Hodges' Model: Welcome to the QUAD: quadrants

Hodges' model is a conceptual framework to support reflection and critical thinking. Situated, the model can help integrate all disciplines (academic and professional). Amid news items, are posts that illustrate the scope and application of the model. A bibliography and A4 template are provided in the sidebar. Welcome to the QUAD ...

Showing posts with label quadrants. Show all posts
Showing posts with label quadrants. Show all posts

Monday, March 23, 2026

Good - Bad AI? c/o FT Magazine et al.

My source: Tim Harford, How can we tell good AI from bad? FT Magazine. 21 March 2026. #1168: pp.9-10.

    'Two new working papers address the tricky issue of verifying quality. In "Some Simple Economics of AGI", Christian Catalini, xiang Hui and Jane Wu (assisted, sometimes gratingly, by generative AI) propose the inevitable 2x2 matrix in which economic activity can be easy to automate, easy to verify, both or neither. Automatable, verifiable output is the stuff that computers do for us. The non-automatable stuff remains reassuringly artisanal.
    The difficult quadrant is where tasks seem easy to complete but are hard to check. Catalini, Hui and Wu call this the "runaway risk zone". It is not a reassuring label and it is not meant to be.
...
    In the second paper, "A model of Artificial Jagged Intelligence", Joshua Gans offers an analogy in which asking AI to perform task is like trying to cross a river over a network of planks supported by occasional pylons. The jagged frontier is represented by the fact that some planks are long and wobbly, while others are short and sturdy. Problem one: even if the planks are typically sturdy, the wobbly planks will require most of your time and attention. Problem two: if you can't predict in advance which planks will let you down, you may quite sensibly prefer to eschew the AI entirely and row yourself across the old-fashioned way.'

Catalini, C., Hui, X., & Wu, J. (2026). Some Simple Economics of AGI. arXiv preprint arXiv:2602.20946.

Joshua S. Gans, 2026. "A Model of Artificial Jagged Intelligence," NBER Working Papers 34712, National Bureau of Economic Research, Inc.


Previously: 'safety' : 'ai' : 'domain' : 'matrix'

Friday, December 19, 2025

ii Learn your lines and the hyperplanes will follow

With these lines, partitions, axes and domains in mind, when a clinical practitioner is presented with a new person, whether as a patient, client, or carer ... they can, using Hodges' model (and other tools!) approach their assessment in an open and receptive manner.

This means that the information provided by the 'patient' can be readily fielded, captured whatever the context and situation.

As noted previously, my study of Hodges' model began in the late 1980s. Application in my work as a community mental health nurse, with an interest in informatics followed quite naturally(?). Primed as I was, for various reasons to carry this forward, I also carried a mathematical learning disability. At the risk of getting bogged down in my thought, use and approach to Hodges' model I need a challenge.

Mathematics is the challenge for me. It's fascinating how we have in-built 'calculators' that can help us catch a ball, and judge fairly well where to throw a ball for interception. There seems then to be an informal or naïve  mathematics, at work unconsciously. Does the same apply to Hodges' model? If so, how can I isolate, and identify it?

  • Is it represented somewhere, implicit in Hodges' model itself?
  • Is it (once again) to be found in the user of the model?
  • Is it (more likely, and obviously) a combination of these two?
  • Or, is it a product of the system, or a series of systems? 

I was reminded of what is a Sober toy, several years ago:

Is Hodges' model a selection machine?

All four original purposes of Hodges' model:

  1. Person-centred, integrated and holistic care;
  2. To bridge the theory - practice gap;
  3. To facilitate reflection and reflective practice;
  4. To support curriculum development;

- are concerned with conjunction and choice, selection. So is life itself through distinction, difference, and differentiation.

Hodges' model is a selection machine, that is both fhuman and machine driven.

A clinician may obtain the referral information through an email, a history of previous contacts can be retrieved from a clinical information system; the context and purpose supporting access to the information.   

A whole series of blog posts describe the role of Hodges' model to help assure parity of esteem across mental and physical health. What does this mean in practice?

For the practitioner, they take selected data from the referral, a history - if available, an initial telephone contact, a conversation with a colleague who remembers the person re-referred and starts to populate Hodges' model. What are the psychological concepts that arise? What are the physical?

If a referral in whatever form, or a database record can be viewed as a bag-of-words, then Hodges' model is a collection of care concepts. Four bags then. Sets or classes. An experienced user of Hodges' model may position care concepts that throws attention on the INDIVIDUAL↔GROUP axis. Lying between the INTRA- INTERPERSONAL and SCIENCES domains, this axis (like all the others) earns its keep. There is work to be done that is also of interest in machine learning:

'A support vector machine (SVM) is a supervised machine learning algorithm that classifies data by finding an optimal line or hyperplane that maximizes the distance between each class in an N-dimensional space.

SVMs were developed in the 1990s by Vladimir N. Vapnik and his colleagues, and they published this work in a paper titled "Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing"1 in 1995.' 

https://www.ibm.com/think/topics/support-vector-machine

Strange to think that perhaps the VERTICAL axis and others in Hodges' model are not precisely S-N-E-W in their bearing? There may also be several vectors at work in fact?

Image: c/o https://www.ibm.com/think/topics/support-vector-machine

The word 'naïve' has been bubbling away for a good-many years. A close colleague Silvana Bettiol, Univ. of Tasmania kindly read my draft on Hodges' model as a mathematical object, and mentioned the introduction points to Bayes theorem even if informally. Even in those initial 'clinical' encounters (and social meetings, that attend to empathy, rapport and engagement...) complex judgements are being made, beliefs tested, from what is often partial and disparate sources of information.

Checking other leads led to Frequentist and Bayesian Approaches

'Statistical inference is a series of methods used to make decisions and draw conclusions based on available data. There are two primary approaches for inference: Frequentist and Bayesian. Each framework relies on a different philosophical perspective on probability and modeling, leading to different techniques and interpretations. Each has its own strengths and drawbacks, so understanding the distinctions between them is vital for researchers, data scientists, and statisticians who aim to choose the most suitable approach for their specific analysis.'
https://www.statology.org/comparing-frequentist-and-bayesian-approaches/

More reading required and threads to run.

Earlier this week I posted re. Cromer's book -

Cromer, A. (1997) Connected Knowledge: Science, Philosophy, and Education, Oxford: Oxford University Press

Before passing the book on, p.198, Chapter 8 notes, #4:

'"Understanding" is a commonly used English word which has no precise meaning. It's sometimes taken to mean the ability to apply knowledge to new situations. In this sense, it is a very high-level skill. Benchmarks for Science Literacy says, "Learning to solve problems in a variety of subject-matter contexts, if supplemented on occasion by explicit reflection on that experience, may result in the development of a generalized problem-solving ability that can be applied in new contexts' (American Association for the Advancement of Science, 1993)." The key word here is "may." 'We really don't know how to help students develop a generalized problem-solving ability, or whether there is such an ability apart from mere knowledge of many different problem-solving strategies. Whatever the case, since we do know how to teach students to solve specific, problems. this should be the primary focus of science education' p.198.

Ack. IBM.

Thursday, December 18, 2025

Learn your lines and the hyperplane will follow i

Take an empty [rectangular] space (A4 paper in landscape)

Blank! Isn't it?

Take a line. Yes, call it that.

Divide the space vertically, and equally, in two. 

Do this again but horizontally.

You can call these lines, partitions if you wish?

Or, as per adopted convention here, axes.

Now, there are four empty spaces.

These spaces can be called quadrants, planes, or domains. The latter term usually adopted here.

Labels can be decided, and assigned to the axes and the resulting domains.

Given a purpose, in practice (initially) the 'empty' spaces have the ability to assign significance to what may be placed within them.

Such decisions are non-trivial, in the sense that context and situation determine what follows, influenced by objective and subjective considerations.

The domains can contain concepts, or keywords with decisions driven by categorical reasoning.

The content of the domains can also be viewed as classes and sub-classes.

ii to follow (with revision here?)

Sunday, August 24, 2025

Nothing new under the Sun . . .

"The quadrangle is the token of a new humanity. The square is to us what the cross was to the early Christians". 

Theo van Doesburg

Tate Liverpool visit 13th June 2008.

Monday, February 20, 2023

C/o Medha Cherabuddi & Intima: "Each quadrant houses its own diversity, ..."

... and these seem to converge in the middle beautifully." *

 INDIVIDUAL
|
 INTERPERSONAL    :     SCIENCES               
HUMANISTIC --------------------------------------  MECHANISTIC   
SOCIOLOGY  :   POLITICAL 
|
GROUP
© The Common Thread by Medha Cherabuddi. Acrylic


Poetry
and much more
invited ...




Image: © The Common Thread by Medha Cherabuddi. Acrylic.

"Each quadrant houses its own diversity, and these seem to converge in the middle beautifully. This piece honors women's myriad of roles in medicine and their common thread. The constant throughout my life is art, especially when I find meaning in it.

Medha Cherabuddi was born and brought up in San Jose, California, and moved to Hyderabad, India, with her family at 9. After growing up with the best of both worlds, she completed medical school in India and moved to Detroit, Michigan, during the peak of the pandemic to begin her Internal Medicine residency at Henry Ford Hospital."


*Yes they do! No endorsement implied.

Tuesday, November 10, 2020

Book review: "The Power of the 2 x 2 Matrix" iv

Yes, it is a literal reading but if I didn't 'see' Lowy and Hood's discussion of "The team goes to work" (p.74) with symptoms identification and "Listen, listen, listen" (p.75) I'd miss a trick.

In healthcare the team really matters; in mental health care (especially) it is a professional and therapeutic* ... duty to listen; symptoms are not enough, we must seek signs too; what goes unspoken? A 2x2 matrix once created and agreed can also help identify positive and negative symptoms, in healthcare we differentiate this in several ways. The individual whether psychosis or cancer; and the group (socially and politically) through the impact of constraints and opportunities. There's a 'Health Magazine Marketplace Matrix' (p.76).

Strategy is central with tactical and operational factors in business and commerce and chapter 6 deals with strategic frameworks. The chapter starts: 

"Strategy is the art and science of competing more effectively than one's competitors." (p.91).

Below are two of the matrices described which I've placed within Hodges' model. Nursing is all about seeking, testing, trying, accepting, parking and respecting unexploited opportunities, not only 'in' the intra- interpersonal domain, but the other domains too. I will let you reflect upon the commodification of health and 'end of life'. 

individual
|
INTERPERSONAL : SCIENCES
humanistic ----------------------------------------------- mechanistic
SOCIOLOGY : POLITICAL
|
group - population
Beyond Customer Led Matrix p.96.
Discontinuity and Life Cycle Matrix p.101


The social and political domains are obviously well represented throughout the book: value, customer, prosumer, civics and much more. An example is the Librarian Scenario Matrix which comprises of the dimensions - Locus of Concern  and Social Contract (p.119).

There's mention of architecture in the book which in a business context is understandable. I can not find where I read it but recently the addition of 'architecture' as in 'care architecture' represents a misuse? This is not architecture. This book and Hodges' model makes concepts the bricks, mortar, spans and splines of architecture. 
 
There is much more I could draw out. The Johari Window, individual frameworks - in which the quadrant's significance (size) varies, Myers-Briggs. In addition to a couple of references with the chapters, a notes section provides a full-list. The index is thorough and there are copyright notices for the many tables and figures.

A great book - just lacking one-other model, but I would say that!

Here are the previous posts:

Q. What is Hodges' model? A. It is NOT a 2x2 matrix



'Proof' of the Four Quadrants

Alex Lowy, Phil Hood (2004) The Power of the 2 x 2 Matrix: Using 2 x 2 Thinking to Solve Business Problems and Make Better Decisions, San Francisco, CA: Jossey-Bass. ISBN: 978-1-118-00879-9

With many thanks to the publisher for my review copy.

 *All effective carers (formal and informal) are 'good listeners' and not just 'good listeners' they respect what is said and if presented with it: a silence.


Friday, October 30, 2020

'Proof' of the Four Quadrants

As I have read (and 'reviewed')  Lowy and Hood's (2004) The Power of the 2 x 2 Matrix in applying a matrix, it first has to be created and the process includes identifying and naming the quadrants of concern. The final step is similar to what I see as a key function of Hodges' model: assurance. They refer to proof, being finalising the matrix asking the question are these quadrants real. Are they correct in this (business, industry and commercial) context?

For Hodges' model the quadrants are predetermined. They are 'fixed' but in a way to reassure both those on clinical ethics committees and involved in corporate governance. Although fixed -

individual
|
INTERPERSONAL : SCIENCES
humanistic ----------------------------------------------- mechanistic
SOCIOLOGY : POLITICAL
|
group - population
INTERPERSONAL
SCIENCES
SOCIOLOGY
POLITICAL

 - the terms used can vary as below:

individual
|
INTERPERSONAL : SCIENCES
humanistic ----------------------------------------------- mechanistic
SOCIOLOGY : POLITICAL
|
group - population
MENTAL HEALTH
PHYSICAL HEALTH
CULTURE & SOCIETY
POLITICAL

 

 'Culture and Society' was a suggestion and I've often wondered about the (meaning) scale and semantic synergy across the terms. Sociology is an academic discipline. As students 'produce' the model, I invariably have them wander about the library with Dewey. 'Politics' maybe a subject of study, but not 'Political'. The context for Hodges' model, however, is the situation in which the patient, nurse, carer, doctor, social worker, occupational therapist, physio ... find themselves. What is political about the situation. Even this is not the whole picture quadrant. What politics are evident? What political aspects should (must) be paid attention to? What is missing politically that is (further) injurious to this patient? (This patient (and carer) who is already helpless, hopeless and vulnerable?)

 In terms of proof, this is of course very important within healthcare. In mental health we often adopt a psycho-social approach and in psychological therapies from counselling to cognitive and gestalt forms in Hodges' model we can distinguish between one-to-one and individual psychology and group therapies and the psychology of a group. As soon as 'self' considers 'other' we also conjoin the model's vertical axis.

 

individual
|
INTERPERSONAL : SCIENCES
humanistic ----------------------------------------------- mechanistic
SOCIOLOGY : POLITICAL
|
group - population

individual
PSYCHOLOGY


SCIENCES
group
PSYCHOLOGY


POLITICAL

 

When I write 'sciences' I'm looking at my school time-table (yes - really!). The sciences for me back then were biology, chemistry and physics (which had to include astronomy). Today, we refer to STEM:


individual
|
INTERPERSONAL : SCIENCES
humanistic ----------------------------------------------- mechanistic
SOCIOLOGY : POLITICAL
|
group - population
INTERPERSONAL
Science, Technology, Engineering, Mathematics
SOCIOLOGY
POLITICAL
 
 
In the summer on twitter ComplexWales asked a question and made a suggestion (I must find and copy the tweet). This set me to task to write during lockdown: so I've a good outline of a short manual for Hodges' model.

In the last post, this is why I'm grateful to Lowy and Hood. I can now also factor this into the manual,  future presentations and workshops.
 
Real proof as an evidence-base goes far beyond this. I can see an exercise with the above components, the axes, the domains and the research subjects being invited to construct something. Amid the quest for data and theory there should be a space for pragmatics too.

Finally, I will leave it to you to reflect on -

Personal, social, health and economic (PSHE) education
 
- in relation to Hodges' model ...
 
More to follow ('care architecture' still) ...

Alex Lowy, Phil Hood (2004) The Power of the 2 x 2 Matrix: Using 2 x 2 Thinking to Solve Business Problems and Make Better Decisions, San Francisco, CA: Jossey-Bass ISBN: 978-1-118-00879-9

 

Tuesday, August 05, 2008

Big pictures: Hodges’ model and Future Studies

I came across a 1996 paper by Richard Slaughter - The Knowledge Base Of Futures Studies As An Evolving Process. The paper highlighted a problem faced by future studies which was (and still may be?) grappling with its knowledge base:

Why, then, is it necessary to have a knowledge base of futures studies (KBFS)? There are several reasons. First, as Norwegian futurist Kjell Dahle pointed out at the World Futures Studies Federation conference in Barcelona in September 1991, the lack of a common knowledge base greatly complicated the work of those preparing courses, planning research, teaching and developing FS projects. The field is well known for its breadth, geographical scope and range of disciplinary paradigms. Where, in all this diversity, should newcomers, particularly intending students, begin? …
As also cited on the h2cm website Slaughter notes the significance of Wilber’s quadrants as a key resource and approach -

I have referred to this work at some length because over several years Wilber’s developing account has reframed my own thinking about present and future options, both personal and collective. Such a framework integrates insights from a wide field and provides FS with powerful new understandings and tools which go beyond one-dimensional thinking (e.g. rationality, technique, forecasting) and a single privileged culture (Western culture). Here, then, is an emerging basis for big-picture thinking and action into the new millennium and beyond. Here too is where some of the most substantial developments in the KBFS are likely to occur.
[My emphasis.]
Health and social care is not only focused on the future -

It is concerned about the PAST, NOW and FUTURE

- BUT it is always future oriented.

So future studies community look over here – now (please!)

Source: Slaughter, Richard A. (1996). The Knowledge Base Of Futures Studies As An Evolving Process, Futures, 28, 9, 799-812.

Wednesday, December 06, 2006

What are you - mathematician, book-reader or book-reading clock-watcher?

Sometimes you don't realise you are on a long-term cherry-picking escapade. I say escapade because this captures the rather haphazard, accidental and part-time nature of my fruit gathering.

In 1992 in the Engineering Computing Newsletter [SERC] Science and Engineering Research Council's EASE programme #38 p.4-5 Michael McCabe asked readers How would you label the quadrants of this diagram? - "How would you label the quadrants of this diagram?"



I cannot find the brief article "Human Factors Aspects of User Interfaces Design" on the web, but I kept the original. It obviously meant something to me, McCabe shows why...

As a mathematician you might choose - from top left clockwise 2,1,4,3

A clock-watcher - from top left 4,1,2,3


from top left 1,2,4,3 - for a book-reader.

And a book-reading clockwatcher - from top left 1,2,3,4

So, how would you label Hodges' model and does this say anything about how you would populate and read the model?