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

Lavoisier: Math - Chemistry; Quantity, Quality, Principle ...

The philosophy of science, can not avoid being viewed historically, which leads us to learn how mathematics literally took hold, from physics, to chemistry and biology. The application of mathematics to chemistry provides many and ongoing insights:

'Curiously enough, Kant’s own student, Jeremias Benjamin Richter (1762-1807), would only a few years later disprove his professor with his PhD dissertation On the use of the mathematical method in chemistry (Richter 1789). It laid the groundwork for stoichiometry as an algebraic approach to chemistry, including what was later called the ‘law of constant proportion’ that John Dalton used for his atomism on chemical grounds (Richter 1792-3, Dalton 1808). Moreover, at the time of Kant’s writing, experimental philosophy was taking over most of the centers of European research to become the mainstream methodology of modern science, which would later denounce the ideal of a priori knowledge in science as ‘mere’ metaphysics. Although some philosophers of mathematical physics still adhere to that ideal today, Kant was a late partisan in the struggle for the methodological priority of mathematics in the study of nature as it was exemplified by the old field of ‘rational mechanics’. Yet, his view on science became marginalized as much as his verdict on chemistry, that it would be alien to mathematics, was refuted.'

The pitfalls presented and Schummer's 2.4 A methodological suggestion for defining mathematical chemistry are helpful.

Joachim Schummer. Why Mathematical Chemistry Cannot Copy Mathematical Physics and How to Avoid the Imminent Epistemological Pitfalls. HYLE--International Journal for Philosophy of Chemistry, Vol. 18, No.1 (2012). pp. 71-89. https://www.hyle.org/journal/issues/18-1/schummer.htm

Maths is filled with tragedy, but the personal manifestation in my lack of ability, pales to insignificance to the many scientific and human tragedies history reveals. Consider Galois, and Lavoisier:

‘Only a moment to cut off that head and a hundred years may not give us another like it,’ lamented the 18th-century French mathematician Joseph Louis Lagrange. The head in question had belonged to the French aristocrat and chemist Antoine Laurent Lavoisier, who was executed at the hands of French revolutionaries on 8 May 1794. Lavoisier’s ideas changed the face of chemistry. He is best remembered for overthrowing the phlogiston theory, but perhaps his greater and more lasting achievement was to impose order on the language and symbolism that have shaped the thoughts of chemists.'

Paul Board, The Aristocrat who revolutionised chemistry, New Scientist. May 7, 1994 (Volume 142, Issue 1924). https://www.newscientist.com/article/mg14219243-300/

In an essay in the Charles Coulston Gillispie's essay in the history of scientific ideas, Chapter VI. The Rationalization of Matter, describes how Lavoisier sought to develop an algebraic approach:

'But what is most interesting is Lavoisier's mode of representing these results, so correct in quantity, so wrong in principle. In order to sec what he was about, one has to follow him into some detail. It is obvious, he writes, that acidification of a metal involves many variables-heat, concentration, chemical affinities, etc. each of which is a force acting with characteristic energy. Therefrom results a problem complex and difficult of solution: [my emphasis]

"Better to exhibit the state of the question in this respect, and in order to show at a glance the result of what happens in metallic solutions, I have constructed formulas of a sort, which could at first be taken for algebraic formulas, but which have not the same object, and do not derive from the same principles . . ."'

Gillispie, Charles Coulston. The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton, N.J.: Princeton University Press, 1960.

Gillispie quotes at length to demonstrate Lavoisier's approach*. There is a more accessible (for me, here) source in -

Stefano Zambelli (2012). Chemical Kinetics, an Historical Introduction, Chemical Kinetics, Dr Vivek Patel (Ed.), ISBN: 978-953-51-0132-1, InTech, Available from: 
http://www.intechopen.com/books/chemicalkinetics/chemical-kinetics-an-historical-introduction

Please see page 6: 3. Chemical equilibrium conception: The law of mass action.

To close, there is reading and advice to be carried forward in:

Guillermo Restrepo & José L. Villaveces, "Mathematical Thinking in Chemistry". Special Issue: Chemistry and Mathematics, Part 1. HYLE--International Journal for Philosophy of Chemistry, Vol. 18, No.1 (2012). pp. 3-22. https://www.hyle.org/journal/issues/18-1/restrepo-villaveces.htm

Gillispie concludes his illustrated exploration of Lavoisier:

'Is this not the most tantalizing memoir in the history of chemistry, and in Lavoisier's the most appealing? Here alone, one gets a sense of modesty. He never claims for these expressions the dignity of algebra. "We are still very far from being able to introduce mathematical precision into chemistry, and I beg, therefore, that no one consider these formulas . . . as more than simple annotations, of which the object is to ease the labors of the mind." (But compare this disclaimer with what he says of algebra itself in the Method of Chemical Nomenclature: "Algebra is the analytical method par excellence: it was invented to facilitate the labors of the mind, to compress into a few lines what would take pages to discuss, and to lead, finally, in a more convenient prompt and certain manner to the solution of very complicated questions.")' p.245.

*in - Lavoisier, A.L. (1782). Considerations sur la dissolution des metaux dans les acides, Mémoires de l’Académie des sciences 1782, pp. 492-527, Available from http://www.lavoisier.cnrs.fr/ice/ice_book_detail-fr-text-lavosier-Lavoisier-49- 5.htm

Is Hodges' model a Self-Organising Hypothesis Network?

"The proposed approach is based on 3 key steps. First, derive knowledge from different sources of information (experimental data, expert learning, machine learning). Secondly, unify the different knowledge representations. Finally, organise the unified knowledge in a way that captures its generalisation hierarchy and facilitates the design of efficient prediction algorithms (Figure 3)." page 2 of 21.

Figure 3 The SOHN methodology. Different sources of knowledge are unified using a common representation based on the concept of hypothesis. The hypotheses can be organised into a hierarchical network to capture the knowledge in a standardised way (page 3 of 21).

Straight away this figure in Hanser et al. (2014) suggested learning and learners and the four care domains of Hodges' model. There are profound differences of course.

The information at the start takes the form of concepts, data, but 'information' also applies. The context in combining chemistry and informatics is radically different when it comes to who, or what is learning in that first arrow. The paper's keywords are:

Machine learning Knowledge discovery Data mining SAR QSAR SOHN Interpretable model Confidence metric and Hypothesis Network.

To a healthcare or social care student the knowledge encountered may well be raw. The principle of Hodges' model encourages the generation of hypotheses within and then across the model's knowledge domains. The learn-er can then attempt to unify these thoughts and reflections, organising them in a variety of ways. Hodges' model is not itself in self-organising, but there is a pattern-learning process for the learner and a pattern-matching process for the expert or specialist.

Hanser, T., Barber, C., Rosser, E., Vessey, J., Webb, D., & Werner, S. (2014). Self organising hypothesis networks: A new approach for representing and structuring SAR knowledge. Journal of Cheminformatics, 6(1), 1-21.

The Periodic Table

individual

|

INTERPERSONAL : SCIENCES

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

SOCIOLOGY : POLITICAL

|

group

Person-centered | | ? ability, age, class, ethnicity, gender, race, religion, sexual orientation
BBC Radio 4 Dramatisation	"Never again!" UN- Periodic or otherwise .... 1945 ... ...?

Periodic Table image:

https://en.wikipedia.org/wiki/Periodic_table

Book image:

https://uk.pinterest.com/pin/184014334744756712/