Transferring Modelling Frameworks Through Analogies

In order to account for how analogies justify pursuit in cases like the liquid drop model, I propose to look more carefully at the relationship between analogies and scientific models. So far, I have been talking as if a model of the kind Gamow developed is more or less equivalent to a hypothesis, as if the pertinent question is whether the analogy shows the model plausible or whether it would be valuable to learn that the model is true. However, in cases like the development of the liquid drop model, this way of thinking is somewhat misleading. For one thing, Gamow knew, or at least had good reasons to suspect, that his original model was incorrect: as mentioned, he had not included free nuclear electrons in the model even though he clearly suspected these would make a difference to the result. His strategy was of course to see if he could obtain some kind of promising results from the simpler model before attempting to develop the more complicated one. As Parker points out (2009), the fact that scientific models are often constructed using deliberate idealisations and simplifying assumptions makes it problematic to write as if it is the model which is tested. Rather, what scientists are interested in is typically some hypothesis about the fit between the model and the world (cf. Giere 2004). Similarly, when applying the decision-theoretic models of pursuit developed in Chapter 2, we need to be careful in specifying which hypothesis is pursued. In the case of to the liquid drop model, we cannot say that Gamow and those who subsequently worked on the model pursued any specific hypothesis about the structure of the atomic nucleus. Rather, they tried to model the atomic nucleus as if it were a water drop in order to construct a potential explanation of some otherwise puzzling phenomenon—i.e. the mass defect curve for Gamow, Heisenberg and von Weizsäcker, artificial radioactivity for Bohr and his colleagues, and nuclear fission for Meitner and Frisch. They were of course still, ultimately, hoping to construct a model which provides

an accurate (or at least empirically accurate) description of the nucleus. But their immediate priority was to formulate a potential explanation of the target phenomenon. Thus, what the physicists pursued in this case was the research project of adapting a

modelling framework to the atomic nucleus for certain explanatory purposes. If we want

to say that they pursued a hypothesis, it was not one of the form “the atomic nucleus has features a, b, c, … analogous to a water drop” but rather something like “modelling the atomic nucleus analogously to a water drop can lead us to formulate a (correct) explanation of phenomena x, y, z, ….”.

This point highlights the overlap between pursuit worthiness accounts and generative accounts, mentioned in Chapter 1. That analogies guide the gradual

development of theories or hypotheses, rather than simply supporting a specific

hypothesis, was also something which Campbell and in particular Hesse (1966: 4-5) highlighted as important to understanding the use of analogies. However, we need to separate two different questions here. On the one hand, many generative accounts focus on spelling out how a given analogy inspired or guided the development of new scientific concepts.97 Here, the focus is on how the analogy helped scientists to formulate genuinely novel concepts which go beyond the conceptual resources of existing theoretical framework. But noticing that an analogy can be helpful for formulating new concepts does not in itself answer the question of why it was reasonable to pursue an analogy-based modelling framework in the first place.

To see how these two can come apart, consider the fact that Campbell explicitly denies that analogies are a help to develop theories:

97 _{Examples include Nersessian (2002) on Maxwell’s development of the concept of the electro-magnetic}

field, and Morgan (1997, 1999) on Irving Fisher’s use a mechanical balance analogy to clarify and reinterpret the quantity theory of money.

Analogy, so far from being a help to the establishment of theories, is the greatest hindrance. It is never difficult to find a theory which will explain the laws logically; what is difficult is to find one which will explain them logically and at the same time display the requisite analogy. … To regard analogy as an aid to the invention of theories is as absurd as to regard melody as an aid to the composition of sonatas (Campbell 1920: 130).

Now, pace Campbell, it might be that imposing constraints actually makes it easier to come up with genuinely novel ideas. However, the core point is that the relevant question is not how to most effectively come up with novel ideas, but rather how to come up with

ideas that are worth pursuing. Sometimes, e.g. if we lack any possible explanations,

coming up with genuinely novel ideas might be intrinsically desirable. But in other cases, e.g. if we are overwhelmed by too many hypotheses, we may instead prefer to restrict ourselves to generating hypotheses of high quality.

So why are modelling frameworks based on analogies more pursuit worthy in cases like the liquid drop model, than trying to develop potential explanations without relying on analogies? I want to propose that these frameworks are more pursuit worthy because they facilitate the transfer of a modelling framework in order to construct explanations in a new domain.98 Now, my point here is not simply that the models constructed through this approach could potentially explain some of the phenomena scientists are interested in. This would not set analogy-based modelling frameworks apart from explanations constructed by other means. Furthermore, I do not here want to argue that explanations based on analogies are somehow more intrinsically interesting, as Campbell suggests,99

98 _{This account is inspired by Hesse’s and Bartha’s idea that analogical inferences “transfer” explanations}

from one domain to another. Morgan (1999: 386-7) has also discussed when it is possible to “transfer” lessons learned within an analogical model to a real-world target system. By contrast, my account here focuses on transferring and adapting modelling frameworks to a new target system. In this respect, it is closer to Hesse’s (1966: 157-177) suggestion that analogies are used in explanation to “metaphorically redescribe” the target domain in terms of the source analogy.

nor do I want to argue that analogy based frameworks are somehow more likely to produce correct explanations, since that would simply take us back to the idea that analogies show the hypothesis more probable.

A better reason is that transferring a modelling framework by analogy can often reduce the costs of pursuit, since trying to adapt an already existing modelling framework to a new domain is typically easier, and less time consuming, than developing a new one from scratch. Thus, in the case-studies analysed in terms of generative accounts, it is not so much the novelty of the explanations generated through analogies which made it reasonable to pursue this particular strategy, but the fact that they provided a cost-effective means of generating new potential explanations.

In my view, this simple cost-effectiveness account does go some way towards explaining why there are often good reasons to pursue analogy-based modelling frameworks. But I think we can say something more directly connected to the epistemic value of analogy-based explanations as well, namely that the benefit of transferring modelling frameworks through analogies can be that such modelling frameworks are themselves already well-understood.

To flesh out this idea, I will employ a distinction between understanding-why and

understanding-with, drawn by Michael Strevens (2013: 513) based on recent discussions

of scientific understanding. Understanding-why is the understanding of phenomenon or state of affairs in the world, e.g., the sense in which we can say whether someone understands combustion, heat conductivity or nuclear fission. It is typically achieved by grasping an explanation using some theory or model which represents the phenomenon of interest with sufficient accuracy. Understanding-with, by contrast, is the kind of understanding one can have of a theory, model or theoretical framework; the sense of ‘understanding’ employed when we say, e.g., that a historian of science understands the

caloric theory of heat. Specifically, one has understanding-with to the extent that one is able to grasp and construct potential explanations based on the theory or model in question. To grasp an explanation here means to understand how the explanation works and why it would explain a given phenomenon if the theory or model accurately represented that phenomenon. As Strevens (ibid.) and others argue, understanding-with is a precondition for understanding-why, at least of the more interesting kind. For a scientist to understand a phenomenon through some explanation, it is not enough that the model or theory used provides an explananation of the phenomenon and that this explanation is factually correct. The scientist must also grasp how the explanation works in order to ‘cash in’ the potential understanding afforded by the model or theory.

This allows us to say more about why transferring a modelling framework to a new domain is a cost-effective way of constructing new explanations. It is not just that it will be quicker or easier to construct these new explanations (though that matters too) but, furthermore, that if this framework can be adapted to the new domain without too much modification, one will already have a large degree of understanding-with of this framework.100 Thus, insofar as the scientists succeed in constructing new potential explanations of the phenomena of interest using this framework, little extra work is required to realise this explanatory potential. One might eventually achieve a similar understanding-with of a new, purpose-built modelling framework, but it would typically require extra effort to achieve the same levels of understanding-with.

Applying this account to the liquid drop model, it can, first, provide a rationale for why Gamow initially chose to pursue a modelling strategy based on the water drop analogy: if this modelling strategy were to succeed, it would provide a readily

100 _{Plausibly, we may also say that to the extent the framework can be transferred without modification, this}

will allow scientists to preserve their understanding-with of the framework. However, this stronger claim is not strictly necessary for my argument here.

understandable model able to support easily graspable explanations of the nuclear phenomena he was interested in, in the first instance the mass defects. Second, when Gamow’s initial work showed that this strategy was indeed feasible, though not initially particularly successful, this confirmed that the strategy was compatible with the theoretical framework of quantum mechanics. Thus, while it did not yet make it especially likely that the model was a correct or accurate representation of the nucleus, Gamow’s model had nevertheless shown that the understanding-with provided by this modelling strategy did not require physicists to sacrifice any of their existing understanding. This further strengthened the pursuit worthiness of the model and provided a rationale for other physicists to pursue the model further during the 1930s.

Finally, this gambit (i.e. to use the liquid drop analogy as a cost-effective means to develop models with a high degree of understanding-with) was spectacularly vindicated in Frisch and Meitner’s explanation of fission. As Stuewer (1994: 112-16) argues, it was because Meitner had worked in the Heisenberg/von Weiszäcker tradition in Berlin, and Frisch with Bohr in Copenhagen, that they were able to combine elements of both traditions to construct their explanation. In my terms, we can say that Frisch and Meitner were able to “pool” the understanding-with, developed separately in Berlin and Copenhagen, in order to develop the model.101 Although Gamow, Heisenberg or Bohr could not have predicted this particular success, pursuing the modelling framework of the liquid drop model proved to be an effective means of generating a high level of understanding-with, thus enabling physicists such as Frisch and Meitner to quickly formulate potential explanations in response to surprising empirical discoveries.

101 _{It is unclear whether Frisch and Meitner deliberately chose to pursue the liquid drop model in order to}

produce their explanation. In Frisch’s recollection (Stuewer 1994: 114-15), it seems rather that Frisch and Meitner simply had the requisite ideas ready to mind and spontaneously brought them to bear in response to each other’s suggestions.

4.6. Conclusion

In this chapter, I have considered several accounts of how analogies can provide reasons for pursuing a model (or modelling strategy) in cases like the liquid drop model. To be clear, I do not claim that the account of analogies developed here—i.e. that they provide a cost-effective means of transferring modelling frameworks with a high degree of understanding-with—is exhaustive of the use of analogies in science. First, pursuit worthiness accounts are compatible and to some extent complimentary with justificatory and generative accounts. The latter two types of accounts still capture interesting uses of analogy. However, I have argued that an adequate pursuit worthiness accounts of the liquid drop model case study cannot simply be subsumed within either of the other two. Second, as indicated, I do not regard my account as the only possible pursuit worthiness account of analogies. Nonetheless, I hope to have provided a plausible account of one way that analogies can be used in science.