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Re: Relational "Space" - Ulanowicz works

Hi Tim,
Your last suggestion is very intriguing to me. I got the book you
recommended earlier on category theory (Lawvere & Schanuel - Conceptual
Mathematics) and am trying to learn - but its tough going.  But here's a
speculation you probably won't like, but maybe will stimulate some
conversation.

Suppose we take the criteria for a category which is A -f->B-g->C with all
the possible associative and identify relations (e.g., A-h->C) indicated by
arrows (can't draw it here). That supposedly is what defines a category
along with the identity and associative rules in terms of functors
connecting A,B,C;  like h o (g o f) =  (h o g) o f, and so forth. (the idea
is much simpler than the notation, I think - its three things in a tight
relationship, with formal rules about how they transform into each other).

Now suppose a simple relationship between A and B (A-f->B) with the inverse
relationship (B-g->A), along with the identity arrows for A and B defines
an RR modeling relation. We can, in the way I have tended to argue the
case, consider that as an explanation for complexity or picture of a
complex relationship, where the inverse does not necessarily commute (f not
equal to g), but f and g can be similar enough such that some functors
based on them could be made to commute, as in a classical reduction).

So then we have that a morphism between two things plus the inverse
morphism and the identities (which are RR's implication and causality
identities) defines a modeling relation, and a basic complexity; and that a
category defines an organism! The A, B, C for example could be:
A = organismic subsystems, the "parts"
B = organism/behavior as the organic "whole"
C = environmental context as the next larger domain within which the
organism derives meaning.

For an organism to exist it must in fact have functors operating between
these three components as a minimum, so I'm thinking that the definition of
a category tells us what can exist (and persist) as a logical relational
structure.

An organism is thus a closed set of these complex relations which meets the
formal rules of a category. That would provide a clear distinction between
complexity and organismic life, the later being a special organization of
the former.

JK

At 10:00 AM 3/19/04 -0500, you wrote:
JohnM, Dan,

JohnM,
I mostly defer to Dan's comments since he is familiar with all this, but I
also see some possible connection to Rosennean complexity. Maybe the way to
look at such a quantitative analysis is to ask: what would be the set of
possible complex natural systems which would accede to such an analysis? In
other words, maybe we need to ask that if this is '"too" redux-scientific',
as you say, then what is that complex thing of which it is '"too"
redux-scientific'?

Dan,
One thing I find very counter-intuitive in the paper is the number R, of the
'roles' or functions. To me, Figure 2 shows ALOT of functions occuring, not
just R=1 as stated in the paper. The more interactions something is having
with other things, the more roles or functions are involved, it seems to me.
Can you help me out with this? Its a conceptual stumbling-block for me.

Secondly, in these weighted networks, where flows are assigned specific
weight numbers which indicate a measure of how large each flow rate is,
don't the fixed weights represent a network with an entirely fixed and
stable dynamical situation? This would seem unlikely in a real ecosystem. It
would seem that in a real ecosystem, each weight (flow rate) would have
dependencies on other parts of the network that lead to all sorts of
variatins or oscillations. Or, perhaps ecosystems really are this stable, or
are these flow rates supposed to be representative of "smoothed" numbers
over some period of time?

The other thing I see is that I think we can take the networks diagrams and
their flows, and convert them to Rosennean atemporal relational diagrams,
with nodes replaced by categories and flow arrows replaced by functorial
relations. I'm not sure where that could lead, I just wanted to mention the
possibility.

Regards,
Tim


> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Dan
> Fiscus
> Sent: Thursday, March 18, 2004 5:08 PM
> To: ***
> Subject: Re: Relational "Space" - Ulanowicz works
>
>
> John,
>
> Not sure if this was meant for Tim or me, but I would reply
> that even though Bob Ulanowicz' work seems conventional
> in that it is highly quantitative and even algorithmic,
> computational, the conclusions, inferences and suggestions
> are all purely in line with Rosen complexity and the total
> necessity of an organic, holistic science. Please don't give
> up - if you read 5 or 10 paperrs and his book Ecology: The
> Ascendent Perspective I think you'll agree that his form of
> science is radically different from mechanistic/reductionist
> science.
>
> The graph of effective connectance per node versus number
> of roles (akin to trophic levels) is the main thing from that
> paper that I was suggesting as a good starting point for
> mapping out what a space of relational dynamics might be
> like, what the dimensions might be like. That x-y coordinate
> system is not cartesian though - both of the axes involve
> dimensions which are not decomposable in the sense of
> particles, entities or even organisms, because both axes
> involve relations between parts and wholes - the axis about
> effective connectance per node involves a connectivity relation
> between nodes (usually species or trophic functional types in
> the ecosystem modeling Bob does) and ALL other nodes and
> a normalization used to make this relative to the connectivity
> of the system as a whole (effective connectance has to do
> with total flux of material or energy); and the axis, dimension
> about number of roles or trophic levels has integrated within
> it the ecological reality that material, energy and causality
> flow in a two-way continuum both bottom up (from plants to
> top carnivores) as well as simultaneously from top down (from
> top carnivores down via predation and also recycling of
> nutrients via excretion and detritus).
>
> The cool thing about Bob's work is that it can be a bridge
> between mechanistic/reductionism because it is so quantitative
> and computational, but it still is able to demonstrate (perhaps
> indirectly but still I think convincingly) the essential wholeness
> of an ecosystem, or more generally between life and life and
> between life and its environment.
>
> Dan
>
> John M wrote:
> > Tim, honestly pls.:
> >
> > do you think that the study in the attachment (Zorach...Pdf) is
> indeed in
> > RR-
> > -complexity and not just a conventional 'complex' situation
> > science-analysis?
> > I found it too much in churning model-based characteristics -
> then again I
> > am
> > thinking in 'my' wholeness terms (extreme as they may be).
> > I did not read it in its entirety, it looked "too"
> redux-scientific to me
> > (quanti analyses, quantities equalized and calculated, a bit towards
> > an engineering study. I know you ARE in such, this is why I ask YOU.)
> >
> > Cheers
> >