.hpc.unsw.edu.au/rks
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Lyapunov Exponent

Phil Henshaw-2
So, I agree, the central phenomenon is the new appearance of the
definable.  

Complexity has other meanings and referents (some of which are almost
the opposite) but that's the main show, and reason for there being any
real interest.   Anyone care to start a list of the defining observables
of emergence?


Phil Henshaw                       ????.?? ? `?.????
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
680 Ft. Washington Ave
NY NY 10040                      
tel: 212-795-4844                
e-mail: pfh at synapse9.com          
explorations: www.synapse9.com    


> -----Original Message-----
> From: friam-bounces at redfish.com
> [mailto:friam-bounces at redfish.com] On Behalf Of Russell Standish
> Sent: Thursday, July 20, 2006 2:11 PM
> To: The Friday Morning Applied Complexity Coffee Group
> Subject: Re: [FRIAM] Lyapunov Exponent
>
>
> Gell-Mann's proposal was a little vague. I have a more
> detailed explication in "On Complexity and Emergence",
> (available from my web page and other select internet
> outlets) and indeed I consider the property of emergence to
> be the crucial characteristic of complex systems. Without
> emergence, algorithmic complexity doesn't really measure
> anything useful from a systemic point of view.
>
> Cheers
>
> On Sat, Jul 22, 2006 at 12:09:10PM -0600, Michael Agar wrote:
> > I'm just back from a week's work in Baltimore on a project to
> > research and improve treatment entry and engagement among
> narcotics  
> > addicts. Reason they invite me is because the characteristics of  
> > complex co-evolutionary systems help them see, understand
> and act on  
> > the problem in new and more effective (we all hope, evaluation to  
> > come) ways. It's less a measure of complexity and more a phase  
> > transition in perception and action on the part of human
> actors who  
> > are part of the system.
> >
> > What about algorithmic complexity, the measure suggested by Gell-
> > Mann, I  think it was? It won't offer an in or out, necessary and  
> > sufficient condition measure, but rather a "more or less"
> evaluation  
> > that allows translation between system patterns and computer code.  
> > The code is then the measure.
> >
> > Mike
> >
> >
> > On Jul 22, 2006, at 11:36 AM, Owen Densmore wrote:
> >
> > > At yesterday's FRIAM, I mentioned the Chaos has the luxury of
> > > reasonably formal techniques, much lacking in Complexity.
>  My point
> > > was that there was an "inclusion principal" for chaos .. a way to
> > > partition processes into those that are chaotic and those
> that are
> > > not.  And naturally, neither set is null.
> > >
> > > The technique used in Chaos is the Lyapunov exponent:
> > >    http://hypertextbook.com/chaos/43.shtml
> > >    http://en.wikipedia.org/wiki/Lyapunov_exponent
> > >
> > > 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.
> > >
> > > BTW: We were having difficulty remembering the name of
> the author of
> > > one of the more popular books.  I believe we were searching for
> > > Robert Devaney.  He is editor of the Studies in
> Nonlinearity series
> > > of books, which includes a rather interesting one by Brian Davies
> > > which has a wonderful set of Java applications/applets
> for exploring
> > > chaos .. a sort of lab if you will.
> > >
> > >      -- Owen
> > >
> > > Owen Densmore
> > > http://backspaces.net - http://redfish.com - http://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
> >
> >
> > ============================================================
> > 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
>
> --
> *PS: A number of people ask me about the attachment to my
> email, which is of type "application/pgp-signature". Don't
> worry, it is not a virus. It is an electronic signature, that
> may be used to verify this email came from me if you have PGP
> or GPG installed. Otherwise, you may safely ignore this attachment.
>
> --------------------------------------------------------------
> --------------
> A/Prof Russell Standish                  Phone 8308 3119 (mobile)
> Mathematics                               0425 253119 (")
> UNSW SYDNEY 2052                 R.Standish at unsw.edu.au
>            
> Australia                                
> http://parallel.hpc.unsw.edu.au/rks
>             International
> prefix  +612, Interstate prefix 02
> --------------------------------------------------------------
> --------------
>
>
> ============================================================
> 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
>
>




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Lyapunov Exponent

Russell Standish
On Sun, Jul 23, 2006 at 08:45:05AM -0400, Phil Henshaw wrote:
> So, I agree, the central phenomenon is the new appearance of the
> definable.  
>
> Complexity has other meanings and referents (some of which are almost
> the opposite) but that's the main show, and reason for there being any
> real interest.   Anyone care to start a list of the defining observables
> of emergence?
>

Surely that varies from system to system. What is the use of such a list,
aside from having a few archetypal examples to inform one's intuition
(eg thermodynamic variables in statistical mechanics or gliders in Game
of Life).

Cheers

--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

----------------------------------------------------------------------------
A/Prof Russell Standish                  Phone 8308 3119 (mobile)
Mathematics                               0425 253119 (")
UNSW SYDNEY 2052                 R.Standish at unsw.edu.au            
Australia                                http://parallel.hpc.unsw.edu.au/rks
            International prefix  +612, Interstate prefix 02
----------------------------------------------------------------------------



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Lyapunov Exponent

Robert Holmes
In reply to this post by Stephen Guerin
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...

Robert


On 7/22/06, Stephen Guerin <stephen.guerin at redfish.com> 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
>
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Lyapunov Exponent

Douglas Roberts-2
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 <http://en.wikipedia.org/wiki/Osborne_Reynolds>
(1842<http://en.wikipedia.org/wiki/1842>
?C1912 <http://en.wikipedia.org/wiki/1912>), who proposed it in
1883<http://en.wikipedia.org/wiki/1883>.
Typically it is given as follows for flow through a pipe:
[image: \mathit{Re} = {\rho v_{s} L\over \mu}]

or
[image: \mathit{Re} = {v_{s} L\over \nu} \; .]

where:

   - *v*s - mean fluid velocity,
   - *L* - characteristic length (equal to diameter 2*r* if a
   cross-section is circular),
   - ?? - (absolute) dynamic fluid <http://en.wikipedia.org/wiki/Fluid>
   viscosity <http://en.wikipedia.org/wiki/Viscosity>,
   - ?? - kinematic fluid viscosity: ?? = ?? / ??,
   - ?? - fluid density <http://en.wikipedia.org/wiki/Density>.

Thirdly, it *is* an interesting measure of system complexity, by nature of
the fact that it is

   1. it is a dimensionless number, and dimensionless analysis can
   provide intriguing information about systems behavior, and
   2. 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.

Fourthly, no physics envy involved at all:  I'm not even sure I *like*
physicists, in general.

;-|

--Doug

On 7/23/06, Robert Holmes <robert at holmesacosta.com> 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...
>
> Robert
>
>
>
> On 7/22/06, Stephen Guerin < stephen.guerin at redfish.com> 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
droberts at rti.org
doug at parrot-farm.net
505-455-7333 - Office
505-670-8195 - Cell
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Lyapunov Exponent

Robert Holmes
Errrr.... not quite what I was asking. Try applying the equation below to an
ant algorithm. What's the ants' viscosity?

Robert

On 7/23/06, Douglas Roberts <doug at parrot-farm.net> 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 <http://en.wikipedia.org/wiki/Osborne_Reynolds> (1842<http://en.wikipedia.org/wiki/1842>
> ?1912 <http://en.wikipedia.org/wiki/1912>), who proposed it in 1883<http://en.wikipedia.org/wiki/1883>.
> Typically it is given as follows for flow through a pipe:
> [image: \mathit{Re} = {\rho v_{s} L\over \mu}]
>
> or
> [image: \mathit{Re} = {v_{s} L\over \nu} \; .]
>
> where:
>
>    - *v*s - mean fluid velocity,
>    - *L* - characteristic length (equal to diameter 2*r* if a
>    cross-section is circular),
>    - ? - (absolute) dynamic fluid <http://en.wikipedia.org/wiki/Fluid>
>    viscosity <http://en.wikipedia.org/wiki/Viscosity>,
>    - ? - kinematic fluid viscosity: ? = ? / ?,
>    - ? - fluid density <http://en.wikipedia.org/wiki/Density>.
>
> Thirdly, it *is* an interesting measure of system complexity, by nature of
> the fact that it is
>
>    1. it is a dimensionless number, and dimensionless analysis can
>    provide intriguing information about systems behavior, and
>    2. 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.
>
> Fourthly, no physics envy involved at all:  I'm not even sure I *like*
> physicists, in general.
>
> ;-|
>
> --Doug
>
>
> On 7/23/06, Robert Holmes <robert at holmesacosta.com> 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...
> >
> > Robert
> >
> >
> >
> > On 7/22/06, Stephen Guerin < stephen.guerin at redfish.com> 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
> droberts at rti.org
> doug at parrot-farm.net
> 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
>
>
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Lyapunov Exponent

Douglas Roberts-2
There are physical analogs, of course.  Treat the ant as a particle, take
into account the dimensions of the ant, the dimensions of its tunnel, ant
"following behavior", ant motivational forces (pheromones, perceived attack,
perceived food sources, queen ant's current mating urgency), etc. etc., and
one could come up with an analog for "ant viscosity".

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 <robert at holmesacosta.com> wrote:

>
> Errrr.... not quite what I was asking. Try applying the equation below to an
> ant algorithm. What's the ants' viscosity?
>
> Robert
>
>
> On 7/23/06, Douglas Roberts <doug at parrot-farm.net> 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 <http://en.wikipedia.org/wiki/Osborne_Reynolds> (1842<http://en.wikipedia.org/wiki/1842>
> > ?C 1912 <http://en.wikipedia.org/wiki/1912>), who proposed it in 1883<http://en.wikipedia.org/wiki/1883>.
> > Typically it is given as follows for flow through a pipe:
> > [image: \mathit{Re} = {\rho v_{s} L\over \mu}]
> >
> > or
> > [image: \mathit{Re} = {v_{s} L\over \nu} \; .]
> >
> > where:
> >
> >    - *v*s - mean fluid velocity,
> >    - *L* - characteristic length (equal to diameter 2*r* if a
> >    cross-section is circular),
> >    - ?? - (absolute) dynamic fluid<http://en.wikipedia.org/wiki/Fluid>
> >    viscosity <http://en.wikipedia.org/wiki/Viscosity>,
> >    - ?? - kinematic fluid viscosity: ?? = ?? / ??,
> >    - ?? - fluid density <http://en.wikipedia.org/wiki/Density>.
> >
> > Thirdly, it *is* an interesting measure of system complexity, by nature
> > of the fact that it is
> >
> >    1. it is a dimensionless number, and dimensionless analysis can
> >    provide intriguing information about systems behavior, and
> >    2. 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.
> >
> > Fourthly, no physics envy involved at all:  I'm not even sure I *like*
> > physicists, in general.
> >
> > ;-|
> >
> > --Doug
> >
> >
> > On 7/23/06, Robert Holmes < robert at holmesacosta.com> 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...
> > >
> > > Robert
> > >
> > >
> > >
> > > On 7/22/06, Stephen Guerin < stephen.guerin at redfish.com> 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
> > droberts at rti.org
> > doug at parrot-farm.net
> > 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
droberts at rti.org
doug at parrot-farm.net
505-455-7333 - Office
505-670-8195 - Cell
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Lyapunov Exponent

Carlos Gershenson
In reply to this post by Owen Densmore
> 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.

Well, no, because every system can be described as complex...
same for emergent properties, it all depends on the context...
In other words, there are no "simple" systems, but certainly there  
are some systems more complex than others, under a specific frame of  
reference.

My notion of complexity is:
The complexity of a system scales with the number of its elements,  
the number of interactions between them, the complexities of the  
elements, and the complexities of the interactions

This is recursive, so you can apply it to any system, you just need  
to set a common level/context to compare any two systems. However, I  
don't think it might be more useful for a particular context where  
there is already an established complexity measure than that  
particular measure.

I first proposed it on
http://uk.arxiv.org/abs/nlin.AO/0109001
(that was some time ago! I need to refresh my philosophical ideas...)
and for those who prefer equations, it is formally expressed in
http://uk.arxiv.org/abs/nlin.AO/0505009 (equation (1))

Best regards,

     Carlos Gershenson...
     Centrum Leo Apostel, Vrije Universiteit Brussel
     Krijgskundestraat 33. B-1160 Brussels, Belgium
     http://homepages.vub.ac.be/~cgershen/

   ?Tendencies tend to change...?




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Lyapunov Exponent

Phil Henshaw-2
In reply to this post by Russell Standish

Well, isn't it good science to know how to identify observable instances
of your subject?   If you learn how to watch what real complex system
agents do, couldn't that make it easier to copy them and improvise, for
example?  That's a standard method isn't it?   I'm amazed that just
because we're still unable to do good testable experiments with
complexity in systems it seems to have turned everyone entirely away
from studying the physical phenomena.  I think it's nuts, well, and also
because we may still not have realized how pervasive these things really
are.  As far as I can tell the only people who have succeeded in
modeling complexity in any way spent half a lifetime closely observing
them.  Then they turn their backs on the real subject.  It's weird.

I also think I'm coming at this from a little different perspective and
don't want to make it look like I'm only wanting to talk about my own
take on it.  

Things That Identify Emergent Complexity:
a) some of the time
a.1 transition from noise to continuity in a measure

b) all the time.
b.1 change of state


got any additions?



Phil Henshaw                       ????.?? ? `?.????
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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> -----Original Message-----
> From: Russell Standish [mailto:r.standish at unsw.edu.au]
> Sent: Friday, July 21, 2006 3:12 AM
> To: sy at synapse9.com; The Friday Morning Applied Complexity
> Coffee Group
> Subject: Re: [FRIAM] Lyapunov Exponent
>
>
> On Sun, Jul 23, 2006 at 08:45:05AM -0400, Phil Henshaw wrote:
> > So, I agree, the central phenomenon is the new appearance of the
> > definable.
> >
> > Complexity has other meanings and referents (some of which
> are almost
> > the opposite) but that's the main show, and reason for
> there being any
> > real interest.   Anyone care to start a list of the
> defining observables
> > of emergence?
> >
>
> Surely that varies from system to system. What is the use of
> such a list, aside from having a few archetypal examples to
> inform one's intuition (eg thermodynamic variables in
> statistical mechanics or gliders in Game of Life).
>
> Cheers
>
> --
> *PS: A number of people ask me about the attachment to my
> email, which is of type "application/pgp-signature". Don't
> worry, it is not a virus. It is an electronic signature, that
> may be used to verify this email came from me if you have PGP
> or GPG installed. Otherwise, you may safely ignore this attachment.
>
> --------------------------------------------------------------
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