"It's an equation Jim, but not as we know it!"

Silver (2013) in “The Signal and the Noise” refers to Drake’s equation, which has fascinated me since my teens. It is a formula that provides a framework for predicting the number of intelligent extraterrestrial species in the galaxy. Due to the high number of parameters and uncertainties that make up Drake's equation, Silver describes how the extreme range of results depend on the initial ‘inputs’. Given the variables presented they are estimates. I made a connection to Drake's work through BBC BASIC programming:

'The Nursing Process'
'Computer-Aided Patient Assessment'
'Blood Groups'
'Shades of Grey'

As time went on the simplicity of 'The NP' gave way to DIM arrays, which can provide data structures, and DEF PROC and DEF FN with parameters. 

The evidence for the elements of Drake's equation has made great strides since the 1990s. Despite the remaining uncertainties, Silver notes that Drake's equation has provided a useful lens for astronomers, plus - philosophers and the lay-person to think about life, the universe and everything.

Is there an implicit theory – an equation – in Hodges’ model?

See also: BBC BASIC

Previously: 'Sagan' : 'SETI' ; 'math' : 'Publication list (2024)'

Nate Silver (2013). “The Signal and the Noise”, Notes 89, London: Penguin. p.488.

Title Ack. the original is often misattributed: https://www.youtube.com/watch?v=FCARADb9asE

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?'

Life, Literacy, Oppositions, Complexity and Information

Literacy in Traditional Societies

"Durkheim's work on primitive classification is being applied to societies within the orbit of major civilizations. The polarities and oppositions of la pensée sauvage turn up in ancient Greece, and tools developed in the study of the narratives of American societies are applied to the Oedipus story, the Book of Genesis and even contemporary literature, with little sense of the basic incongruity involved.

Polarities of some sort are of course present in all societies; their significance, however, varies widely. Aristotle describes one Pythagorean theory in the following terms:

 

Others of this same school say that there are ten principles, which they arrange in ten columns, namely:

limit unlimited
odd even
one plurality
right left
male female
at rest moving
straight crooked
light darkness
good bad
square oblong

. . . How these principles maybe brought into line with the causes we have mentioned is not clearly explained to them [quoted Guthrie 1962: 1, 245]."

Goody, J. (1968) Literacy in Traditional Societies, Cambridge: CUP. pp.10-11.


Taking each of these in-turn as may relate to Hodges' model (I may update/edit these):

limit  unlimited

As a template the model invites both a limit (boundaries) and some-thing unlimited.

odd  even

There is a symmetry - evenness to the model, but the invitation noted above is also a prospect for odd-ness. This may extend to the frustration experienced when a phenomena, account (patient's narrative . . .) defies explanation and classification.

one  plurality

This polarity is key in Hodges' model. 'One' refers to the person, patient, carer, any - individual who the model is applied to. In respect of plurality this can include the dyad of patient - nurse, couple, family, team, community, national or global population (and Biosphere).

 

right  left
 

The horizontal axis is not the last word in Hodges' model, as intra-domain we also find right and left. Of course, the vertical axis (indeed, the whole model if required?) can also be repeated in a domain.

 

male  female

 

You quickly recognise the potential for disagreement* which is fundamental in dichotomous situations, a point further reinforced below.

at rest  moving

 

The model is 'at rest' as a snap-shot, but as a frame it can represent the change over time and so has its own dynamic potential.

 

straight  crooked

 

The axes as continua are 'straight' but this distinction (as noted above) has distinct psycho-socio-political connotations. In the model, line-of-sight is acknowledged, while 'crooked' might suggest what is uncertain, and unseen?

 

light  darkness & good  bad

 

Again, these two oppositions seem 'loaded': especially socially - politically.

Tread carefully. If you have light, that's good, but if lost: bad.

 

square  oblong

 

Viewed as containers, or sets the model's domains can be represented as several shapes, as long as the axes are retained as part of the structure. The adopted rectilinear form is an affordance of the (underlying) HTML, and the traditional (paper-based) tabular format. From the domains being of equal area, the point where the axes intersect could be shifted, such that a single domain is enlarged (prioritised?), at the expense of another.

*Incredible harmony too!

Then prior to an anticipated move, and sorting through books and papers:

Complexity:
Life on the edge of chaos

“The discovery that universal computation is poised between order and chaos in dynamical systems was important in itself, with its analogies to phase transitions in the physical world. It would be interesting enough if adaptive complex systems inescapably were located at the edge of chaos, the place of maximum capacity for information computation. The world could then be seen to be exploiting the creative dynamics of complex systems, but with no choice in the matter. But what if such systems actually got themselves to the edge of chaos, moved in parameter space to the place of maximum information processing?” p.54.

Lewin, R. (1993) Complexity: Life on the edge of chaos. London: Phoenix.

The conclusion? 

Perhaps, the ubiquity of polarity, opposition and dichotomy is that they anticipate and presage an increase in information processing (for good or ill: there we go again!). 

This is also a ( the ) function of Hodges' model.

Previously:

Opposition  . . . See also - Polarity , Dichotomy , Literacy . . .