I read the communication below and your own description at the site
http://www.newciv.org/ISSS_Primer/asem26tm.html. I would like to point
out that I completely agree with your approach. As far as I can see by
now, it is in congruence with what I have written. (I will send that to
you as soon as possible.) The only difference is that I make my
statements with lots of examples, which is more attractive to readers
from the social sciences and the humanities, who are very often lay
people concerning formalization.
There is a similar notational apprach that was published in 1965 by the
renowned Polish mathematician and economist Oskar Lange ("Wholes and
Parts - A General Theory of System Behaviour", Pergamon Press, Oxford,
England, 74 pages; original Polish edition of 1962). That book was one
of my gateways to systems thinking.
My question as to such notational approaches is: Should they REPLACE the
disciplinary scientific conceptual systems OR merely COMPLEMENT them ?
I advocate the latter, but some colleagues argued for the former.
The two ways of presenting basics of systemics could very well be
integrated parallel, for different readerships, in a revised Primer.
With best wishes
apl.Prof., Dr.phil., Dipl.-Volkswirt
Institute of Environmental Systems Research
University of Osnabrueck
D-49069 Osnabrueck, Germany
Tel. ++49/541/969-2511 Fax: -2770
Internet homepage: http://www.usf.uos.de/~eberhard
> *Nothing is impossible; there are ways that lead to
> everything, and if we had sufficient will we should
> always have sufficient means. It is often merely for
> an excuse that we say things are impossible.
> La Rochefoucauld (1613-1680)*
> In a message dated 6/29/2004 9:53:35 PM Central Daylight Time,
> email@example.com writes:
> June 29, 2004
> Department of Mathematics, Statistics and Computer Science
> University of Illinois at Chicago
> Chicago, Illinois 60607-7045
> To Whom It May Concern:
> I am writing this letter in behalf of Tom Mandel and his work
> on an insight of startling simplicity, and the notational model
> that he
> developed from this insight. I shall describe in my own terms the
> structure of this insight, but the reader of this letter is
> encouraged to
> look directly at Tom Mandel's constructions and to encourage him to
> communicate concerning them.
> The question is the nature of a system, or a description in the widest
> possible sense. We find "things" in the world and are most
> concerned with
> how those "things" are related to one another. Tom's favorite
> example is
> the two sides of a coin, separate and yet related (and brought into
> existence) by the body of the coin itself. Any two apparently separate
> things are related, but the story can become quite complex.
> the relationship between the pen and one's ability to write, or the
> relationship between the electron and the operations of the internet.
> A fundamental notation would be one that leaves room, given two
> entities, for the relationship that goes between them. This
> can seem to arise from the individuals (as a conversation arises
> among its
> discussants), or it can appear that the individuals arise from the
> relationship itself (as electron and positron arise from
> space/energy/photon, or as world and observer arise from awareness).
> One should make one's own notations. Each such notation is itself
> an instance of the ideal of relationship in one its many
> Tom uses
> R |----------C
> or algebraically
> where C stands for the (whole) dividing/ arising from A and B, and
> R the connection/relation of A and B.
> Such notation is simple, yet
> insistent, calling for the articulation of unity C, the relation
> R and the
> "parts" A and B.
> Why is this important? The answer is: Because such notation and the
> attitude behind it continually call the question of relationship
> and the
> nature of relationship. All descriptions, all systems, are built
> this way.
> But we keep forgetting the glue and putting it into the
> background. Here
> all three fundamentals in any distinction are brought into the
> and we want to know them and their dialogue. (Powerful Guru, Da
> Free John,
> lead his students again and again with the question "Avoiding
> Relationship?". There is no place to hide.)
> There is an important symmetery here. If we bring forth the
> relationship, then we can ask both how the parts create the whole,
> and how the whole comes to be divided into parts.
> We are all too familiar with
> myriad ways of building from parts, but it is all too easy to lose
> of the whole. To turn around into the whole, to ask how does this
> become a multiplicity, is the essential question of science. It is the
> question that leads to theory, understanding, unification,
> and practical understanding. Without the question of the whole, we
> only recipes for the building of structures from known parts.
> The essential insight that we all have and lose, again and again,
> is that
> sense of the whole and an intuition of how the multiplicity arises.
> There is no multiplictity!
> In relationship, all parts cohere into the whole.
> There is a multiplicity!!
> It is obtained by ignoring the relationships the
> return to the whole.
> To the degree that systems are seen as evocations of
> a whole or larger structure, there is an opening for plasticity,
> creativity and new knowledge.
> Having found this insight and his notation, where will Mandel go from
> here? Really, the question is, where will we go in our
> relationship to
> him and to each other in this quest for unity in multiplicity?
> Yours truly,
> Lou Kauffman
> P.S. There are many existing and possible mathematical, scientific and
> philosophical continuations of this discussion. Prominent among
> them, for
> me, is "Laws of Form" by G. Spencer-Brown, a book with a notation and
> insight very close to the above remarks and to Tom's essential
> Ludwig Wittgenstein said "The limits of my language are the limits
> of my
> We have the opportunity to expand our language, to expand
> beyond imagination our world. Mathematics is all about
> relationship, and the formal images of its patterns. Graph theory in
> particular is concerned about the diagramming of entities in such
> a way
> that significant relationships are indicated. Topology is the
> attempt to
> formulate the notion of a continuous whole (a topological space)
> and to
> find the appropriate ways of dividing the space into parts that
> reveal its
> global strucuture. The themes are always there: mathematics,
> logic, music,
> biology, physics, astronomy/cosmology, linguistics, philosophy, ...
> All reflections of
> the possibility
> of saying anything at all
> to anyone,
> about the