[FRIAM] Do you know? Do 'swarms' follow random walks?
Phil Henshaw
sy at synapse9.com
Fri Sep 8 07:47:14 EDT 2006
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 <stephen.guerin at redfish.com> 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:stephen.guerin at redfish.com]
> Sent: Wednesday, September 06, 2006 11:55 PM
> To: sy at synapse9.com <mailto:sy at synapse9.com> ; '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:sy at synapse9.com]
> > 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: 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 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: pfh at synapse9.com
> > > explorations: www.synapse9.com
> > >
> > >
> > >
> > >
> > > ============================================================
> > > FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at
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> > >
> >
> >
> >
> > ============================================================
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> > at St. John's College lectures, archives, unsubscribe, maps at
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