The alchemy of terminology, symbols, and signs ...

Or, 'What is a nurse doing … in a chemistry class?' [Ack. See Estrada]

In reading, I was reminded that chemistry adopted mathematical symbols for its own use. Not only that, but as a core science (with physics and biology, emerging from natural philosophy) there is a historical development from the time of alchemy:

Please see (with a graphical abstract):

C.Wentrup, The Transition from Alchemical to Modern Chemical Symbolism: from Bergman and Guiton de Morveau to Hassenfratz and Adet, Higgins, Richter, Dalton, and Berzelius. ChemPlusChem. 2024, 89, e202400033. https://doi.org/10.1002/cplu.202400033

This journey matters today as the use of symbols, in mathematics or other fields can be a barrier to learning and hence personal and disciplinary progress:

Ollie Hunter. Lost in translation: Demystify scientific symbolic language to help your chemistry students overcome any potential learning barriers. Royal Society of Chemistry, 23 May 2022.

As acknowledged many times, it is easy to take a word, or concept from one discipline and 'fit' it to - or in another. Or is it? Estrada concludes:

“The complexities of modern science and modern society have created a need for scientific generalists, for men trained in many fields of science.” This is a paradigm of science in the XXI century, where the advent of such fields like the study of complex systems requires multidisciplinary approaches. But the previous phrase was not written in the XXI century. It is the starting sentence in The education of a scientific generalist” published in Science in 1949 (Bode et al. 1949).' p.161. 

'Mathematics has been defined as the science of patterns. Thus, mathematicians search for “numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on” (Byers 2010). Once a pattern is identified either in chemistry or in mathematics, the researcher can proceed to the clarification of the systematic rule which is behind that pattern. This is evident in the analogy used here between code-breaking and structure elucidation. This attachment to patterns makes both chemists and mathematicians very prone to the use of pictures. An organic chemist hardly can say anything about the chemical reactivity (or any physical or chemical property) of a molecule from its exact quantum-mechanical Hamiltonian. However, she will construct a complete narrative about the physical and chemical properties of a molecular structure drawn in a piece of paper, even if such a molecule is completely imagined. The power of pictures in mathematics is discussed in the book Mathematics and the Unexpected by Ivar Ekeland (1990) where its value is recognized as fundamental in the early stages of the development of mathematical ideas. This also introduces a very important analogy among chemists and mathematicians. Namely, that they use a proper language in their respective fields. While physicists use the mathematical language in their investigations, chemists use the sophisticated language of chemical formulas and specific symbols to represent charges, rearrangements, partial equilibria, etc. These “invented” languages mainly appear only in Chemistry and in Mathematics, making them unique intellectual activities.' p.162.

With thanks to the author, Ernesto Estrada IFISC for additional thoughts and insights:

Estrada, E. What is a mathematician doing…in a chemistry class?. Found Chem 26, 141–166 (2024). https://doi.org/10.1007/s10698-023-09497-4

Wittgenstein's - Tractatus

Apparently, Wittgenstein walked away from philosophy after publication of the Tractatus. He thought he had solved the problems of philosophy, logic and reality.

In trying to ‘see’ Hodges’ model, in mathematical terms, there may be lessons in Wittegenstein’s approach, both in content and style. Of course, as a non-mathematician, I probably should leave well-alone; and stick to nursing. But that is the problem: from 1987-88 there is a need for a different perspective, even if this is a personal challenge. As with many ‘reviews’ here, we can look at Wittengenstein’s work, reflect upon it, and consider how it relates to the purposes, structures and content of Hodges’ model.

The Tractatus’s first line then, offers a warm welcome.

‘The world is everything that is the case.’ [I]

Making the decision to become a nurse and enrolling as a student makes you an educational and workforce demographic case.

Once a student in the university lecture theatre, you hopefully whether consciously, or not are exposed to the theory – practice gap; as you yearn to be on your first placement. Now it you who is seeking ‘cases’. As we live, and statistics roll and tally, the question of caseness (and categories) is key, one that is carried around even if not always active, recognised as such.

As noted in the previous post, we can for Hodges’ model (and other models, frameworks it must be said) think of ‘case’ as a, or the situation. 

A mathematical approach to Hodges’ model involves looking at things, concepts, people as objects. This includes patients and carers. In terms of a project worthy of pursuing in nursing and other disciplines involved in healthcare, this mathematization presents a non-trivial challenge. A fully-deserved response would be: 'What have you done to the aptitude for care and caring attitude? You've cancelled - subtracted it!' Humour aside:

'In order to know an object, I must know not its external but all its internal qualities.' [2.01231] 

Is this equivalent to us getting to know our patient / client and their socio-political context? 

‘The way in which objects hang together in the atomic fact is the structure of the atomic fact.’ [2.032] 

It is a help that Wittgenstein points to structure (crumbs of understanding are welcome here, as incremental steps). In formulating Hodges’ model we first identify the axes. It is the axes that then provide a space, four domains in total, to frame the objects that we decide; or, as the situation dictates, what concepts are placed in the domains of Hodges' model.

There is a successive series that follows, combining place, space and logic: ‘The proposition determines a place in logical space: the existence of this logical place is guaranteed by the existence of the constituent parts alone, by the existence of the significant proposition.’ [3.4]

‘The propositional sign and the logical coordinates : that is the logical place.’ [3.41]

‘The geometrical and the logical place agree in that each is the possibility of an existence.’ [3.411]

‘Although a proposition may only determine one place in logical space, the whole logical space must already be given by it.
(Otherwise denial, the logical sum, the logical product. etc., would always introduce new elements -in co-ordination.) 
(The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)' [3.42]

While Wittgenstein came to view ‘the picture theory of meaning’ as incorrect, as a conceptual framework and diagrammatic resource Hodges’ model is closely tied to this form of representation.

Of course, the logic at work here, is far from mathematical, but there is surely a logic.

'Formal concepts cannot, like proper concepts, be presented by a function.' [4.126]

'There is therefore really a sense in which in philosophy we can talk of a non-psychological I.
The I occurs in philosophy through the fact that the "world is my world'".
The philosophical I is not the man, not the human body or the human soul of which psychology treats, but the metaphysical subject, the limit - not a part of the world.' [5.641] 

'Although the spots in our picture are geometrical figures, geometry can obviously say nothing about their actual form and position. But the network is purely geometrical, and all its properties can be given a priori.

Laws, like the law of causation, etc., treat of the network and not of what the network describes.' [6.35]

There is much more in this work, and much that remains a challenge. Many commentators have written and said in interviews that the Tractatus rewards re-reading and some sentences stay with you for life (The Great Philosophers BBC TV). 

I'm still seeking mine.

https://www.gutenberg.org/files/5740/5740-pdf.pdf

c/o Joan Didion 1934-2021: "Let Me Tell You What I Mean"

"All I know about grammar is its infinite power. To shift the structure of a sentence alters the meaning of that sentence, as definitely and inflexibly as the position of a camera alters the meaning of the object photographed. Many people know about camera angles now, but not so many know about sentences. The arrangement of the words matters, and the arrangement you want can be found in the picture in your mind. The picture dictates the arrangement. The picture dictates whether this will be a sentence with or without clauses, a sentence that ends hard or a dyingfall sentence, long or short, active or passive. The picture tells you how to arrange the words and the arrangement of the words tells you, or tells me, what's going on in the picture. Nota bone:

It tells you.

You don't tell it."

 INDIVIDUAL

|

 INTERPERSONAL    :     SCIENCES               

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

SOCIOLOGY  :   POLITICAL 

|

GROUP

"Let me show you what I mean by pictures in the mind. I began “Play It as It Lays” just as I have begun each of my novels, with no notion of “character” or “plot” or even “incident.” I had only two pictures in my mind, more about which later, and a technical intention, which was to write a novel so elliptical and fast that it would be over before you noticed it, a novel so fast that it would scarcely exist on the page at all. About the pictures: the first was of white space. Empty space."...

My source: BBC Radio 4

Let Me Tell You What I Mean: A New Collection of Essays by Joan Didion

---

Episode 4

Book cover: goodreads.com

Text source:
New York Times archive - Why I Write, By Joan Didion, Dec. 5, 1976.
https://www.nytimes.com/1976/12/05/archives/why-i-write-why-i-write.html

Previously on W2tQ: Book: "The Empty Space"

Alzheimer’s spotted early using AI cookie theft test

self - individual - person

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INTERPERSONAL : SCIENCES

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

SOCIOLOGY : POLITICAL

|

dyad ... family - group 

 

Changes in how people describe this simple drawing can be analysed using AI

Cummings, Louise. (2019). Describing the Cookie Theft picture: Sources of breakdown in Alzheimer's dementia. Pragmatics and Society. 10. 151-174. DOI: 10.1075/ps.17011.cum  https://www.researchgate.net/publication/332061806_Describing_the_Cookie_Theft_picture_Sources_of_breakdown_in_Alzheimer%27s_dementia

 

My source (and image):

Knowles, T. (2020) Alzheimer’s spotted early using AI cookie theft test, The Times, 24 October, p.47.

ii) A map as well as an app...? - c/o John Kulvicki

"Maps are picture-language hybrids." p.149.

"The features covering maps are like lexemes of a language that play a predicative role." p.149.

"Maps are pictorial in their use of space." p.149.

"Maps, pictures, and diagrams differ from language not in whether
they make use of predication, but in the way they organize predicates.
In maps, predicates are introduced holistically, in groups, as degrees of
freedom to which any location on a map must commit.
This proposal constitutes a different way of understanding the
coarse-grained distinction between maps, pictures, and diagrams
on the one hand, and linguistic representations on the other." p.150.

"In maps, failing to indicate the presence of something—a town, a river, a road, or an island—is tantamount to indicating its absence." p.150.

Kulvicki, John, Maps, Pictures, and Predication, Ergo, Volume 2, No. 07, 2015

DOI: http://dx.doi.org/10.3998/ergo.12405314.0002.007

https://kulvicki.org/

See also: i) A map as well as an app ...

Njideka Akunyili Crosby - “À la Warhol"

NJIDEKA AKUNYILI CROSBY (Nigerian, b. 1983), “À la Warhol,” circa 2005-06

My source: Gerlis, M. FTWeekend, Merry-go-round of the fairs, Collecting|Arts, 7-8 April 2018. p.15.

Image source: Title link.

Bliss + Symbols = Language for Care?

As I have written before on W2tQ the initial attraction of Hodges' model was its relation to brainstorming, mind-mapping, diagrams and the possibility of iconic languages. In addition, in the 1980s graphical user interfaces GUIs were introduced on microcomputers and PCs. There followed a rapidly expanding literature on icons, visual languages and interfaces. I had also heard of a Charles Bliss [ Charles K. Bliss (1897-1985) ] and Bliss Symbolics. So, to brainstorming ... we can add ideographs and pictographs.

This past week BBC Radio 4 explored the life and work of Charles Bliss and the application of Bliss in literacy, care and special needs education. The programme presented by Michael Symmons Roberts is available for 4 weeks. For its 30 minutes length the programme introduces Bliss himself, his life, aims, the challenges he and his wife faced and the ongoing legacy of his work. It could be argued - and has been - that this is a step backwards to hieroglyphs; but the programme is broader in its reference to 'care'...

individual

|

INTERPERSONAL : SCIENCES

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

SOCIOLOGY : POLITICAL

|

group

'bliss'	Wikipedia - Portal:Constructed languages
BBC Radio 4 The Symbols of Bliss	Ideal of Universal - International Languages

In the 1990s I received some copies of a journal devoted to 'Unish' a constructed language. The link to unish.net does not seem to work, but the Wikipedia site below includes some details.