Abstract
Both ecologists and statistical physicists use a variety of highly idealized models to study active matter and self-organizing critical phenomena. In this paper, I show how universality classes play a crucial role in justifying the application of highly idealized ‘minimal’ models to explain and understand the critical behaviors of active matter systems across a wide range of scales and scientific fields. Appealing to universality enables us to see why the same minimal models can be used to explain and understand behaviors across these different systems despite drastic differences in the causes and mechanisms responsible for the behaviors of interest. After analyzing these cases in detail, I argue that accounts that focus on identifying common causes or mechanisms in order to explain patterns are unable to accommodate these cases. In contrast, I argue that the justification for using these minimal models is that they are within the same universality class as real systems whose causes and mechanisms are known to be different. I also use these cases to identify several different kinds of explanatory autonomy that have important implications for how scientists ought to approach the modeling of multiscale phenomena.
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Notes
While the ‘universality account’ has been applied to number of case studies in (Batterman & Rice, 2014; Rice, 2017, 2018, 2020), it is still routinely claimed that such an account only applies to cases of renormalization. Thus, one aim of this paper is to argue that the universality account is more general than has been assumed and to clarify the scope of its application. That is, I aim to provide further support for the claim that such an account is generally applicable to a wide variety of cases that include instances of self-organized criticality.
In this way, the model is similar to the alignment of spins used in Ising models of ferromagnetic phase transitions.
Since all the particles are assumed to have the same magnitude of their velocity, this average is determined solely by the various directions of the particles in the system that are continuously reorienting to align with the average direction of the particles in their neighborhood.
This implies that, “we can assume that in the thermodynamic limit our model exhibits a kinetic phase transition analogous to the continuous phase transition in equilibrium systems” (Vicsek et al., 1995, 1228).
In addition, these modelers propose that their model will likely be applicable to drastically different physical systems; e.g. the clustering and convection involved in a system of disks floating on air.
Once these essential minimal features were identified, several recent studies began investigating the different universality classes associated with slightly altered versions of ‘Vicsek-like’ models (Ginelli, 2016, 2114).
This analysis contrasts a bit with Roman Frigg’s (2003) negative evaluation of the explanatory success of these models. While the models are certainly highly idealized and can be fruitful in the ways Frigg suggests, I contend that further investigation of these models over the last twenty years has provided a clearer sense of which features of real systems these behaviors depend on and why many of the features idealized by these models are irrelevant to whether or not the system displays the universal behaviors of interest. Consequently, in contrast with Frigg’s discussion, I will argue that these models can provide a plethora of information about dependencies and independencies that hold in real-world systems without faithfully representing the features of those systems.
In fact, BTW (1987) originally argued that the hallmark of SOC is the lack of any scale in time as well as space, but the necessity of the lack of spatial scale is debated by some physicists (Jensen, 1998).
It is worth noting here that I agree with Frigg (2003) that many of the claims of the ubiquity of SOC behaviors have been exaggerated beyond what is warranted by the empirical evidence. In particular, I don’t think we have reason to believe that SOC shows us generally ‘how nature works’ or ‘how everything evolves’. However, I do think that scientific modelers have shown that many of these behaviors are quite universal in the sense that they are widely applicable and largely autonomous of the particular features of real (and model) systems.
For example, Malamud et al., (1998) use a minimal model from statistical physics to explain the frequency-area distributions of actual wildfires and to study the recent fire history in Yellowstone National Park.
There are several different ways that this toppling threshold can be calculated. Some models assume that simply having enough grains at a particular site will result in toppling (e.g. the site having more than 4 grains). Others, such as the model described here define toppling in terms of the slope/difference between the number of grains at the site and the number of grains at its neighboring sites. Throughout the paper, I’ve tried to present the examples in their simplest form unless the details make a difference to the arguments or conclusions I defend. Thanks to an anonymous reviewer for noting this difference between the ways these models are implemented in different cases.
Although these features appear to be both necessary and sufficient for the systems in this universality class to display SOC behaviors, the necessary features for inclusion in a universality class will not always be sufficient (on their own) to display the macroscale behaviors characteristic of that class. For example, while several universality classes in physics show that the system’s symmetry of the order parameter and dimensionality are essential to determining the universality class of the system, merely having those features (alone) is not sufficient for the system to display the macroscale behaviors of interest (e.g. phase transitions) since those features only result in the critical behaviors of interest when they are incorporated within particular systems with myriad other features.
In particular, specifying the scope of the causal pattern shows that the same causal pattern is embodied across different systems.
Etiological explanations describe the causal history of the explanandum; whereas constitutive explanations describe the mechanism that underlies the phenomenon.
If there are differences among the causes/mechanisms that produce the different instances of the pattern, these authors suggest that we can explain the pattern by abstracting away from those differences and identifying the common features of the causes or mechanisms that produce each instance of the pattern.
Thanks to an anonymous reviewer for suggesting this possible reply.
Thanks to two anonymous reviewers who raised this possible reply and for pushing me to clarify which of the critiques of the CCP view depend on the assumption that all explanations are causal and which are independent of that assumption.
Thanks to an anonymous reviewer for raising this objection.
Indeed, like the cases discussed above, applying renormalization techniques often enables scientists to identify extremely minimal models that are within the same universality class as the real systems of interest (Batterman & Rice, 2014).
An anonymous reviewer suggested that this kind of objection is proposed by Franklin (2019). Franklin’s discussion is specifically tied to RG explanations of universality so it isn’t entirely clear just how those arguments would apply here since RG is not the only way to explain a universal pattern. However, I’ve tried to respond to what I take to be the general line of objection here. Since I don’t have the space to work through all of my responses to Franklin’s view, I will, instead, direct the reader to Robert Batterman’s paper (2019) that provides many of the same responses I would give.
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Acknowledgements
This paper is dedicated to Margaret Morrison for all the kindness she showed me over the years and for her work that has inspired so many. Thanks to Robert Batterman, Julia Bursten, Jennifer Jhun, and three anonymous reviewers for helpful feedback on previous versions of these ideas and drafts.
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Rice, C. Modeling multiscale patterns: active matter, minimal models, and explanatory autonomy. Synthese 200, 432 (2022). https://doi.org/10.1007/s11229-022-03885-7
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DOI: https://doi.org/10.1007/s11229-022-03885-7