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

In Browder, 'care' is mentioned over 150 times!

OK - so now you're teasing ...

'Surgery theory investigates the homotopy types of manifolds, using a combination of algebra and topology. It is the aim of these notes to provide an introduction to the more algebraic aspects of the theory, without losing sight of the geometric motivation.' Ranicki, 2001. 

'IV. Surgery and the Fundamental Theorem

In this chapter we develop the techniques of surgery for constructing normal cobordisms and use them to prove the Fundamental Theorem. The ideas of surgery have their origins in the theory of 2-manifolds, in the process of "cutting off handles", and in general, in the theory of Marston Morse of non-degenerate critical points of differentiable functions.' Browder, 1972.

In Browder, care is mentioned over 150 times!

'Poincaré' that is.

individual

|

INTERPERSONAL : SCIENCES

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

SOCIOLOGY : POLITICAL

|

group-population

	'The Classifying Spaces for Surgery and Cobordism of Manifolds'
Try to - follow the language* ...	"Follow the money!"

Ranicki, A. (2001) An introduction to algebraic surgery. Surveys on Surgery Theory, Volume 2, edited by Sylvain Cappell, Andrew Ranicki and Jonathan Rosenberg, Princeton: Princeton University Press, 2001, pp. 81-164. https://doi.org/10.1515/9781400865215-005

Browder, W. (1972) Surgery and the Fundamental Theorem. In: Surgery on Simply-Connected Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 65. Springer, Berlin, Heidelberg.

https://doi.org/10.1007/978-3-642-50020-6_4

Madsen, I. H., and Milgram, R.J., (1979) The Classifying Spaces for Surgery and Cobordism of Manifolds. Princeton University Press.

Image: https://m.media-amazon.com/images/I/41THEeVvpdL.jpg

*concepts!

Rain, Library, and a Poem on a Neon Line

'It is raining in the library,

and leaking between theory and practice.'

Rain by Faroese poet and novelist Carl Jóhan Jensen

My source: BBC Radio 4 The Verb. Poetry and performance with Ian McMillan.

8th June 2025. 1710-1750. https://www.bbc.co.uk/sounds/play/m002d88g

Previously: 'theory' : 'practice' : 'library' : 'poetry'

THE GRID by Eli Payne Mandel

individual

|

INTERPERSONAL : SCIENCES

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

SOCIOLOGY : POLITICAL

|

group

[125] 'Therefore, a mathematician babbles when he refers to cutting a given line in two. The actual line that he shows to us on the abacus has length and width. But the line he has in mind is a stroke with length and no width. What is drawn on the abacus cannot be such a stroke, and he who goes about cutting it cuts not the line that is but the line that is not.' (Sextus Empiricus, Against the Mathematicians 9.282) (n.b. The above is printed upside-down on the page.) Scatter the trace of the vessel from the ash. Pythagoras here is riddling about confusion and mental cloudiness, for if one wants to do philosophy one must pass over physical and sensible demonstration in favor of abstract argumentation. The ash is analogous to the dust on the abacus in which diagrams are delimited and proofs brought to an end.  (Iamblichus, Exhortation to Philosophy 34)' p.55

'[1] In ancient Greek, an abacus is a sand table. 'The abacist draws lines and maybe moves pebbles around the lines. When done, she wipes the sand blank.  [2] A board or slab for drawing, computation, games; a cutting board. Technical term, likely to be a loanword, but conjectured origin in Hebrew abãq "dust" remains unproven. --  Pierre Chantraine, Dictionnaire etymologique de la langue greque.' p.10.

'[122] The abacus computes and it erases. It tells a life. Then gambles it away. Achilles and Ajax sit down to play a game of dice. They have hung up their shields. They lean on their spears. They are tired. The Anatolian air is cold off the water. Attendants wrap them each in wool cloaks thick with eight-pointed stars. The stars wander along eddies and meanders. The only straight lines are servants of error. Their fingers are on the abacus, but Achilles and Ajax do not play, do not speak, lost in the maze of their cloaks. [124] The first reference in Western literature to written language is in the Iliad. An unsuspecting  man in a story is carrying semata lygra / grapsas en pinaki ptukto thymophthora polla: baleful signs written on a folded tablet, utterly soul-  destroying. The words, which some scholars conjecture to be Linear B, spell out the man's death, and the reader murders  the unreading man. After the murder, Death Wipes the tablet  blank and folds it back again.' p.54.

'[3] Because dust blows away and only the slab remains, an abacus is also the part of a column in immediate contact with what it supports. If that structure no longer survives, the abacus upholds the edifice of the sky.' p.10.

THE GRID by Eli Payne Mandel, Carcanet Press. 2023.

https://www.elipmandel.com/

Previously on W2tQ (with overlap):

arts :: drama :: poetry :: literature :: narrative

There is this thing - 'universal construction'

The problem of bugs in software is an ongoing problem across all IT industries. For application that are safety critical we are still reminded of the risk implications and consequences if bugs are software is not tested and bugs - errors identified and corrected.

Back in the 90s during BA(Joint Hons. Philosophy & Computing) studies, I was introduced to the formal specification language 'Z'. It was designed for definition, and modelling of computer software, working from specification to implementation, as per these images:

https://personalpages.bradley.edu/~young/CS592M120_OLD/handoutZed.pdf

https://personalpages.bradley.edu/~young/CS592M120_OLD/handoutZed.pdf

To be clear I've never worked as part of a software project and my 'tinkering' - Drupal, Pharo, online groups, hosting platform - reveals how the development stack and work processes have developed apace. The challenge is keeping up. Simultaneously, there is the sense of being on the bank of deep water; or, a vertiginous cliff:

A little learning is a dang’rous thing;
Drink deep, or taste not the Pierian spring:
There shallow draughts intoxicate the brain,
And drinking largely sobers us again.
Fir’d at first sight with what the Muse imparts,
In fearless youth we tempt the heights of arts,
While from the bounded level of our mind,
Short views we take, nor see the lengths behind,
But more advanc’d, behold with strange surprise
New, distant scenes of endless science rise! 

Pope. https://interestingliterature.com/2021/09/a-little-learning-is-a-dangerous-thing-meaning-analysis-origin/

 Acknowledging the need for an 'evidence-base' and theoretical underpinning the effort to 'push' Hodges' model forward is ongoing. Maths remains an alien territory to me, but the 'secret garden' is as tantalizing as ever. Over the years I have posted - with much overlap about:

• maths
• relation
• logic

- and more recently:

• isomorphism
• category theory
• and as previously posted - laws of form.

In an effort to get to grips with the above, I'm following various online videos, books and papers. Bartosz Milewski's videos, blog and publications are aimed at programmers, but are very interesting nonetheless. The first video provides an introduction to the motivation and philosophy of category theory. In another, Milewski refers to 'universal construction' on YouTube and in a blog post about 'Function Types'.

The 'universal' figures in healthcare too: universal health access, and universal health coverage appear to over-shadow 'universal health care'. The quality of 'universal' also creeps into assessment. Data gathering is not merely complete, it is comprehensive. It has to be, to contribute not just to a care plan, for one that is (supposedly) person-centred, with risks identified, strengths, weaknesses - needs, history, social network, and much more. The care plan informs and orchestrates the interventions; then evaluation follows. Are we delivering? What is the patient's (client's, carer's) level of satisfaction. Have care stages and actions been completed as per policy (in time!)? (More on this to follow later this year in light of UK mental health/illness news.)

So as I consider (wrestle with...) initial, and terminal objects, sets and categories … I can hopefully, especially with help, extend the number of posts tagged 'universal' here on W2tQ. In this vein, is Hodges' model a universal construction? There may not be a universal truth to reveal, but it will prove a marvellous learning journey.