I'm
using the definitions used to study Darwinian evolution, which may slightly
differ from yours. I'm not sure. There the term describes
random variation that is accumulative, such as the endpoint of a random process
is considered as the beginning point for the next iteration of the same random
process. It's is said to be modeled on Brownian motion.
My
problem is that the current standard for evolution theory is to assume that
populations vary by random walks under this definition too. I'm
saying, wait a minute. Individual particles of dust, and molecules, may bounce
randomly and subsequent paths may be an accumulation of the mean free paths of
those random events, but a glass of water doesn't behave like one of its
molecules. There you've got a larger system, and evolution
theory seems to ignore that to the point they are quite unable to get the idea
of considering the physical feasibility of their default
assumption.
I see
the problem of population random walk as being that you'd have to explain how
that might feasibly result as the sum of all the progressions of its
members. The statistics are crystal clear that the mean value of any
property of a population of individuals displaying random walk in that
property does not change at all. The collection of random
walks moves equally in all directions. They people who use the
idea don't want to talk about that. I think the only way
a population can produce a random walk is if all its members are closely
following some third variable that happens to have a mean free path and random
interactions....
I
wrote a couple papers on it in relation to reconstructing the shapes of
processes underlying data curves:
methods -http://www.synapse9.com/fdcs-ph99-1.pdf application-http://www.synapse9.com/GTRevis-2006fin.pdf,
but can't get the latter one published on this and similar objections.... just
not the way 'we' think seems to be the problem, and I'm trying to double check
to make sure I'm not nuts or just missing something.
Phil
Phil,
Following on from Steve's comments, the mean distance of a randomly-walking point from its origin is of the order sqrt(N) where N is the number of steps in its walk. Steve's flocks don't exhibit this behaviour, so it's safe to say that no, swarms do not generally display random walk behaviour.
Robert
On 9/7/06, Stephen Guerin <[EMAIL PROTECTED]> wrote:Phil,
I now see where 'accumulated variance' is used in the context of Principal
Components Analysis where it represents how much of the variance is explained by
a set of component vectors. Is this how you're using the term?
Given this usage, I would guess that if you described the agents' states with
position and velocity vectors, a given number of principal components would have
increasing accumulated variance as the swarm becomes more organized.
Or, perhaps you are talking about describing the motion of the swarm as a single
entity? In that case, I would say it depends on the parameters of the model.
Some settings yield swarms that break symmetry in linear momentum and move at a
constant rate in a given direction. Other settings in a model yield more
stationary swarms that buzz around much like gnats around a light. These swarms
may exhibit random-walk dynamics.
FWIW, We have a swarm model/visualization at
http://www.redfish.com/projects/SwarmEffects/ where you can vary agent behaviors
to get different macro swarms. Focus on changing the "Average Position", "Avoid"
and "Average Direction" sliders. These sliders weight how much a given behavior
contributes to a summed vector that is an agent's next move.
-Steve
> -----Original Message-----
> From: Stephen Guerin [mailto:[EMAIL PROTECTED]]
> Sent: Wednesday, September 06, 2006 11:55 PM
> To: [EMAIL PROTECTED] ; 'The Friday Morning Applied Complexity
> Coffee Group'
> Subject: Re: [FRIAM] Do you know? Do 'swarms' follow random walks?
>
> Hi Phil,
>
> > Has anyone checked to see if any alife 'swarms' display
> accumulative
> > variance?
>
> I haven't come across the term 'accumulative variance'
> before. Do you have a web pointer?
>
> As a swarm organizes, the agents' directions and velocities
> become more correlated with each other. ie agents become more
> constrained as they lose degrees of freedom. Would you
> interpret this to be decreasing variance?
>
> -Steve
>
>
>
> > -----Original Message-----
> > From: Phil Henshaw [mailto:[EMAIL PROTECTED]]
> > Sent: Wednesday, September 06, 2006 8:24 PM
> > To: 'The Friday Morning Applied Complexity Coffee Group'
> > Subject: [FRIAM] Do you know? Do 'swarms' follow random walks?
> >
> > Has anyone checked to see if any alife 'swarms' display
> accumulative
> > variance?
> >
> > If you were to design one to do that, would it have a structure
> > comparable to populations of organisms living in ecologies?
> >
> > -In case anyone's curious I have a high quality direct measure of
> > accumulative variance.
> >
> >
> > Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸
> > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > 680 Ft. Washington Ave
> > NY NY 10040
> > tel: 212-795-4844
> > e-mail: [EMAIL PROTECTED]
> > explorations: www.synapse9.com
> >
> >
> > > -----Original Message-----
> > > From: [EMAIL PROTECTED]
> > > [mailto:[EMAIL PROTECTED]] On Behalf Of Phil Henshaw
> > > Sent: Tuesday, September 05, 2006 8:30 PM
> > > To: 'The Friday Morning Applied Complexity Coffee Group'
> > > Subject: [FRIAM] nature walks!
> > >
> > >
> > >
> > > I am dually impressed at Amazon's ability to know what
> > undergarments
> > > it's random visitors might be advised to
> > > try....:) (just marvelous!) but still I have some questions about
> > > reality 101.
> > >
> > > If molecules in thermal motion follow random walks, do
> > fluids composed
> > > of molecules in thermal motion do so as well? I've run into the
> > > strangest confusion among Darwinian theorists, both from
> > journals of
> > > paleontology and evolutionary biology. I have a quite good paper
> > > that's unpublishable because I stick my neck out to say
> populations
> > > have no non-extraordinary mechanisms for changing by random walks.
> > >
> > > a) am I wrong and there are some? a.1)clue me in..
> > > b) do you know a journal for people literate in evolution
> > theory that
> > > might be willing to consider the issue based on physical
> mechanisms?
> > >
> > >
> > > Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸
> > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> > > 680 Ft. Washington Ave
> > > NY NY 10040
> > > tel: 212-795-4844
> > > e-mail: [EMAIL PROTECTED]
> > > explorations: www.synapse9.com
> > >
> > >
> > >
> > >
> > > ============================================================
> > > 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
> >
> >
>
>
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> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
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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
