Tricotyledons, systems and social problems

'If scientists and engineers are to be able to attack social problems with the same validity and effectiveness with which physical problems have been attacked, then a much more sophisticated and rigorous system design methodology is needed.

Such methodology, called the tricotyledon theory of system design, has been developed as a synthesis of: empirical and speculative approaches to system design [2], the methodology of operations research [10], classical optimization techniques [18], results in specialized branches of mathematical system theory [1,4,6,7], and the constructs of general mathematical system theory [12,13,14].

Experimental applications of the tricotyledon theory of system design to several problems in widely differing contexts [3,4,8,9,16,17] indicate that the methodology holds great promise for validity and effectiveness in attacking any large-scale, complex, man/machine system design problem with precision and rigor. There are no theoretical limitations (such as differentiability, linearity, finiteness, or discreteness) for the problems that can be attacked within the tricotyledon theory of system design.

In this short abstract the theory is only described in terms of set and system theoretic concepts as presented in Reference [12), [13], or [14]; no exploitation of the theory, either theoretical or practical is attempted here.' ..' p.224-225.

'The task of defining a large-scale, complex, man/machine system design problem P=(S,T,α,β,γ,D) often requires an interdisciplinary team in practice. An interdisciplinary team requires, in turn, that the above definitions be translated into non-mathematical methodology. This has been done in Reference [15].' p.229.

15. Wymore, A.W., Systems Engineering Methodology for Interdisciplinary Teams, unpublished manuscript. (Another loss?)

Wymore, A.W. (1975) The Tricotyledon Theory of  System Design. In. Category Theory Applied to Computation and Control: Proceedings of the First International Symposium, San Francisco, February 25-26, 1974 (Lecture Notes in Computer Science, 25) by E.G. Manes (Editor).

See also: 

https://en.wikipedia.org/wiki/A._Wayne_Wymore

http://sysengr.engr.arizona.edu/wymore/bookreview.html 

https://lockywolf.wordpress.com/2019/02/16/a-mathematical-theory-of-systems-engineering-the-elements-by-a-wayne-wymore/ 

style="font-family: helvetica; font-size: small;"

Working title: 'Can Hodges’ model provide a foundation for a mathematically informed ...

... epistemology and relational ontology? Part 1'

Abstract

Aims: To begin a process of examining a ‘model of care’ and conceptual framework known as Hodges’ model as a mathematical object. This paper examines the structural elements of this model, its axes and domains through a formal, logical and mathematical lens. To establish the extent to which a combined relational understanding and mathematical approaches can provide avenues for further research.

Design: This study adopts the design of a two-part exploratory and descriptive paper, using an inquiry-based approach throughout.

Methods: The method is interdisciplinary, descriptive, and involves conceptual analysis. Rather than Hodges’ Model acting as a model of, and for care, here the model is used to investigate how health and social care can be better conceptualised. The question is: What is the result when Hodges’ Model is treated as a mathematical object? Here, Hodges’ model is used as an inquiry-based model with reflection and critique.

Results: Readers will see the development of ideas, driven by the structure of a model of care, existing taxonomy defined by nursing theory, associated with foundational mathematical concepts.

Conclusion: The questions introduced and deliberated here will identify avenues for further study. And highlight Hodges’ model to other researchers; less familiar with Hodges’ model, and yet more skilled – adept mathematically.

What does this paper contribute to the wider global clinical community?

Re-assert the importance of theory development in nursing and health disciplines.

Draw attention to the relational (and reflexive) potential of Hodges’ model and in healthcare to abstract the collective dimensions of healthcare, especially those that are political.

Given the problems faced in the century to follow, encourage researchers within and without healthcare to further develop these ideas.

Impact:

Extend the relevance and scope of mathematical abstraction, in healthcare disciplines and the humanities, beyond statistical analysis.

This paper confirms: the conceptual utility of Hodges’ model; the challenge of requisite mathematical skills; the need for interdisciplinary cooperation.

Theorists in health and social care, policy makers and researchers seeking to apply mathematical techniques, especially category theory in the social science may find this work helpful and encouraging.

Reporting Method: N/A

Patient or Public Involvement: This study did not include patient or public involvement in its design, conduct, or reporting.

Keywords: nursing, theory, relational ontology, health, Hodges’ model, mathematics

See also: Draft notes - 'Hodges' model - Locus of Care & Control?'

Sets in Hodges' model

INDIVIDUAL
  |

     INTERPERSONAL    :     SCIENCES               

HUMANISTIC --------------------------------------  MECHANISTIC      

SOCIOLOGY  :   POLITICAL 

|

GROUP

'The emotions that we want to infer are the seven basic emotion categories. Concretely this set is E = {Anger,  Contempt, Disgust, Fear, Happy, Sadness, Surprise}.' p.111.*	Sets - Venn diagrams Physical obs = { Temperature, Pulse, Respiration, Blood Pressure, Gait ... }
Social = { Friends, Family, Work colleagues, Neighbours ... }	Politics { [Freedom], - Elections, Law, Policy, Government, MPs, Ministers, PM-President ... }

David Sanchez-Mendoza, David Masip, Xavier Baro, and Agata Lapedriza. Emotion Detection Using Hybrid Structural and Appearance Descriptors. In. MDAI 2013: Proceedings of the 10th International Conference on Modeling Decisions for Artificial Intelligence - Volume 8234 November 2013. Pages 105–116 https://doi.org/10.1007/978-3-642-41550-0_10

*I am unable to double-check this reference and hope it is correct(?).

See also:

UNIVERSAL EMOTIONS: Paul Ekman Group

Venn : diagram

The naïve approach

Categories, Bundles and
Spacetime Topology  

'First steps' are by their nature plagued by uncertainty of intent and direction, ungainliness, missteps, stumbles and ('finally') possibly falls.

Finding a starting point can be difficult.

Where to find a hand-hold, place one's foot, or other anchor?

At Lancaster University library I came across this book, first published in 1980. The cover displayed is from the 1988 edition.

In order of appeal I read:

applications, categories, spacetime and topology.

Section I starts with Preliminaries: Notation and Abbreviations; always useful (reminder).

The next, Section II Naïve Category Theory, had my immediate attention. We often speak of learners as being naïve. As lifelong learners we all meet this descriptor. I keep revisiting this word, concept - 'naïve'.

Naivety is a starting point for practitioners in health and social care too. Hence the need for supervision, mentors, the tokens of probationary (driver) and 'newly qualified'. 

Many posts on W2tQ stress the diagrammatic quality of Hodges' model. It is visibly a 2x2 matrix, (once again..) beloved of management consultants, psychologists and change agents. In Section II Dodson recognizes the London Underground map as a graph. A small example is developed, explained and illustrated on p.6. 

Graph example, drawing on the London Underground. p.6.

Section II may be a small part of the overall book but it is invaluable to me. As the photo above suggests, the book is old, especially as 1st edition. I will try to access the 2nd edition. If this work is a project with which you can (more ably!) assist, I would greatly appreciate your input. The aim is to signpost Hodges' model as a potential focus for all researchers. Especially researchers interested in trying to conjoin the sciences and humanities and develop visualization in the latter. 

C.T.J. Dodson. Categories, Bundles and Spacetime Topology. 1st Edition, Shiva, Kent. 1980.

Previously: 'math'

'Diagram' resources listed on former, now archived website.

Person to object: Surely you're joking* ...!

 INDIVIDUAL
  |

     INTERPERSONAL    :     SCIENCES               

HUMANISTIC --------------------------------------  MECHANISTIC      

SOCIOLOGY  :   POLITICAL 

|

GROUP

identity person choice	identity person, age integer
people father - mother	election voting age

 

By @Eyesomorphic - https://www.youtube.com/@Eyesomorphic 

"A gentle introduction to the study of Category Theory and Abstract Algebra, done from the ground-up by exploring the mathematical weapon of abstraction. This video aims to give an overview of the fundamental tool at the forefront of pure mathematical research: abstraction. By seeing this tool in various contexts, and how it allows us to encounter Category Theory in a natural and intuitive manner, we'll see how beautiful the abstract can really be."

  ― Timestamps ― 

 0:00 - Intro 

1:49 - Abstraction and Algebra 

7:30 - Examples of Abstraction 

8:49 - Set Theory 

13:25 - Category Theory 

21:16 - Outro 

― Credits ―
All animation and voiceover created by Eyesomorphic. Background music: 'Abstraction', composed by Caleb Peppiatt.

― Further Reading ―
Category Theory for Programmers: The Preface, by Bartosz Milewski: https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

Category Theory for Computing Science, by Michael Barr & Charles Wells (Book)

 *Person to object - and back again - assuring and preserving the humanistic.

Draft papers: The heat is always on ...

Writing is never easy here. My 'pen' runs pell-mell and I invariably follow; dragged and teased from discipline-to-discipline, while trying to pick up any semblance of a coherent thread.

Perhaps that's the cost of being naturally(?) drawn to mind-mapping, Hodges' model specifically and the substrate - structure it affords.

While painful, the papers I've produced show (as listed in bibliography and with others) that I can get there.

In February I posted:

Call for Papers (i) Community Development and Preventative Care With Older People:

New Values and Approaches

Call for Papers (ii) Community Development and Preventative Care With Older People ...

In truth, of course, there was no way I was going to complete a submission by July. I've been intent to throw caution to the wind, even at risk of being blown flat on the my face (and worse?).

Winding back further to October and December 2021 and the 12,000 word draft: "Society, Technology and COVID19 in Hodges' model":

https://hodges-model.blogspot.com/2022/10/draft-papers-iii.html

I approached a journal regards the draft 'Society, Technology and COVID19 in Hodges' model'. Having reduced the original 12000 words to 7700, the paper is of interest, but is (as expected) too long. There is the possibility of reducing the word count to 5000, or splitting the essay.

Duly resubmitted, the feedback from the reviewers, all three, is spot-on. 

Since the (N.) spring, I've tried to re-structure and provide a meaningful discussion. In conclusion. It's  not happening.

One reviewer noted: 

"I still do not have a clear understanding of where the model comes from and what its axioms are."

Repeating myself no doubt, the book chapter on the work of Michel Serres:

Jones, P. (2008) Exploring Serres’ Atlas, Hodges’ Knowledge Domains and the Fusion of Informatics and Cultural Horizons, IN Kidd, T., Chen, I. (Eds.) Social Information Technology Connecting Society and Cultural Issues, Idea Group Publishing, Inc. Chap. 7, pp. 96-109.

- resulted from an earlier draft which was well-shredded by the nurse journal reviewers. They did help - I've a paper to review myself.

Out of flames though that chapter quickly emerged and took flight (well, was 'completed' at least). So if you are writing and struggling - take heart.

Avoiding nursing journals (enough = enough? Nobody is interested): 

I now think I have an improved plan for two papers. The first will consider the axioms of care within Hodges' model; plus (please don't laugh!) what insights might follow if I/we treat Hodges' model as a mathematical object?

Can I claim mitigation by suggesting this (folly) is not entirely my fault . . ?

"Thus, the author can take a different approach and with a structured discussion of ideas, the author can generate testable hypotheses to move forward with a research paper. A more structured theoretical approach would also help to pique the interest of more advanced readers, especially academic audiences such as faculty who want to learn about something outside of their own research areas."

STRANGER IN
A STRANGE LAND

I feel I've no choice but to respond to the reviewer quite literally. As a non-mathematician, perhaps I can pique the interest of more advanced readers and faculty? The aim of the former archived website and this blog is to pass-on this baton² 😉to others; people who can understand it anew and apply it to the problems (solutions ...) of the century.

So in part two, the 'Society, Technology and COVID-19 in Hodges' model' piece will be structured (re-written) using hypothetical examples that ask questions of Hodges' model, the audience, and most definitely - me! It might, if not too grandiose, even ask questions of mathematics too and the humanities(?) - hence reading to follow. A real trick would be if these two papers could also stand alone.


n.b. After attending the UKSS Conference today, I must consider systems too (but don't panic - it's OK!) - to inform a title: re. humanistic & mechanistic systems? Yesterday, I really enjoyed 3 hours chatting to two fellow systems enthusiasts, who work in public health; and business / management respectively. We met in Oxford, at the Ashmolean cafe. 

UKSS Conference is bound for Oxford next year and when I have details I will post here.

Book cover:
https://www.hachette.com.au/robert-a-heinlein/stranger-in-a-strange-land
div>

"Naive Set Theory" Book and Text

INDIVIDUAL

|

INTERPERSONAL    :     SCIENCES               

HUMANISTIC --------------------------------------  MECHANISTIC      

SOCIOLOGY  :   POLITICAL 

|

GROUP

	Naive Set Theory

From the Serving Library:

"To Summarize:

1. A total absence of information about a given subject usually solicits no curiosity: without an awareness of its existence, we can’t possibly care about it.

2. When we come to realize the existence of something we never knew was there before, our curiosity is sparked: What is it? How does it work? What should we call it? Why is it there? But we remain in the early stages of our ability to recognize and read it.

3. We attempt to accumulate information, and while additional research provides many answers, it also reveals additional questions, fueling more curiosity still.

4. At a certain point—at the top of the bell curve — we come to a place where effective discussion and debate is possible, but much still remains speculation. It is a moment of intense scrutiny and educated hypothesizing when questions, answers, contradictions, controversy, desire, violence, disappointment and determination make up a complex system."

. . .  

Continued ...  – “Naive Set Theory,” Anthony Huberman, Dot Dot Dot #15, 2008.

https://www.servinglibrary.org/collection/poster-for-naive-set-theory

Halmos, Paul, Naive Set Theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. ISBN 0-387-90092-6 (Springer-Verlag edition). Reprinted by Martino Fine Books, 2011. ISBN 978-1-61427-131-4 (Paperback edition); 2017 Dover reprint ISBN 9780486814872

http://people.whitman.edu/~guichard/260/halmos__naive_set_theory.pdf

My source: Book - Tate Liverpool

Paper - "The concept of legal space: A topological approach to addressing multiple legalities"

 INDIVIDUAL

|

 INTERPERSONAL    :     SCIENCES               

HUMANISTIC --------------------------------------  MECHANISTIC      

SOCIOLOGY  :   POLITICAL 

|

GROUP

"5 An early reference to topology in psychology has been developed by Kurt Lewin, Principles of Topological Psychology (McGraw-Hill, New York, 1936). Linking literature and topology, Angus Fletcher, The Topological Imagination: Spheres, Edges, and Islands (Harvard University Press, Cambridge, MA, 2016). For an overview of philosophical approaches related to topology, see Daniel Parrochia, Mathematics and Philosophy (Wiley, Chichester, 2018) Ch 11. Using a topological approach to law, Müller-Mall (n 4). This last contribution constructs a topological approach for assessing perspectives in law (such as reflected in judicial decisions on a certain legal question) and situating them within ‘reference frames’ (in particular 117 et seq)." p.520.

"Law is fragmented ‘along issue-specific rather than territorial lines’, as exemplified by regulatory regimes for environmental and health issues or the private regulation of the cyberspace and of transnational commercial activities.20 Some authors have described this as a ‘deterritorialization’ of law.21 One reason for such a deterritorialization is the increasing amount of regulatory objects that cannot, or can only with difficulty, be linked to any territory – particularly salient in the case of digitalized data and its fluid location." p.522.

"... the notion of legal space suggested here comprises various features that are guided by concepts from topology, a branch of mathematics that analyses the qualitative nature of spaces. This approach has been adopted in an interdisciplinary manner, including in various disciplines of social science."5(See above). pp.519-520.

Global Constitutionalism

Burchardt, D. (2022). The concept of legal space: A topological approach to addressing multiple legalities. Global Constitutionalism, 11(3), 518-547. doi:10.1017/S2045381722000041

Head-Smashed-In ... Maths

In 1979, with a friend and still one of four (yes - I know!) we went to Calgary, Alberta for three weeks.

This was a key holiday, one to remember. I was able to return in 1989, with my then wife, eldest son and the (very) youngest - at the time - as we learned. With a new edition of the same tourist map, it was amazing to see the change in the cities footprint across a decade.

Our travels supported by the love and hospitality of two Brits who emigrated to Canada, sadly no longer with us. We talked of migrating for a time: Canada, or New Zealand.

In Alberta, one trip took us past:

Head-Smashed-In Buffalo Jump (and photo source)

Ever since school, it is maths that has head-smashed-in mine. The (personal) history here revolves around the Eleven-plus exam [ https://en.wikipedia.org/wiki/Eleven-plus ] which I failed.

Yes, that's -'11+' - I'm sure you can see the irony?

Perhaps, in the near future the future will resolve around the diagrammatic form of Hodges' model and the model's acting as a baton to pass to others with the knowledge and skills to apply mathematics and logic to Hodges' model.

Here is some of the history of this geophysical feature:

https://www.audleytravel.com/canada/places-to-go/alberta/head-smashed-in-buffalo-jump

"The buffalo jump was used for 5,500 years by the indigenous peoples of the plains to kill bison by driving them off the 11 metre (36 foot) high cliff. Before the late introduction of horses, the Blackfoot drove the bison from a grazing area in the Porcupine Hills about 3 kilometres (1.9 mi) west of the site to the "drive lanes", lined by hundreds of cairns, by dressing up as coyotes and wolves. These specialized "buffalo runners" were young men trained in animal behavior to guide the bison into the drive lanes. Then, at full gallop, the bison would fall from the weight of the herd pressing behind them, breaking their legs and rendering them immobile. The cliff itself is about 300 metres (1000 feet) long, and at its highest point drops 10 metres (33 ft) into the valley below. The site was in use at least 6,000 years ago, and the bone deposits are 12 metres (39 feet) deep. ... The importance of the site goes beyond just providing food and supplies. After a successful hunt, the wealth of food allowed the people to enjoy leisure time and pursue artistic and spiritual interests. This increased the cultural complexity of the society.

In Blackfoot, the name for the site is Estipah-skikikini-kots. According to legend, a young Blackfoot wanted to watch the bison plunge off the cliff from below, but was buried underneath the falling animals. He was later found dead under the pile of carcasses, where he had his head smashed in.^{"
https://en.wikipedia.org/wiki/Head-Smashed-In_Buffalo_Jump}

With COP27 on-going we are all participants in a 'drive' ...

ii Seeds in 'architecture'

There is something seductive in architecture, the imagination of ideas on paper, the promise of the cornerstone, the reality of the construction, the space it grasps and the space it bestows.

Arriving at Younés paper, the history and reference to Valéry's Eupalinos ou l'architecte, Socrates and Phaedrus had me captured. 

Healthcare is dialogue. Spoken and unspoken. Discourse. Dialectic. Perspective: One : Shared : (the) Many.

What is said, gestured, and unsaid. Valéry's dialogue sounds worthy of follow-up, appreciating Plato and this form of theatre and learning. There is a latent architect in us all. Patiency too - but not yet - let us build first. Every day and night we construct (hopefully). When necessary we know when to disassemble, de-construct, to initiate change.

Reading Younés I can readily relate the paper to nursing, Hodges' model, and healthcare generally. The paper's three main questions concern (of course) architectural theory:

1. the causal relation between building and theory;
2. the necessary mental conditions that precede theory;
3. a definition of theory in its scope, discourse, and nature.
   

There are many points of note (reading my yellow highlighter) here. 

'Reflection precedes realization, but theory does not necessarily precede practice'. p.234.

'Theory however, is a systemic elaboration that operates based on definitions and concepts, in the sense that definitions build concepts, and concepts in turn build a theory, but not the reverse of the sequence.'

'Theory, then, comes 'late', only because it is the synthesis of a content that was already present'. It is constructed after a prolonged reflection over many experiences, based on common, comparative, or contrasting sets of criteria.

Younés focus is specific the development of theory in architecture, but as he writes: 'there is some element of reflection which can be termed the building's efficient cause' p.234. I wonder about Nursing Theory and the nurse's theory based on the person - in-person: reflection of care, assessed, planned, delivered, evaluated and recorded. There are nurses still preoccupied with Q.1, even if the (primary) focus is within academia(?).

Q.2 seems an invitation for philosophy (as per the journal's title!). Being non-judgemental, if not starting to build nursing Theory, then especially for the nurse co-constructing, co-designing a theory of care with the patient/family. Hodges' model is not just a series of set squares, facilitating design; it is an empty set. Never completely empty, due to the structure. A structure that contradicts. A structure paradoxical as it constrains and releases, records and forgets.

Q.3? Did someone call - continuity? Yes, (and how!) we can carry on from Q.2. Scope - yes. See the space? Listen to all the dimensions. Reduced to those that count, in discourse and nature, by nature.

Person-centred? New patient. RESET. Re-build - but remember humanistically.

See also:

Seeds in 'architecture' i

Seeds in 'architecture' iii

Younés, Samir. “Constructing Architectural Theory.” Philosophy 78, no. 304 (2003): 233–53. http://www.jstor.org/stable/3752046.

 

Carvalho - "The Paths to Narrow Identities" 2021

"The Dasgupta-Goyal Model of Narrow Identities"

Seeking the logic(s) in the 'health career' model

  

 

 Self - Individual - Person
|

 INTERPERSONAL    :     SCIENCES               

HUMANISTIC ----------------------------------  MECHANISTIC

SOCIOLOGY  :   POLITICAL 

|

Community - Group - Population

"DG recognize that narrow identities form through social interactions and that groups play an important role in this process. This is a major advance. Because narrow identities are an equilibrium phenomenon they cannot be undone through individual will and right thinking alone. Specifically, DG’s model consists of a finite population of individuals, N, and two groups, A and B. Individuals and groups are ex ante identical. Individuals can choose to join one or both of the groups. Only the extensive margin (membership) is considered, not the time or effort devoted to each group. The payoff from joining group k ∈{A, B} is increasing in the size of group k and is also a function of the size of the other group k′ ≠ k. An individual i is said to have a narrow identity if i joins only one of the groups. Society can be said to have narrow identities when each individual i ∈ N joins exactly one group. Note that narrow identities can exist in a monomorphic equilibrium (where all individuals join one group) or a polymorphic equilibrium (where different individuals join different groups)." p.79.

 

Jean-Paul Carvalho. The Paths to Narrow Identities. Erasmus Journal for Philosophy and Economics,Volume 14, Issue 2,Winter 2021, pp. 77–86. https://doi.org/10.23941/ejpe.v14i2.615 

The above paper is part of an "ARTICLE SYMPOSIUM on “Narrow Identities”.

'health career' - life chances. 

My source: @PhilosL @LiverpoolPhilos

 

"EEEE..." and not a cloth-cap in sight

"The acronym EEEE abbreviates

individual

|

INTERPERSONAL : SCIENCES

humanistic ----------------------------------------------- mechanistic

SOCIOLOGY : POLITICAL

|

group - population

"everything	enfolds
everything	else"

 

 - where the word 'enfolds' means 'contains within itself'. A theory in which some interpretation of the EEEE principle holds, is said to possess (the property of) wholeness; that is, each part contains, within itself, the whole (more precisely, the near-whole: every other part). We first discuss classical set theory and wholeness. We then interpret EEEE set theoretically and investigate whole set theory. A method is described by which classical set theory can be made to manifest a degree of wholeness, and further lines of investigation are suggested. A brief discussion of various examples of the EEEE principle is given in the Appendix" 

Blizardo, W. (1989). EEEE: SET THEORY AND WHOLENESS. Logique Et Analyse, 32(127/128), NOUVELLE SÉRIE, 215-239. Retrieved September 4, 2020, from http://www.jstor.org/stable/44084274

Please note in posting this, I am not trying to suggest that I understand the paper: as a whole - or even several parts!. 

n.b. Posted in Wigan - just a cloth-cap insight.

Poetic license ack: “Eee lad, we’re off to that there North England”

https://twitter.com/BarristerSecret/status/1223260008256765953?s=20

Emphasising 'naivety' and collections of things: The Serving Library

individual
INTERPERSONAL : SCIENCES

humanistic ------------------------------------------- mechanistic

SOCIOLOGY : POLITICAL

group

NAÏVE SET THEORY
by Anthony Huberman

1. A total absence of information about a given subject usually solicits no curiosity: without an awareness of its existence, we can’t possibly care about it.

....

7. Eventually, we have a dictionary definition.

See the pdf below and the title link for many other items within this journal:
http://www.dextersinister.org/MEDIA/PDF/NaiveSetTheory.pdf

My source: Visit to The Serving Library exhibition at Tate Liverpool

Image source: Goodreads.com