'Oh Thomasina!' Such a drama in a diagram

Arcadia

Last evening I really enjoyed a performance of Tom Stoppard's Arcadia at the Duke of York's, or soon to be - The Tom Stoppard Theatre:

Act I, Scene 2  

'Septimus ... You should no more grieve for the rest than for a buckle lost from your first shoe, or for your lesson book which will be lost when you are old. We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew? ...'^ p.20.

 Act II, Scene 3

'Lady Croom We are intruding here - this will not do, Mr Hodge. Evidently, nothing is being learned. (To Noakes) Come along, sir! 

Thomasina Mr Noakes - bad news from Paris! 

Noakes Is it the Emperor Napoleon? 

Thomasina No. (She tears the page off her drawing block, with her "diagram" on it) It concerns your heat engine. Improve it as you will, you can never get out of it what you put in. It repays eleven pence in the shilling at most. The penny is for this author's thoughts. 

She gives the diagram to Septimus who looks at it.' p.74
...
Now Septimus retrieves his book from Thomasina. He turns the pages, and also continues to study Thomasina's diagram. ... 

Septimus Why does it mean Mr Noakes's engine pays eleven pence in the shilling? Where does he say it? 

Thomasina Nowhere. I noticed it by the way. I cannot remember now. 

Septimus Nor is he interested by determinism -------

Thomasina Oh... yes. Newton's equations go forwards and backwards, they do not care which way. But the heat equation cares very much, it goes only one way. That is the reason Mr Noakes's engine cannot give the power to drive Mr Noakes's engine. 

Septimus Everybody knows that. 

Thomasina Yes, Septimus, they know it about engines! 

Pause. He looks at his watch 

Septimus A quarter to twelve. For your essay this week, explicate your diagram. 

Thomasina I cannot. I do not know the mathematics. 

Septimus Without mathematics, then.' p.75.

 
Tom Stoppard, (1993) Arcadia (Playscript), Faber & Faber, pb. ISBN 9780571169344.
https://www.faber.co.uk/product/9780571169344-arcadia/

My text source:
https://collegearts.yale.edu/sites/default/files/attachments/arcadia_by_tom_stoppard.pdf 

^ n.b. This was therapeutic, but I still mourn the losses from Alexandria and other libraries ... today.

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.

Paths, lines, corners, edges and axes . . .

'If a farmer has made a path, he is able to saunter easily up and down it. That is what the path was made for. But the work of making the path was not a process of sauntering easily, but one of marking the ground, digging, fetching loads of gravel, rolling, and draining. He dug and rolled where there was yet no path, so that he might in the end have a path on which he could saunter without any more digging or rolling. Similarly a person who has a theory can, among other things, expound to himself, or the world, the whole theory, or any part of it; he can, so to speak, saunter in prose from any part to any other part of it. But the work of building the theory was a job of making paths where as yet there were none.' 

Gilbert Ryle, The Concept of Mind (1949; Penguin, 1999), p. 272.

path

https://hodges-model.blogspot.com/search?q=path

line (line of sight)

https://hodges-model.blogspot.com/search?q=line

corners

https://hodges-model.blogspot.com/search?q=corners

edges

https://hodges-model.blogspot.com/search?q=edges

axes: STRUCTURE

domains: CONTENT

Frayn, Michael (2006). The human touch: our part in the creation of a universe. Notes. London: Faber & Faber. p.425.

Previously: 'Frayn on maths'

I will keep this book a bit longer - chapter 'Home Address' (the self) a good read.

Hodges' model? Ah! You mean the naïve conceptual framework that ...

... thinks it's a theory! (i)

Yes, I suppose it is naïve, now you mention it. It's naïve in a number of ways:

1. The assumed state of students - new learners; although of course, in healthcare and other professions for many years mature students - far from naïve - can make up a notable proportion;
2. When a patient assessment begins, especially upon initial (and first) referral, the data gathering, our knowledge should then be assumed to be naïve.
3. The quest for a theoretical underpinning of Hodges' model, may display naïve associations between concepts that are misplaced, misunderstood and wholly inappropriate.

Worth noting in #1, that policy-makers and recruitment specialist hope to increase the number of mature entrants, given demographic pressures.

If you consider the way nursing as a profession has received 'nursing theory', or in a similar vein, consider the status of nursing theory, and models of care in nurse (and healthcare) curricula today, then the approach is pragmatically naïve? From the 1970's -

Vinner, S. (1976). The Naive Concept of Definition in Mathematics. Educational Studies in Mathematics, 7(4), 413–429. http://www.jstor.org/stable/3481947

Vinner writes:

"As a matter of fact, all of us start to deal with definitions at a very young age when we start to leam our mother tongue. At this stage, various types of definition occur and the subject is too complicated to be dealt with here. After several years, especially at school, one type of definition becomes dominant; the lexical definition. In a lexical definition, the meaning of a certain word (or words) is explained by means of other words (we shall deal here only with the case in which the word and its definition are at the same language). This type of definition generally occurs in mono-lingual dictionaries." p.425.

"The sentence: 'A rectangle is a quadrangle that has four right angles' does not have in it any underlying assumptions about the role of definition in mathematics. It can be interpreted in any of the following three ways:

1. We (math teachers and math students) hereby agree that instead of saying, "a quadrangle that has four right angles" we will say: "a rectangle" (The formalistic approach).
2. In the mathematical community the meaning of the word rectangle is a quadrangle that has four right angles (The lexical approach from the expert's point of view).
3. The object denoted by the word 'rectangle' is a quadrangle that has four right angles (The lexical approach from the naive standpoint). 

Thus, not adding anything to definitions like the above we let the student choose his own interpretation out of the three mentioned (or even possibly more) interpretations. We claim that in most cases the student's choice will be the third one." pp.427-428.

Does the diaeresis here point to forms of parity of esteem, oppositions, polarities, dichotomy?

"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

No Body... No Mind...

Hodges' model: an open conceptual space for the naive beginner and expert alike...

individual

|

INTERPERSONAL : SCIENCES

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

SOCIOLOGY : POLITICAL

|

group

NO BODY...!?	NO MIND...!?

"I also find it helpful to be both expert and naive. Following Shunryu Suzuki’s saying, “in the beginner’s mind there are many possibilities; in the expert’s mind there are few,” I find it helpful to approach each client with an attitude of “we don’t really know anything about this, let’s explore it together.” On the other hand, clients expect (and have a right to expect) some level of expertise and the fact as clinicians is we do have a body of knowledge which is valuable. By being both “expert and naive,” simultaneously teacher and student, we can model a kind of being-with-a-problem, which is most paradoxical but most essential: I (and you) are both healthy and ill, distressed and just fine." p.23.

Rosenbaum, R., & Shahar, Golan. (2012). Thoughts on Mrs. T: No Body, No Mind. Journal of Psychotherapy Integration, 22(1), 19-26.

Naivety [I] ever unfolding : ever present - SCIENCES

naivety [naɪˈiːvtɪ], naiveté, naïveté [ˌnɑːiːvˈteɪ]n pl -ties, -tés

1. the state or quality of being naive; ingenuousness; simplicity

2. a naive act or statement

My source:
http://www.thefreedictionary.com/naivety

There are times when we are all naive. It can be so embarrassing! When you realise, or more severely are made aware by others the abrupt learning is suddenly resolved. Within the bounds of the health career model, naivety can be found and is expressed in so many ways.

Hodges' model may appear naive in its simplicity, but behind that simplicity there are several assumptions. When you act as scribe, reader or doer you exercise the model's structure. You potentially demonstrate several levels of literacy.

If the health career model can represent most 'everything', then naivety should be no problem. So, if we visit each of the care domains in turn what can we find?

SCIENCES

I came across a post: 'We are all naive scientists' on The Financial Philosopher blog which includes this quote:

"It is clear, then, that the idea of a fixed method, or a fixed theory of rationality, rests on too naive a view of man and his social surroundings." ~ Paul Feyerabend

Regularly, I ask myself if I am naive in this particular domain. Am I right to assume that there are questions in nursing that can be answered (or at least reflected upon) using Hodges' model? Furthermore, can this use, this application be demonstrated in a scientific (evidenced) way?

Does experience of programming in BBC Basic as an enthusiast really help equip me now to get to grips with PHP, using Drupal and even Ruby?

Is information (and informatics) really the all encompassing Swiss army knife of a concept I take it to be?

The most extreme naivety here is not mine, however; it is as Feyerabend suggests the one that is in diagonal opposition. It is the scientific naivety of the masses in the social domain. Is this ignorance? In some cases, yes. But the tabloid (gutter) press shouts aloud when science gets it wrong; or, more accurately industrial processes based on science totally mess up.

The masses are not divorced from science. True, there was (still is?) a promised intimate relationship borne of equality and egalitarian ideals (education), but this naivety matures in real (social) time also known as life-chances. Its cost is not just red-faced, but illiteracy and exclusion at a time when literacy, inclusion and engagement are paramount.