Modelling Matter

26-28 March 2008

Sponsored by the British Society for the Philosophy of Science, the British Academy and Durham University's Institute of Advanced Study and Faculty of Arts and Humanities

 This symposium, held in Durham over three days from 26 th to 28 th March 2008, brought together historians and philosophers not just of chemistry, but of a variety of physical and life sciences to explore the strategies and techniques that scientists of past and present have employed to model and representations of matter. A dauntingly wide brief, but as it quickly became clear, with particular historical and philosophical themes that proved to be significant across all the scientific disciplines dealing with matter and its behaviour. One example of such a theme is the relationship between such models with the empirical evidence from which they are drawn and the theories which they purport to represent. Another theme, of particular interest to historians of chemistry, was the role and evolution of tangible representations of models of matter and a third, again of particular interest to chemists and historians of chemistry was the way in which the representatives of different disciplines viewed each other’s models.

The first speaker was Professor Nancy Cartwright of London School of Economics and the University of California, San Diego. Professor Cartwright spoke on “Models: Parables versus Fables”. Her discussion drew on a consideration of the problems arising from unrealistic assumptions in models with a particular focus on Galilean thought experiments. She showed that the abstraction from the particular to the general involved in the construction of a model is crucial to the determination of the interpretative conclusions that can be drawn from it. And finally, she argued for a view of models as parables rather than as fables as G E Lessing claimed, showing that as the moral of a parable needs to be brought in and defended, so too does the theoretical interpretation of a model need to be ‘written in’ by invoking a network of background theory and experience.

The second speaker was Professor Ronald Giere, Emeritus Professor of Philosophy at the University of Minnesota, who offered a new, multi-layered hierarchical account of theories and models and argued that a hierarchies could take different forms depending either from a single theoretical principle, multiple principles or indeed no principles at all. He also introduced his division of models into ‘principled models’ and ‘representational models’, arguing that principled models are drawn from the relevant theoretical principles of the relevant science, while representational models require a certain amount of interpretation of terms and identification of elements of the model with elements of the actual system under consideration. He gave brief examples of all three hierarchies, showing that in the case of the no principle account, as there are no theoretical principles, there are correspondingly no principled models and accordingly all that such accounts contain are representational models. Perhaps of most interest to historians and philosophers of chemistry is his multiple-principle hierarchy, in which many principled models that do not need to be compatible can be drawn on to create a single representational model.

The last speaker on the first day was Professor Seymour Mauskopf of Duke University on “Modelling Chirality”. Professor Mauskopf focused on the early developments of structural chemical models that preceded Louis Pasteur’s 1848 discovery that crystals of sodium ammonium racemate exhibited small hemihedral facets, sometimes on the right and sometimes on the left. Professor Mauksopf emphasised the influence of the 18 th century models of of René-Just Haüy which represented crystal structure as carefully built of integrant molecules added to a primitive nuclear form, and linked physical form to chemical composition. Touching on the models of Dalton, Ampére, Mitscherlich and Laurent, Professor Mauskopf traced the links between Gabriel Delafosse who was taught by Haüy and who passed on modifications of Haüy’s models to his student, Pasteur (Pasteur’s lecture notes survive). He also pointed to the influence of August Laurent’s extension of Haüy’s crystal model to chemical taxonomy, arguing that Pasteur’s work might be seen as a Laurentian research programme.

Dr Matthew Eddy, of Durham University and (currently) Caltech began the second day with his talk “Spatial Models, Print and Linnaeus’ Philosophia Botanica” which gave a close reading of Linnaeus’ 1751 work. This included a taxonomical system that ordered and classified the canon of natural historical works, including Linnaeus’ own which might be read as a model of natural history as a discipline. The Philosophia itself, Linnaeus classed as a ‘compendium’, a collection of other, already published, texts. Thus one genre in the taxonomy encompassed other genres in the same system. Dr Eddy also explored the spatial arrangement of the main contents of the work, which Linnaeus organised into tables of aphorisms. He showed that the meanings of the words of the text were closely related to their arrangement and textual style within the tables. Linnaeus employed a system of differentiation of particular words in the aphorisms by italicising, capitalising etc., to emphasise those aspects that he considered to be important, and this differentiation allowed the text to be read in a variety of ways. This kind of spatial modelling of the printed page added a number of extra dimensions to Linnaeus’ text, enabling a limited fluidity of interpretation of the text.

The fifth lecture was given by Professor Michel Morange of l’Université Paris 6 and the Cavailles Centre for the History and Philosophy of Science on Models in Molecular Biology and their Present Evolution. Professor Morange used an example of a particular molecular biological model, of the VEGF receptor, to point to some notable characteristics of the models used in molecular biology. These kinds of models combine structural and dynamic components, according to their significance in the context under consideration. In particular he emphasised and the ability of these kinds of models to represent generalisations drawn from a variety of different datasets. These kinds of models can operate as boundary objects, crossing disciplines with only slight modification, and they allow a number of different processes to be represented at once which can then be examined separately. He also emphasised the pedagogical and aesthetic strength of these kinds of models. However, the ambiguity of certain components, such as arrows, which might have a number of different meanings in a single model, and their tendency to accumulate more and more information detracted from their usefulness. He concluded his talk with a brief look at the current direction in which these models were evolving, noting the introduction of an ‘engineering spirit’ in biology that was evident in the models that are being used. These are more mathematical, more formal and more abstract – reflecting perhaps a change in what is regarded as ‘understanding’, from explanation to replication, analysis and synthesis.

Dr Michael Weisberg of the University of Pennsylvania spoke on “Models for Modelling Matter”. He focused on a topic dear to the hearts of many chemists, as well as philosophers and historians of chemistry: the nature of the explanations that chemists are looking for from their models in particular contrast to those that physicists consider satisfying. In particular, he sought to explain why chemists continue to rely on highly idealized models to explain properties of matter. In answering this question, Dr Weisberg adduced the fact that the kinds of questions that chemists ask are ‘contrastive why’ questions. Drawing on Roald Hoffman’s division of understanding into horizontal and vertical modes, Dr Weisberg argued that chemistry seeks the former kind of explanation which groups phenomena into chemically important kinds with common properties and trends, and that these are contrastive explanations. In order to compare a chemical phenomenon with a model, he suggested that the phenomena be abstracted and then paramaterized to give a paramaterized target system which could then be compared with the model. Models were subject to intentional notions of assignment, intended scope and fidelity criteria and the choice of an model with appropriate scope allowed the answering of chemical, contrastive why questions.

Dr. Eric Winsberg of the University of South Florida spoke on 'The epistemology of simulation,' arguing against a widely held view of simulation (in, for instance, meteorology), according to which what is epistemologically distinctive about it is mathematical. On this view, there are two mutually independent processes by which numerically intensive models are evaluated. The idea behind the distinction is that in order to deal with a mathematically intractable theory, scientists use a more tractable model that will (perhaps in some restricted domain) mimic the behaviour of the theory. Verification is the process by which scientists justify the assumption that the model does indeed mimic the theory's behaviour, while validation is the process, common to all theory testing, by which the theory is evaluated as a representation of the target phenomena, via predictions and explanations afforded by the model. Relating his argument to recent work on the scope of scientific theories, Dr. Winsberg argued that the two kinds of evaluation are not independent.

 David Knight of Durham talked about models made of wood and iron, and their slow deployment by chemists. W.H. Wollaston piled up wooden spheres and spheroids to explain how atoms might compose crystals of different forms; but when constructing formulae he favoured ‘equivalent weights’ rather than atoms, recipes rather then structures. Berzelius’ symbols represented volumes rather than atoms, and thus again algebra rather than geometry. Thomson hoped to construct an inductive chemistry based on analyses, but Laurent advocated a hypothetico-deductive approach that favoured models. In illustrating the abstract ‘type’ theory, Hofmann in 1865 moved from tables to little tin boxes (volumes) and on to croquet balls and wires: he realised the illustrative power of what he had done, and the new era opening up in chemistry as structures were revealed; saturation, homologies and substitution could be readily accounted for; and properties predicted. But his vision remained two-dimensional: models that had begun as tables remained flat. Van’t Hoff in 1874 saw that the four wires sticking out of the carbon atom would point to the corners of a tetrahedron instead: and he could thus explain what had puzzled Pasteur, how atomic structures, crystal form and optical activity might be connected: he recommended a supplier of models reflecting his ideas. Chemists, schooled since Lavoisier in scepticism about hypothetical entities, had not taken Daltonian pictures or Wollastonian models seriously enough. Thinking with the fingers, not merely doing experiments but also constructing toys, paid off.

Professor Sir Arnold Wolfendale FRS, Emeritus Professor of Physics at Durham University then gave us a lightning historical tour of “Some of the Models of Physics” from the earliest days of Galileo and Hooke through the wave/corpuscle controversy through the various physical models that had held sway of light, atoms, elementary particles and cosmology. The symposium also featured an exhibition of artwork by Steve Sproates entitled “The Space between Models and Knowledge”, and Sir Arnold’s talk was concluded by Mr Sproates who gave a brief presentation on one of his pieces.

The day ended with a presentation from Keith Moore, Head of the Library and Information Services at the Royal Society on the Royal Society’s scientific archives and their plans for the 350 th anniversary in 2010.

The final day began with a talk by David Kaiser of MIT on “Searching for Stability: Theory, Experiment, and the Hunt for Superheavy Elements”. Dr Kaiser explored the relations between explanatory models and theory in the field of nuclear physics. Arguing that this particular discipline lacks first principles from which to derive models, he talked his audience through a number of the models utilised by nuclear physicists in their endeavours to explain phenomena. He showed that these models are carefully tuned to match empirical data, and so any testing must be based on a predictive extrapolation from the models. Attempts to detect superheavy nuclei on the basis of such predictions were unsuccessful; experimenters struggled to find the predicted nuclei, while theorists’ predictions varied wildly with only tiny shifts in the parameters of their models. An apparently successful experimental detection of superheavy nucleus 118 at Berkeley which agreed strongly with predictions from a cold fusion model prompted other nuclear theorists to alter their own favoured models to agree more closely with the empirical data. However, failure to replicate the experiments led to re-examination of the original data, which was found to have been fabricated. Dr Kaiser concluded that in the field of nuclear physics models were regarded as successful on the grounds of their empirical adequacy, and were neither derived from nor contained within any given theory. As no vertical relations could therefore be distinguished between theory, models and phenomenological laws, such relations would be better characterised as ‘horizontal jostling’.

Dr Robin Hendry concluded the symposium with a paper on “Models, Diagrams and Disciplinary Identity in Quantum Chemistry”. Dr Hendry compared the ‘view from physics’ with the ‘view from chemistry’ of molecular orbital and valence bond theories. He focused in particular on the views of John Clarke Slater, Linus Pauling and Charles Coulson. The first presented both theories as approximation methods and argued that a proper understanding of chemical bonding should be based on fundamental principles rather than on particular methods of calculation or particular models. For Slater, models were merely proxies for intractable exact equations derived from fundamental quantum mechanical principles. In contrast, Pauling’s valence-bond theory was a ‘classical chemical theory’ which tied the quantum-mechanical notion of resonance to G.N. Lewis’s chemical bonds and thus made it intelligible in chemical terms. Charles Coulson, on the other side of the bonding debate promoting molecular orbital theory, argued, like Pauling, that resonance and the bond should stand and fall together – but for Coulson, so much the worse for the bond! Instead Coulson showed chemists how to interpret molecular orbital theory in terms of familiar chemical concepts. Dr Hendry argued that the approaches taken by these three individuals illustrate the different views taken in physics and in chemistry to molecular modelling. Although Coulson and Pauling adopted different models, their attitude towards those models was similar. Where Slater had emphasised the priority of physical theory and a proxy view of models, they promoted a view of quantum chemistry as a synthesis of physical and chemical theory and concepts, and of autonomous models consistent with classical chemical concepts.

Georgette Taylor & David Knight