Medicine - Mathematics & History

'We now come to the input of mathematics into medical history, and to the related questions of arithmetic and quantification, ratio and proportion, geometrical argument and diagrams, and probability. Mathematics (consisting in arithmetic, geometry, astrology and music) had an established place in the quadrivium of the medieval arts course; its application to medicine is demonstrated in such textbooks as the Articella, which include treatises on weights and measures, and in studies of proportion and ratio such as those of the medieval Oxford calculators which Italian doctors among others caused to be revived at the beginning of our period. In the sixteenth century, it was a vigorously debated subject; there is a well-documented discussion of the certainty of mathematics, concerning its status in respect to the logical adequacy of its proofs, in which some natural philosophers and doctors (notably Cardano) take part. It will come therefore as no surprise that it was prescribed for doctors by most Renaissance pedagogical writers;  this prescription is often specifically linked to Galen's geometrical (axiomatic) method whose operations are the constitution of objects from elements, the comparison of existing objects and their reduction into their constitutive elements.

Associated with mathematics are diagrams, that is, abstract quantified spatial representations. There is a modern debate about the contribution of technical innovations in illustration in the Renaissance (most notably perspective) to the scientific revolution: this is only relevant here insofar as some participants in this debate argue for the importance of diagrammatic symbolisation of mental abstractions above those, like perspective, which are still representations of the real world, and see the former as a step on the path to full algebraic notation of geometry. Not all Renaissance thinkers were persuaded of their usefulness: Argenterio describes the diagrams of Manardo and Akakia reproduced below as 'vain and false tables and figures'; but I shall argue here that they were related to the uptake of doctors from the arts course insofar as well-known logical diagrams reproduced above (4.3:3) were adapted by them for their own purposes.' pp.171-172.

Maclean, Ian. 2002. Chapter 5, Beyond logic: geometry, proportion, quantity. In Logic, Signs, and Nature in the Renaissance: The Case of Learned Medicine. Cambridge/New York: Cambridge University Press.

Related to ongoing reading, Maclean provides two (among several) historical illustrations (with apologies for the quality) on pp.174-175, the first is from the Wellcome Collection:

Dubois, Jacques, 1478-1555 (Boe͏̈, Jacques, Bois, J. d., Boë, J., del, Boë, J., Del Boë, J., DelBoe͏̈, J., . . . Sylvius/de Bois). (1548). Methodus sex librorum galeni in differentiis et causis morborum et symptomatum in tabellas sex ordine suo conjecta paulo fusius ne brevitas obscura lectorem remoretur & fallat. de signis omnibus medicis, hoc est salubribus, insalubribus, & neutris, commentarius / ... per jacobum sylvium ..Paris: Retrieved from https://www.proquest.com/books/methodus-sex-librorum-galeni-differentiis-et/docview/2090356749/se-2

Jacobus Sylvius, 1539

Which Maclean then translates / interprets (p.174):

Maclean. Figure 5.1, p.174.

'Manardo goes further, and causes and symptoms adapts the square of contraries to represent not only all the possible combinations of temperaments (combinations of cold and hot and wet and dry are cleverly excluded) but also inserts a mediate point to represent the absolutely temperate body: see fig. 5.2.
This adaptation of the square of contraries (which has precedents in the medieval period) shows the appropriation for their own use by doctors of the logical instruments at their disposal.

As we have seen, it is a feature of medical thinking to take into account many circumstantiae or variables, and, over time, the numbers of variables taken into consideration increases.' p.174-175.

Figure 5.2 Giovanni Manardo, p.175.

individual

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INTERPERSONAL : SCIENCES             

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

SOCIOLOGY : POLITICAL   

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group

quality logic	quantity past - present - future diagrams symptoms - signs
subjective	objective

Previously: 'medicine' : 'history' : 'diagram'

Mary Kelly - Post-Partum Document

From a visit to Liverpool Tate 13.6.2008:

 (Experimentum Mentis III: Weaning from the Dyad)

Individual

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      INTERPERSONAL    :     SCIENCES               

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

 SOCIOLOGY  :    POLITICAL 

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Group

Post-Partum Document. Documentation III: Analysed Markings And Diary Perspective Schema (Experimentum Mentis III: Weaning from the Dyad)

1975, Mary Kelly  © Tate 

'Chalk and crayon drawings by Mary Kelly’s son are overlayed with transcriptions, annotations and reflections based on their interactions as he began nursery. These panels are the third group of a six-part series, each documenting a formative moment in Kelly’s son's early life. Kelly has stated that Post-Partum Document is not ‘autobiographical’. She instead uses her story to suggest ‘an interplay of voices – the mother’s experience, feminist analysis, academic discussion, political debate’. The work subverts romanticised depictions of the mother-child relationship, presenting the experience as inevitably bound up with societal norms and gendered expectations.'

See also: Mary Kelly

  dyad : perspective : art

'Domain-specific is wider than specific domain knowledge' Kalyuga (2013)

 'Developing learner ability to apply knowledge in relatively new situations is an important aim of learning and instruction, and many instructional programs and materials explicitly state this goal. However, not many of them demonstrate a consistency in achieving this goal using sufficiently well-specified instructional procedures and techniques. According to a popular view, transferable knowledge and skills in complex domains result from problem solving experiences (e.g. Inagaki and Miyake 2007). At the same time, there is evidence indicating the importance and effectiveness of explicit learning generalized theoretical frameworks and abstract conceptual knowledge for deep understanding of tasks and en hancing transfer capabilities (Karpov and Bransford 1995; Hinds et al. 2001). Gick and Holyoak (1983) convincingly demonstrated the value of the acquisition of abstract schémas as mediators of analogical transfer between very different task areas.'

'Many studies in expert problem solving have demonstrated that relying on highly contextualized domain-specific knowledge associated with concrete situations is the most effective way to solve problems in familiar task areas and that expert performance is largely based on the acquisition of organized domain-specific knowledge structures (schémas; Chi et al. 1982). ... For example, the game of chess has traditionally represented a classical example of expertise based on the acquisition of a huge amount of highly specific knowledge structures (chunks) corresponding to various concrete game situations (De Groot 1965; Chase and Simon 1973). However, more recent studies have indicated that experts use not only concrete chunks but also more general patterns, such as "templates" (Gobet and Simon 1998) or generalized chunks (Walczak and Fishwick 1997) representing typical classes of chess positions with substantial variations in concrete board locations. Based on his observations of the behaviour of rats in maze situations, Tolman (1948) was one of the first to discuss the role of broad vs. narrow cognitive constructs (cognitive maps) in both animal and human learning. 

Domain-specific knowledge that is applicable only to a limited range of tasks represents the most powerful tool for dealing with these tasks in terms of efficiency of achieving immediate results. On the other hand, knowledge that can be applied more broadly is likely to be less efficient for solving specific problems since it would require additional searching, reasoning, and elaborating activities, whilst specific knowledge directly leads to a definite solutions.' pp.1478-1479.

Kalyuga, S. (2013). Enhancing transfer by learning generalized domain knowledge structures. European Journal of Psychology of Education, 28(4), 1477–1493. http://www.jstor.org/stable/23580919

Laws of Form - Society, Conference, and Journal (to follow)

Finding out last minute at the end of last week, I attended the Laws of Form Conference at the Old Library, Liverpool University, 19 Abercromby Square L69 7ZN, UK. It was 17 minutes away by rail, so I made the short walk from Lime Street Station, as pre-existing commitments allowed.

The Society, devoted to the ideas and work of George Spencer-Brown is quite new 2023. I was greeted with a welcome that actively encourages the widest range of ideas as relates to LoF, the AGM also revealed future plans.

Laws of Form Books: Source lof50.com 

I've been on the LoF mail list for many years and every so often I've replied to themes that also touch thinking on Hodges' model. Now trying to look at Hodges' model more formally, learning of the conference I had to attend.

At the close today the vote of thanks expressed for the support of University of Liverpool and West DenHaag was shared here.

After the introduction, the first session by Andrew Crompton, of The Alternative Natural Philosophy Association, How to Make a Horse Vanish included insights into the scope of George Spencer-Brown's thought, combining philosophy, design, and architecture with great visuals. All the sessions were interesting, helpful and stimulating, including several that were technical detailing applications of Laws of Form:

".. Spencer-Brown has pointed out that he discovered an arithmetic that underlies Boolean algebra. This arithmetic is the Spencer-Brown Calculus of Indications generated by the mark <> (here written in typographical form) subject to the relations of calling, <><>=<>, and crossing, <<>> = , where, in crossing, the two marks are erased in the plane of writing. .." 
KEYNOTE Louis H Kauffman, Arithmetic in 'Laws of Form' - also Weds 7th Aug. 

Even though I could not understand the approach, listening to purposes, application and and the terminology is useful. 

I was online Thursday, and only followed the first two sessions. I have been exasperated with the various -isms, a response possibly shared with Jonathan Mize, Mind, Your Business: Reimagining business, art and science:

"The world is aching for a fresh approach to how we interact with one another. A popular prescription for our ailment is some type of new “ism,” some meticulously engineered set of dictums that propose to “fix society” once and for all. In this paper, I offer no “isms,” no grand new paradigms and no set of rules that humanity “must follow,” lest they slip into oblivion. What I offer is something very simple—a re-seeing of our approach to our everyday lives, a lifting of the vision from the “ills” and the “evils” of the world to the potential for our collective creation and experience. ..." Thurs 8th Aug.

Secondly, Diego Lucio Rapoport Campodonico, presented The Geometry and Topology of the Primal Distinction: Phenomenology and cosmo-sociomorphisms. If the public's understanding of science can be represented as a morphism, then it was extended here so I will explore.

There was a slide in the session of Florian Grote, Playing the Game of Counting to Two: On the question of requisite re-entries in communication including artificial intelligence (Friday 9th August), that I could immediately relate to Hodges' model:

"In the poem which provided the title for the book Only Two Can Play This Game, James Keys (1971) aka George Spencer-Brown provides the reader with a thorough reflection on the unlikely inevitability of a communicative – a social – world."

I can't cover all the examples of interest, but over the years systems, systems theory invariably crop up. Through the UKSS and Open University I have come across people with ties to the Schumacher Inst.. This thread continued 10th Aug, with Laws of Context with Philip Franses.

Hans Rudolf Straub's The Form and the Bit as Basic Building Blocks of Information: A comparison stood out as a source of reading conjoining LoF and informatics.

Marcus J. Carney's talk (also Sat 10th) Letting Go. The Form of Mourning reminded me of what does a single discipline mean when it uses the term 'applied'? Nursing a cold I didn't want to use the mic, but I think Marcus's work could support theory given the attention on trauma-informed care and therapy at present. There were obvious immediate connections in the abstract, borne out (well delivered!) in his presentation.

"Threnos in antiquity was understood as the activity of mourning. S. Freud dichotomised mourning with melancholia, entangling both in libido. A. and M. Mitscherlich took this up in the 1960s for the German people post Holocaust as their “inability to mourn”. J. Ruesen tried “Trauer” in this context again in the 1990s as “mourning humaneness”, bloating its abstraction. While M. Rothberg introduced the notion of “implicated subject” to the field/s of historical violence and injustices to modify R. Hilberg’s perpetrator-victim-bystander triad in 2019, the German “Historikerstreit 2.0” was raging, but not about Rothberg’s “implication”, yet about his 2009 concept of “multidirectional memory”, wherewith he demonstrated how the Holocaust had enabled the articulation of other histories of victimisation at the same time that it had been declared "unique" among human-perpetrated horrors, while uncovering the more surprising fact that public memory of the Holocaust emerged in part thanks to postwar events that seemingly had little to do with it."

As noted in a previous post, there's also the approach of Parallel Histories. You wonder from where dialogue can follow: Israel and Palestine ... but it must. On Wednesday the recent rioting impinged on proceedings with directions to close earlier and dining plans impacted. 

After too many years I must explore George Spencer-Brown's Laws of Form and try to apply it to Hodges' model as an additional and alternative theoretical resource.

The GSB Society have a forthcoming journal which I will post about here as details follow.

The next conference is in 2026 and will be based in Cambridge - a great prospective source of ideas.

Security of Tools for Community Care and Elsewhere: Take this 'one' with you...?

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

Image sources:

http://picphotos.net
http://www.ebay.co.uk
https://www.signkits.co.uk
https://i.pinimg.com

My source: Following some van, some where...