Abstract
This paper addresses a set of issues involved in modeling systems across many orders of magnitude in spatial and temporal scales. In particular, it focuses on the question of how one can explain and understand the relative autonomy and safety of models at continuum scales. The typical battle line between reductive “bottom-up’’ modeling and “top-down” modeling from phenomenological theories is shown to be overly simplistic. Multi-scale models are beginning to succeed in showing how to upscale from statistical atomistic/molecular models to continuum/hydrodynamics models. The consequences for our understanding of the debate between reductionism and emergence will be examined.
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Notes
- 1.
Without doing a literature survey, as it is well-trodden territory, one can simply note that virtually every view of emergent properties canvassed in O'Connor's and Wong's Stanford Encyclopedia article reflects some conception of a hierarchy of levels characterized by aggregation of parts to form new wholes organized out of those parts (O'Connor and Wong 2012).
- 2.
Some examples, particularly from theories of optics, where one can speak of relations between theories and models where no part/whole relations seem to be relevant can be found in Batterman (2002). Furthermore, it is worth mentioning that there are different kinds of models than may apply at the same scale from which one might learn very different things about the system.
- 3.
See (Lauglin and Pines 2007, p. 261), quoted above.
- 4.
Exceptions appear in some discussions of universality in terms of the renormalization group theory of critical phenomena and in quantum field theory. However, universality, etc., is ubiquitous in nature and more attention needs to be paid to our understanding of it.
- 5.
See Batterman (2013) for further discussion.
- 6.
This discussion follows (Christensen 2005, pp. 36–37).
- 7.
This is because the inclusion is of the same material as the matrix.
- 8.
Note that if the inclusion is empty, we have an instance of a porous material. Thus, these methods can be used to understand large scale behaviors of fluids in the ground. (Think of hydraulic fracturing/fracking.).
- 9.
I too have been somewhat guilty of contributing to what I now believe is basically a host of confusions.
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Batterman, R. (2015). Autonomy and Scales. In: Falkenburg, B., Morrison, M. (eds) Why More Is Different. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43911-1_7
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