Subject: [NECSI] Boundaries Date: 10,12,18 January 2000
With : Yaneer Bar-Yam, JohnMikes,
[Bar-Yam] 10 January 2000"A few thoughts about boundaries.
Actually, this is not really about boundaries but about physical entities which sometimes
serve in a way that is relevant to boundaries .
For some time I have been intrigued by the emergent properties of walls. I am not aware of detailed discussions of the relevance of walls to complex systems thinking. Perhaps someone has a reference to provide. It seems however that the wall is a useful example of emergent properties in a simple system. Any general formal theory of complex systems and their emergent properties should also be able to encompass this.
A wall provides a direct realization of the concept of the collective as greater than the sum of its parts. The wall exists only because of the existence of all of its parts. Taking any of the parts away, making a hole, changes fundamentally the nature of the wall. The story of the child with his finger in the dike comes to mind of course.
Thinking about this more carefully, the concept of scale enters. The size of the hole does matter. Windows and doors are also relevant.
Among the other issues to consider are the relevance of the anchor of the wall, i.e. what keeps it fixed in place. It is not enough for a wall to be whole, it has to be immovable to some degree in order to serve its purpose. This is somewhat different from a full enclosure. For example, a closed box in the weightless vacuum of space, where we would have to reconsider what the anchoring of the box as a whole does.
The usual biological examples of membranes, etc., have probably been discussed at greater length in this context but I don't recall a reference. I am not talking about membranes as boundaries of complex systees, but rather of the membrane itself as an emergent system. The membrane has the emergent property of serving in some way as a boundary.
In physics models which explain the concepts of quantum mechanics, walls play an important role (particle-in-a-box models). Walls are taken for granted rather than explained thoroughly because
the properties of a material can only be studied well after the properties of the quantum mechanics
of a point particle are explained. I recently devoted some time to understanding why the particles in
a box are generally discussed as having a well defined momentum but not a well defined position, while the walls are considered to have a well defined position but their momentum is neglected. The
upshot of this work was that position uncertainty is transfered from massive to light particles, and the
momentum uncertainty is transferred from light to massive particles. The derivation can be done in
Newtonian mechanics rather than quantum mechanics. This means that the particle ends up being in an uncertain position, while the wall has a definite position as far as the particle is concerned.
Going back to such simple models and understanding them more thoroughly is sometimes very enlightening."
Yaneer Bar-Yam
President
New England Complex Systems Institute
http://necsi.org This list is sponsored by www.NECSI.EDU
====Yaneer,
Making the case for 'wall' as a complex system is difficult, even if boundaries are observed attributes of complex systems. Your astute post really honed in on several important issues, which, unsurprisingly, I have something to comment on for each. :-).
To make clear my personal notion of boundaries and walls .. and 'formal systems' ... I hold that there are in fact no perfectly closed or bounded systems. There are only conditionally closed or sufficiently closed systems. Your comments about the different qualitites of wall vs content of quantumly defined systems was just to the point. No wall is perfectly inert. Its mere presence must contribute black-body radiation to the contents. The contribution may, for statistical purposes, be ignored, but in practice the container affects the contained - both space wise and momentum wise, as you note.
Since it seems obvious then that wall (as entity) and contained-gas (as environment) {instead of the other way round} interaffect each other, then it becomes problematic to make the case that "wall" is an emergent complexity. A 'boundary' attains to that quality not from the inside
out, but from the presence of an extenuating 'external'.
A Spanish Colonial wrought iron fence is a boundary to most human-relevant material objects but no boundary at all to rolling mists or sparrows or insects. A stockade designates a sufficiently closed region, but not an absolute one. Even a mathematical function - a circle for example - is 'sufficiently bounded' to contain x number of loci ... but not all loci. The 'environment' is all possible loci and the equation will define those which are boundable so as to satisfy the relationships we wish to consider or evaluate. A wall or boundary is no more 'emergent' than an equation is. It assumes some of its properties when the context is there.
"Between" is a prime example .. and as far as I know is a problematic quality to topologically define with absolute precision. Eg, of three loci on a circle, which is 'between'? How can they all be? And yet they are.
But even before that, 'between' "exists" only when two or more other loci exist and there is a continuum which separates their locations. Between is 'heterotelic' ... it arises or exists only conditionally, when something else does 'first' or 'co-presently'. There is no such thing as "between" in and of itself. The same holds true for wall or boundary or formal-system.
This leads to the natural conclusion that no systems are absolutely closed nor perfectly formally bound, only satisfactorally or sufficiently - in ways that satisfy what we do deal with or want to deal with, either physically or theoretically.
Being "more than the sum of its parts" infers the production or enactment of relationships not priorly present. They can arise from internal productions or externally related productions. This, in contrast to the basic Complexity notion that only internal relations are
important. (And isn't this just another version of the 'nature vs nurture' debates of the past century? !?!?!)
But, more broadly, why fixate on closure or formality? A 'boundary' doesn't just distinguish domains ... it bridges them. In a more fundamental way than 'separating them' a boundary is the 'connector' which ties the relevencies of distinguished domains together. Which is why for
years I've gone on and on about the concept errors of the restricted Godelian paradigm.
When you examine the Godel Incompeteness Theorems in light of infinity and infinitely extended environments, then you are forced to consider systemic qualities which overpower his deductions of closure and deficiencies. Closure & boundedness - even in formal axiomatic systems - are "conditionally closed" by acceptance or rejection of allowed and disallowed parameters or relations. Which status infers that the 'formalities' are essentially randon, being a subgrouping of extended possibilities. Now, if you accept the possibility that those
formalities can be any series of combinations ... with the covering condition that any
formalities will be viable whether included or not ... you are brought to important trans-Godel relationships:
1) internal partitionings will allow you to examine subsets as if you were 'external' to them, so, you are now in a position to validate or confirm the fallicy of notions which may bleed into the external domain. Ie. any system may indeed prove general axioms of which the system is constructed. Essentially ... validity in one place is validity in all places ... when not restrictedly defined.
2) there exist qualities on the outside of Godel Limits which are compatible with those inside. (otherwise the variable godel limit would be permanently fixed and not open-able, nor the interior addable to). Ergo, we know something about the qualities of existence in a region of
existence which Godelian thinking says we should know NOTHING about. We shouldn't even be able to project 'compatibility' of next and unknown.
3) systems are completed when there is 'external' translimit environments. Since all systems are connected across bridging boundaries, all systems are completable. Which is an important destinction from "boundaries make a system incomplete". My best way of explaning this is to use my time honored example. The skin of an apple is it's 'godel limit', the boundary of its existence in the world. That being the case, we are forced to conclude that the 'set of all apples' is mutually exclusive from the 'set of all colors'. Color only exists in the free photon washed universe ... where an apple doesn't. Color is the external interaction of photons with the 'external' boundary limit of 'apple'. Apples themselves have no color, intrinsically or not. An apple alone, if it were the only object in the universe, would have no color. There is no Platonic 'Ideal' possible either.
Oh, in a Godel universe there is. But not in the more accurate trans-godel universe. Colorful apples do indeed exist ... only and because of their present and existential relationship with existence 'beyond the boundary'. Where communication completes the qualia of sets, and defines/completes the relations of existence.
The openness of full Complex Systems simply requires that they be dignified as 'complete-able', rather than that they are insufficient/incomplete/'inaccurate'. The challenge of the Halting Problem is not 'proving closure', its 'allowing closure' and then expecting 're-opening' ... allowing the Turing Machine to restart even IF/WHEN it ever does stop.
A boundary "binds" not disembodies.
At least that's the view from the ceptual bridge. :-)
Ceptual Institute Jan 11, 2000 10PM PST
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[John Mikes] 18 January 2000Apologies to the list: as many times, I am late with my response. It may interfere with some posted idease during the time of my delay. I like to think about it.
This post is worth reading and saving. Not only, because the position in it is close to mine <G>, it is well crafted, underlined by close and distant examples and leading to a logical conclusion.
Nevertheless I have a remark (not specifically to your argumentation, but) to the topic of "boundaries" in general. I will snip a lot from your post (sorry) and leave only what seems relevant to my addition (to me).
>Yaneer,
>
>Making the case for 'wall' as a complex system is difficult, even if
>boundaries are observed attributes of complex systems. Your
>astute post really honed in on several important issues, which,
>unsurprisingly, I have something to comment on for each. :-).
>
>To make clear my personal notion of boundaries and walls .. and
>'formal systems' ... I hold that there are in fact no perfectly closed
>or bounded systems. There are only conditionally closed or
>sufficiently closed systems. Your comments about the different
>qualitites of wall vs content of quantumly defined systems was
>just to the point. No wall is perfectly inert. Its mere presence
>must contribute black-body radiation to the contents.
>The contribution may, for statistical purposes, be ignored, but
>in practice the container affects the contained - both space wise
>and momentum wise, as you note.
Sounds perfect - in our human observation and interpretation, as the present epistemic evolutionary level of our mind allows it. May have been exotic in Y1K and may be naive in Y3K. And Y1K was way after the much referred-to Greek etc. science and Y3K is only in a +0,01% addition in the ongoing timeframe of our human development. We "see" boundaries, consider higher interrelated- ness 'within' than 'without' in a selective view (why would the interaction of the organelles (within) be greater than e.g. a bolt of electric discharge destroying the whole cell - coming from without?)Our selection is restricted furthermore by our theories, e.g. to consider layers, strata, which science can handle in consistent principles, - rather than grouping things according to connections which may be difficult and different from our habitual physical observational methods.
In the total interconnectedness of a universal system every grouping is artificial - but works well in the reductionist scientific methods. And we shouldn't forget that this was (is) the way how our scientific cognitive inventory was collected. Not satisfactory anymore? Right. But still needed and useful in its own place.
>SNIP<
I believe a closely related train of thought led to your statement:
>...This leads to the natural conclusion that no systems are
>absolutely closed nor perfectly formally bound, only
>satisfactorally or sufficiently - in ways that satisfy what we
>do deal with or want to deal with, either physically or theoretically.
I have some argument with the following statement - derived from the ubiquitously quoted Aristotelian phrase:
>Being "more than the sum of its parts" infers the production or
>enactment of relationships not priorly present. They can arise from
>internal productions or externally related productions. This,[is?] in
>contrast to the basic Complexity notion that only internal relations
>are important. (And isn't this just another version of the 'nature vs
>nurture' debates of the past century? !?!?!)
I usually paraphrase the Aristotelian quote into "different from the sum of its (materially listed) parts". Including ALL relationships, qualities etc. (we cannot do that) may result in 'exactly' the 'total'. Consequently I credit Aristotle with presuming that a complexity is more than its material components. And once we override the 'boundary syndrome' we have no problem with "internal" and "external" not even in the topological considerations. They are our artifacts.
>SNIP<
You explain this systems-view beautifully in your Gödelian evaluation:
> Which is why for years I've gone on and on about the concept errors of the restricted
> Godelian paradigm.
>
>When you examine the Godel Incompeteness Theorems in light of
>infinity and infinitely extended environments, then you are forced
>to consider systemic qualities which overpower his deductions of
>closure and deficiencies. Closure & boundedness - even in formal
>axiomatic systems - are "conditionally closed" by acceptance or
>rejection of allowed and disallowed parameters or relations.
Meaning: 'our view' of those systems (see above).
>SNIP<
I like the logic of your points 1), 2), and 3) and cannot wait how those, in formalistical thinking, will argue against them.
> My best way of explaning this is to use my time honored example. The skin of an apple is it's
> 'godel limit', the boundary of its existence in the world.
Snipping your Gődelian apple-argument, your conclusion:
> The openness of full Complex Systems simply requires that they be dignified as
> 'complete-able', rather than that they are insufficient/incomplete/'inaccurate'.
> The challenge of the Halting Problem is not 'proving closure', its 'allowing closure'
> and then expecting 're-opening' ... allowing the Turing Machine to restart even
> IF/WHEN it ever does stop.
>
>A boundary "binds" not disembodies.
>
>At least thats the view from the ceptual bridge. :-)
>
An additional view may be offered from the scaling side: boundaries, layers, strata, units, systems are all in the restriction (boundary?) of our human scale view. A good example shows in colloidal science - (although still within the reach of our physicl orders of magnitude) where the changing of the size of discontinua (called: particle size) changes the 'nature' of the entities and the system. Just
consider surface adsorption of a cm-cube, or of micron size cubes which we make it up from: instead of a 6 cm^2 working area you have working surface in higher order of magnitude - overwhelming several characteristics of the original cube behavior, including adsorption. Make it
nm size: the system gets even further away from the original 'macroscopic' behavior. The example is more 'educative' if we consider the effect of the surface adsorption an "across-boundary" effect.
We look at nature from the position of our human scaling, naturally, we look for justification within our theories - and find some - we consider effects only within our "present" observational limitations (of course), which, however, do not limit nature. Our epistemic evolution opens up newer and newer vistas and we should leave room for additional findings.
> >Ceptual Institute
>Jan 11, 2000
>10PM PST
John Mikes
http://pages.prodigy.net/jamikes
