GST conceptual framework development

[Janet Singer]

Aleksandar, Is this a matter of the ‘development of conceptual frameworks based in general systems theory’ being pursued first, while ‘facilitating communication among scientists and professionals from various disciplines [etc]’ is deferred?

One could argue that a GST-based conceptual framework that rose to the level of a technological advance would be adopted and put into practice whether or not its development had involved facilitating communication among disciplines. The use of the framework would then presumably enable the secondary goal.

Janet

The overall purpose of the ISSS is to promote the development of conceptual frameworks based on general system theory, as well as their implementation in practice. It further seeks to encourage research and facilitate communication between and among scientists and professionals from various disciplines and professions at local, regional, national, and international levels."- http://isss.org/world/administration/bylaws

Is that article by Rousseau et al. (and other articles from the same publication) and Ken Lloyd's comment facilitating communication between and among scientists and professionals from various disciplines and professions at local, regional, national, and international levels?

Aleksandar

On Sat, Sep 22, 2018 at 3:07 AM Ken Lloyd <kall...@gmail.com> wrote:

James,

 

In re: Rousseau’s Systemic Semantics (Systemic Semantics: A Systems Approach to Building Ontologies and Concept Maps)  in developing an ontology for systems engineering and science, there has been a historical problem inherent in over-reliance on the “systems thinking” approach. This problem, identified by Rousseau’s “confusion” characterization relates to vast differences between an individual “authority” as an expert and the dispersion of concepts in a groups > 7 (i.e. the INCOSE Fellows attempts at the definition of a system). We found similar dispersion in working with a BFO implementation WRT experts.

 

One promising solution may be to apply OpenAI Five (or something similar, such as ES-HyperNEAT) in NLP to relate and refine concepts in linguistic terms (the conceptual encoding is not directly language driven, but offers indirect representations to languages). The general strategy is to use competitive co-evolution between the machine’s knowledge base (encoded as a meta-neural network that generates other neural networks in various contexts) and the diverse human knowledge bases. The result can be empirically compared with alternative strategies. Furthermore, a meta-ontology may be developed. This strategy is well known and (for AI and NLP at least) reasonably mature. For example, see https://blog.openai.com/openai-five/ in relation to the game Dota.

 

K A Lloyd

 

 

From: syss...@googlegroups.com [mailto:syss...@googlegroups.com] On Behalf Of James Martin
Sent: Friday, September 21, 2018 12:41 PM
To: SSWG <syss...@googlegroups.com>
Subject: [SysSciWG] Fwd: Systems, Volume 6, Issue 3 (September 2018) Released

[Jack Ring]

A conceptual framework is expressed in a language regardless of what it is based on. Shall the language be mine, yours or ours? 

What is the locus (span of disciplines) of ours?

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[Aleksandar Malečić]

http://lentroncale.com/wp-content/uploads/2011/12/1984c-What-Would-GST-Look-Like-sm.pdf - “What Would A General Systems Theory Look Like If I Bumped Into It?” by Len Troncale

I first and foremost think (and occasionally write) about how it might be contained within and expressed by nature itself. Speaking of Rousseau et al. (different articles are by different co-authors), I prefer (it might be because I've actually read every page; I'll read the new one) this publication:  http://www.systema-journal.org/issue/view/47 On the other hand, that Ken Lloyd's comment increases jargon (I should reread it in order to understand what it's about), just like activities and publications by many people (arguably including this one: https://www.wiley.com/en-us/Systems+Thinking%3A+Creative+Holism+for+Managers-p-9780470845226).

Aleksandar

[Aleksandar Malečić]

This discussion was (is) a continuation of this one: https://groups.google.com/forum/?fromgroups#!topic/syssciwg/ic7yT4-q5Hs (i.e. David Rousseau et al.'s contributions to that publication).

I hope we at agree there is only one reality out there and that with this notion goes only one best description. It is like a maze (a labyrinth in any other language that isn't English) with choices of a path that bring people closer or farther from the truth. Here are some choices to be made in order to (mis)understand systems:

Systems are trivial and any search for some deeper knowledge about them should be ridiculed be serious and grown-up people. The rest of this list is rubbish. Yes or no?

Consciousness, life, and interpretations of quantum mechanics (and/or physical causation) are both systems and frontiers of science in the future. Yes or no?

More knowledge/consensus about consciousness, life, and physical causation would reveal what different systems are capable of. Yes or no?

Such knowledge is irrelevant if you can't apply it. Yes or no?

There is only one most accurate schematic representation of all kinds of systems. Or a unification of accurate representations (John Sowa, Robert Rosen, Kent Palmer, Stafford Beer, Kenneth Lloyd, Len Troncale...). Yes or no?

Wrong turns (choosing a wrong schematic representation) can (unintentionally) cause a lot of damage. Kent Palmer is the master of wrong turns. Yes or no?

Rousseau Billingham's article "A Systematic Framework..." (https://www.mdpi.com/2079-8954/6/3/27) suffers from acceptance of right and wrong turns within the maze as legit. It insists on pluralism and rigour and loses the truth. Yes or no?

Aleksandar

[janetm...@gmail.com]

Aleksander – Are you taking each of the positions stated and indicating that you would like to hear views from others, pro and/or con? That wasn’t clear from the framing. Maybe you could rephrase and clarify.

Janet

[Aleksandar Malečić]

Views from others, pro and/or con - First I should be clear to myself about my own views, right?

The point I tried to make is that systems aren't trivial or philosophical, but the most difficult scientific challenge ever and that only one walk through that whole maze is correct. When people make more than one choices about their views, it's in Kenneth Boulding's case at the same time systems science is the skeleton of science and “all we can say about practically everything is almost nothing”, in David Chalmers' case consciousness is a fundamental component of reality (on the same or comparable level as for instance energy and matter) even though he supports the strong artificial intelligence view (desktop computers will be conscious), according to Douglas Hofstadter strange loops are necessary for self-awareness even though one paragraph in his book was enough for him to write that it's "obvious" that we don't have free will (we are neither strange nor loopy), David Deutsch's constructor theory is about (physically and mathematically) possible and impossible tasks and he embraces Georg Cantor's actual infinity as a possible "task". The list goes on and someone else might find examples more directly relevant to engineering or management.

I have nothing against people mentioned here. They are just examples. Wong and Huang tried in their paper from the ISSS 2016 annual meeting (http://journals.isss.org/index.php/proceedings60th/article/view/2865) to unify their understanding of traditional Chinese medicine with Kent Palmer's schemas theory. Kent Palmer in his papers mentions many philosophers such as Jacques Derrida and Martin Heidegger. Does Derrida's neologism "differance" reveal to other people something important and practical about their profession or activities? How about Heidegger's "beyng" or Hegel's subjective, objective, and absolute spirit? Some people mentioned in this message are (the) leading authorities on their fields. They have made some correct and some arguably wrong choices within that maze about reality.

And there goes the trickiest part - How to apply this or some other relevant knowledge (the reason why I'm questioning my own views)?

Aleksandar

[Janet Singer]

Thanks Aleksandar, that helps – though more specifics about “some correct and some arguably wrong choices within that maze about reality” would be a way to stimulate discussion (perhaps using a more politic term than ‘wrong’!).

My view is that your examples of conflicting views reflect the inadequacy of language to capture in one fixed representation what is fundamentally complex – and performative – in reality. 

The simple view that I think has done the most harm for development of a GST conceptual framework is reflected in Boulding’s “all we can say about practically everything is almost nothing”. That’s poetic and clever in one sense, but if it is taken as the literal final word on the subject it shuts down pursuit of general systems science before it begins. That violates Peirce’s dictum for scientific progress: “Do not block the way of inquiry”. Actually the other cases you cite could be examined in that same light, e.g., Hofstadter saying it is ‘obvious’ that we don’t have free will blocks the way of inquiry as well.

Janet

[kall...@gmail.com]

Jack,

 

It has taken me months to get around to answering this question – my very happy retirement keeps getting in the way.

 

Many physical, cognitive, linguistic, computational and informational scientists (systems, all) around the world – esp. China, France, the UK and the US – have realized that “mathematical” structures can encode concepts in contexts. These can be extraordinarily complex concepts. By mathematical, I refer to constructs identified by W.W. Sawyer in Prelude to Mathematics (ca. 1955): “Mathematics is the science and study of all possible patterns”, but not specifically as numerical or algebraic. These structures resemble artificial neural networks (ANNs), and “genetic artificial networks” (i.e CPPNs) that can generate ANNs. One of the early problems in studying the mathematical properties of ANNs was having a mathematical language rigorous and robust enough to 1) describe their functioning, and 2) to illustrate an understanding the how and why of their functioning.   Of course, that mathematical language had to be abstract enough to describe functioning all along the homological chain of complexes from abstraction down to any particular physical realization – including any and all of the representational natural languages.

 

In this regard, I offer a snapshot overview of the solution from John Baez (UC) and Mike Stay (Google), Physics, Topology, Logic, and Computation – A Rosetta Stone.

 

To avoid the error of “The definition of <insert term here> is whatever I (or we) define that term to be” due to some assumption of the mantle of authority, the usual methods deal with convergence toward an attractor that is coherently consistent with forward and opposite (wrongly called Inverse) models by Inverse Theory ala Tarantola.

 

A Framework is the adaptive alignment that results from convergence of conceptual patterns (when, indeed it converges), even when its behavior is “strange”.

 

I think that due to the distances from the 20^th Century Paradigms of Science, what I have identified will not make any sense to many, today. Already valid, it is evident that it will be found to be “true” in the near future.

 

Ken Lloyd

[Steven Krane]

One reality?  No.  We don’t even have the same Now.

Is the word “system” an abstract or concrete noun, or it depends on context of dialogue, or it doesn’t matter?

For me, it’s abstract and it matters.

On Oct 30, 2018, at 4:59 AM, Aleksandar Malečić <ljma...@gmail.com> wrote:

[Aleksandar Malečić]

Did I have free will when I was deciding whether or not to write this? It might be an interesting question or not, but it has only one correct answer. My "story" and perception of reality does differ, but we (for instance) either do or don't live in a computer simulation: https://www.simulation-argument.com/simulation.html. These might be dumb or irrelevant examples to someone, but reality is still the same.

In my story (but in everyone else's reality) when I was an undergraduate student of electrical engineering and reading Carl Jung's books, I was trying to "prove" (as much as a student of something else would dare) him wrong about quaternions (http://quaternions.klitzner.org/?p=83) and, as a future engineer would, started thinking about it as an (correct or incorrect) algorithm or a machine. In the process (a few years later), I was the first person in the world to ever compare Carl Jung and Robert Rosen. Jung is very briefly and indirectly (someone else writing about Jung) mentioned here: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sres.2502 And this comparison either is onto something or it isn't. It can't be both. Mind you, this is just an example.

Aleksandar

[Jack Ring]

Ken, 

As usual your clarifications are very useful. Thanks.

Seems to me this highlights the error of calling something a system without confirming that it has all the attributes that a system must have. 

Jack 

[kall...@gmail.com]

Jack,

 

This is at the heart of most problems “system”. I characterize (note: not define) a system as anything with an aggregation of two or more coupled* (i.e. component) objects whose coupling (i.e. bonding, etc.) allows communication (*in the broadest sense of the word – the exchange of matter, energy, information or entropy), and due to that coupling the whole at least partially subsumes the identities of the components, creating a new entity. Sine qua on.

This means that an atom is a natural system consisting of aggregations of protons, neutrons and electrons where the different couplings create various different elements, and so on for different molecules. Example, the difference between iron oxide and table salt.

 

In this regard, there are (equally valid) natural systems, human devised systems, social systems, political, legal, economic systems, enterprise systems mathematical systems of equations and computer hardware and software systems – which means that it is possible that everything, down to the abstract objects of the **standard model is a system. Notice, however, that contrary to Stafford Beer, the purpose of any system is not inherent within the system, but purpose is imposed on systems by an external intelligence or agency that leverages its properties for purposes at hand.

 

** https://www.quantumdiaries.org/2014/03/14/the-standard-model-a-beautiful-but-flawed-theory/ This theory is, today, incomplete.

 

It would seem to me that, too often, SEs only consider man-made systems when their systems of systems are “composed” of natural and somewhat abstract components. Here, the word “composed” is telling WRT my use of Category Theory to indirectly represent all things “system”.

 

So, it is possible that calling something – anything - a system is a safe bet because it approaches tautology, at some generalization, abstraction or aggregation scale.

 

Ken

[kall...@gmail.com]

Free will? This is an undecidable proposition (from within the context of our existence). This is why, from both an engineering and scientific point-of-view, we should think in terms of possibilities and probabilities instead of the certainty of universal “laws” (i.e. Agung Budiyono’s concept of system’s imaginability in addition to be-ability) http://cds.cern.ch/record/918999/files/0512235.pdf .

 

Will Rogers probably correctly stated: “It’s not what we don’t know that gives us problems, it’s what we know that ain’t so.”

 

From: syss...@googlegroups.com <syss...@googlegroups.com> On Behalf Of Aleksandar Malecic
Sent: Sunday, November 11, 2018 3:33 AM
To: syss...@googlegroups.com
Subject: Re: [SysSciWG] GST conceptual framework development

 

Did I have free will when I was deciding whether or not to write this? It might be an interesting question or not, but it has only one correct answer. My "story" and perception of reality does differ, but we (for instance) either do or don't live in a computer simulation: https://www.simulation-argument.com/simulation.html. These might be dumb or irrelevant examples to someone, but reality is still the same.

[Duane Hybertson]

Ken - I agree with your characterization of a system as (a) having two or more coupled component objects and (b) forming a whole entity. But your last statement--"calling something – anything - a system is a safe bet because it approaches tautology"--seems to contradict that characterization. That is, although those two properties (a) and (b) admit a vast number of systems and types of systems, they also exclude a large number of entities from being considered a system.

Thanks,

Duane

[Steven Krane]

Re: free will or not and only one correct answer

https://aeon.co/essays/do-i-have-free-will-in-zen-the-question-makes-no-sense

Re: proof of theory

Review the fundamental principles of the practice of science.  That idea is antithetical to the practice.

My 1-1/2 cents

[Aleksandar Malečić]

We find different things interesting or relevant, but does that mean there is more than one reality? Alright, if free will isn't a good example (Is stochastic and turbulent deterministic or not? Whatever the case, it must be consistent (without eggs spontaneously unbaking themselves).), then how about artificial intelligence? Is there any possibility for machines to ever become self-aware and why not? What I'm personally more interested is creativity, so is creativity computable (a million-odd dollar question https://www.statista.com/statistics/607716/worldwide-artificial-intelligence-market-revenues) and why not? It can (could) also be applicable to institutions and infrastructure allowing or disallowing their improvements and/or resilience (and resilience of society and the environment they are affecting). And all that within one reality (with many possible perspectives about it).

Aleksandar

[kall...@gmail.com]

Please name something that is not a system, and let’s proceed from there.

[do...@parshift.com]

A one dimensional point?

[Curt McNamara]

A point is a mathematical abstraction (similar to line and plane, they don't exist in the real world). Useful for teaching concepts though!

So yes, anything less than 3D is not a system.

        Curt (channeling my inner Bucky Fuller)

[Duane Hybertson]

Ken - OK. In addition to the candidates mentioned by Rick and Curt, I offer these example categories of non-systems: One category is all the primitives at the bottom of a composition hierarchy. In the physical universe, we don't yet know exactly what these primitives are; possibly quarks, or fermions, or bosons, or strings, or branes, or some mix of these. But whatever they are, they do not have component objects, and therefore are not systems. Another category is sets of objects that are not coupled--for example, my car in Virginia and a specific tree in Cusco, Peru. I presume they are not coupled and thus do not form a system. (Perhaps if I took my car to Cusco and parked it under that tree, it might be argued that the two objects then can form a system.) Unless one assumes that every object in the universe is coupled with every other object, then for a given object A there are other objects B etc. which are not coupled with A; and therefore the aggregation of A and B does not form a system. Note that my first category satisfies the characteristic of "whole" but not of component objects; whereas my second category satisfies the characteristic of component objects but not of a whole. To be considered a system, both characteristics must be satisfied.

Thanks,

Duane

[Steven Krane]

The car and tree are coupled by gravity and have probably exchanged a couple molecules of CO2.  Cars and trees, generally, have a strong atmospheric couple.  The significance of interaction is a subjective matter.  If it reaches a threshold, the concept “system” becomes useful to the observer/participant.

[Jack Ring]

A configuration of entities and interrelations that is Not responding to a stimulus.

Ion 

[kall...@gmail.com]

A point is, indeed, an object, however it fails to qualify as a system on two (ahem) points. 1) it is only one object containing no other objects in an aggregation, and 2) alone, it is not obviously coupled with any other objects. Actually, to recognize any point beyond its entity there is a monomorphism called the identity (1object) that references the entity. So whenever you identify ”this” point (an object), you are referencing a system of entities and identities.

 

Moving beyond considering that exclusive point devoid of context, however, things may get murkier. I apologize for the, now, category-theoretic context in which to consider “a point”. Topologically, if we were to embed that singular point into (/mapsto) into a metric space, we have a different scenario altogether. That point now shares information regarding its “be-able” as a location with and in that space. It also exhibits the potential to inhabit other alternative locations – its imaginability – in other locations in that space (notice we have the rudimentary makings of a system).

 

Let’s go one small step further. If we were to add (embed or map) another point in that space, at some scale we have a topological neighborhood, or site, that minimally relates those two points.

 

The concept of “a point” (p), actually a zero-dimensional construct whose singular identity is p^0 = 1 exists as a duality between a category (with no elements in its aggregation) and every possible object that may be realized from that category as points (the duality is that categories are an object, and objects are derived as realization from their categories – more than you really wanted to know). So it depends which aspect of a “point” you are considering – the categorical, or the object – and THAT is an important point. I take that “a one dimensional point” is a point existing at a location on a one dimensional construct – a degree of freedom,  a line – which would easily qualify as a system

 

We see that, minimally, a point exists as an abstract concept and dually as a category and object in a platonic mathematical context. The bi-directional relationship between the abstract concept and its somewhat less abstract, but still abstract platonic realization, does indeed create a system (in this case a “formal” language).

 

Ken

[janetm...@gmail.com]

The question of whether Duane’s car and the tree in Peru IS a system in absolute terms is undecidable. A judgment can only be made relative to a proposed set of assumptions which are asserted by the proposer to have value (like Jack’s system vs configuration definitions, or Ken’s preferred framing).

A more productive approach is identifying which sets of assumptions people have found to be valuable, and in which contexts. The discussion can then be about usefulness and constraints on usefulness rather than metaphysical truth.

[Jack Ring]

Ken, 

Pls clarify whether the coupling ‘allows communication’ vs, 'accomplishes communication.’

Else, pls clarify the difference, if any,  between system and configuration.

And a comment on Curt’s "anything less than 3D is not a system” will be appreciated.

Jack

[do...@parshift.com]

This investigation of what is not a  system is informatively thoughtful, and would have been a useful contrast in the debate that tried to defne what is a system. It addresses the essence of systemness independent of what “I” think qualifies as a system in “my narrow context” of interest at the moment. Thank you Ken.

 

---------------------------------------------------------------

Rick Dove

Paradigm Shift International, Inc, and

Stevens Institute of Technology

2051 La Lama Rd, HC-81 Box 17

Questa, New Mexico 87556

575-586-1536 (Forwarded to cell on travel)

575-770-7101 (Cell, usually off when not on travel)

 

From: syss...@googlegroups.com <syss...@googlegroups.com> On Behalf Of kall...@gmail.com
Sent: Monday, November 12, 2018 7:45 AM
To: syss...@googlegroups.com
Subject: RE: [SysSciWG] GST conceptual framework development

 

A point is, indeed, an object, however it fails to qualify as a system on two (ahem) points. 1) it is only one object containing no other objects in an aggregation, and 2) alone, it is not obviously coupled with any other objects. Actually, to recognize any point beyond its entity there is a monomorphism called the identity (1object) that references the entity. So whenever you identify ”this” point (an object), you are referencing a system of entities and identities.

[Curt McNamara]

At the atomic level, a noble gas might be considered a closed system.

    Curt 

https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/ionic-interaction

[Duane Hybertson]

I agree with the criterion of usefulness. We invoke the concept of system when it useful to do so. To modify my example, in typical circumstances, my car and my neighbor's car would not be usefully considered to comprise a system. But if I am driving down the road next to or behind my neighbor's car, then it might be useful to consider the two cars (along with the drivers--whether human or automated, other cars in close proximity, the road, the local weather, the force of gravity, and other interacting entities) as a system.

[kall...@gmail.com]

Re: Allows communication vs accomplishes communication is interesting. It is difficult, if not impossible to identify “system-ness” at complete equilibrium, even though the potential for being a system exists.

 

The term system is an abstraction and representation of structure, behavior and morphism – consisting of two aspects: “be-able” and “imaginable”. I caution that imaginable has nothing to do with human mental ability, but inherent in the objects, structure, behavior and morphism to exhibit states other than it currently exhibits.

 

Every object (including categories) MUST exist in at least one, but often many more contexts. Curt’s comment is incomplete to a fault. Systems can an do exist in even in any number of dimensions including fractional dimensions. It is a problem of restricted paradigm. See for example search system using Peano or Hilbert patterns.

[Curt McNamara]

Agreed that it is an academic exercise to consider any one "thing" (for example a point) in isolation. It is always in relation to something or part of a set as Ken notes. Either of those add more dimensions to our consideration.

If I further channel my inner Bucky: we can create models of systems which may not tested for "closure" i.e. could they enclose a "space".

If the model doesn't contain enough "points" (minimum = 4 for a tetrahedron in 3-space) then the model can't have closure and doesn't (entirely) represent the system.

Could the model still be "good enough"? Sure, all models are wrong yet all are useful.

However :-) if you say the model represents a system yet it doesn't have closure -- by definition the model (of a system) can't be separated from Universe, and therefore is probably a part of a larger system. For example, the model could represent a surface of a system (which does exist in 3D). This could probably be tied to requisite variety ...

            Curt

[Steven Krane]

I disagree that “any one thing IS A part of a set.”  WE make sets.  It is not an attribute of what we are observing.  Pluto did not change when it was then wasn’t a member of the set of planets orbiting our star.

[Jack Ring]

Note that this presumes the car and tree are actually interacting instead of just having the ways and means to interact.  Potential vs Kinetic.

[kall...@gmail.com]

Steven,

 

Since the thrust of this discussion is generally in re: systems science and engineering, but not predominantly mathematics or philosophy, I would suggest folks do some research with respect to the fundamental difference between categories (in Category Theory) and sets (in Set Theory). As a foundation for mathematics, one can validly have a “class” of categories “conditioned” (functorially) to represent the more narrowly bounded class of sets.

 

Again, I caution not to consider categories in the traditional sense of a classification schema such as a hierarchy, taxonomy or ontology (although they may be used to construct these schemata). In this sense, a category only adds or imposes structure on an aggregation of objects.

 

While an over-simplification, one can, without paradox, have a “category of all categories”. One cannot have a “set of all sets” without such paradox, however. The oversimplification has to do with different levels of abstraction in the existence of categories. Abstraction (BTW quite different from generalization / specification) becomes useful in systems science and engineering precisely because it allows us to use a formalism to model systems – without complete and explicit knowledge of the particulars of that system. The way that works is similar to Bayesian Inference – how new information affects the “prior” as that system becomes “realized”. Since this deals with the rather deep epistemological subjects of modularity and plasticity of concepts, I won’t go there (that is academic to the max), but this is the way artificial neural networks “work” (and perhaps natural, even human minds, too).

 

Ken Lloyd

[kall...@gmail.com]

Both cases – potential and actual – must be considered when engineering a system. “Ya just never know which path the future will take”.

[Jon Awbrey]

Ken, Steven, All,

Another thing to keep in mind here is the difference between
General Systems Theory, following on Bertalanffy et al., and
what is variously known as Dynamical Systems Theory (DST) or
Mathematical Systems Theory (MST). GST spends a lot of time
studying part-whole hierarchies while DST/MST deals with the
state space of a system and the possible trajectories of the
system through it.

Mathematical category theory is especially useful in the latter application,
abstracting or generalizing as it does the concepts of mathematical objects,
functions, and transformations.

Regards,

Jon

On 11/14/2018 8:11 AM, kall...@gmail.com wrote:
> Steven,
>
> Since the thrust of this discussion is generally in re: systems science and engineering, but not predominantly mathematics or philosophy, I would suggest folks do some research with respect to the fundamental difference between categories (in Category Theory) and sets (in Set Theory). As a foundation for mathematics, one can validly have a “class” of categories “conditioned” (functorially) to represent the more narrowly bounded class of sets.
>
> Again, I caution not to consider categories in the traditional sense of a classification schema such as a hierarchy, taxonomy or ontology (although they may be used to construct these schemata). In this sense, a category only adds or imposes structure on an aggregation of objects.
>
> While an over-simplification, one can, without paradox, have a “category of all categories”. One cannot have a “set of all sets” without such paradox, however. The oversimplification has to do with different levels of abstraction in the existence of categories. Abstraction (BTW quite different from generalization / specification) becomes useful in systems science and engineering precisely because it allows us to use a formalism to model systems – without complete and explicit knowledge of the particulars of that system. The way that works is similar to Bayesian Inference – how new information affects the “prior” as that system becomes “realized”. Since this deals with the rather deep epistemological subjects of modularity and plasticity of concepts, I won’t go there (that is academic to the max), but this is the way artificial neural networks “work” (and perhaps natural, even human minds, too).
>
> Ken Lloyd
>

--

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache

[Jack Ring]

Re: we can create models of systems which may not tested for "closure” 

No we can’t. We can create models of configurations which may not tested for "closure” but these are not systems sans Purpose and identification of the context that fulfills Purpose.

jack ring

On Nov 13, 2018, at 20:29, Curt McNamara <cur...@gmail.com> wrote:

Agreed that it is an academic exercise to consider any one "thing" (for example a point) in isolation. It is always in relation to something or part of a set as Ken notes. Either of those add more dimensions to our consideration.

If I further channel my inner Bucky: we can create models of systems which may not tested for "closure" i.e. could they enclose a "space".

If the model doesn't contain enough "points" (minimum = 4 for a tetrahedron in 3-space) then the model can't have closure and doesn't (entirely) represent the system.

Could the model still be "good enough"? Sure, all models are wrong yet all are useful.

However :-) if you say the model represents a system yet it doesn't have closure -- by definition the model (of a system) can't be separated from Universe, and therefore is probably a part of a larger system. For example, the model could represent a surface of a system (which does exist in 3D). This could probably be tied to requisite variety ...

            Curt

On Mon, Nov 12, 2018 at 8:45 AM <kall...@gmail.com> wrote:

A point is, indeed, an object, however it fails to qualify as a system on two (ahem) points. 1) it is only one object containing no other objects in an aggregation, and 2) alone, it is not obviously coupled with any other objects. Actually, to recognize any point beyond its entity there is a monomorphism called the identity (1object) that references the entity. So whenever you identify ”this” point (an object), you are referencing a system of entities and identities.

 

Moving beyond considering that exclusive point devoid of context, however, things may get murkier. I apologize for the, now, category-theoretic context in which to consider “a point”. Topologically, if we were to embed that singular point into (/mapsto) into a metric space, we have a different scenario altogether. That point now shares information regarding its “be-able” as a location with and in that space. It also exhibits the potential to inhabit other alternative locations – its imaginability – in other locations in that space (notice we have the rudimentary makings of a system).

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