•  92
    This paper considers the relationship between continuum hydrodynamics and discrete molecular dynamics in the context of explaining the behavior of breaking droplets. It is argued that the idealization of a fluid as a continuum is actually essential for a full explanation of the drop breaking phenomenon and that, therefore, the less "fundamental," emergent hydrodynamical theory plays an ineliminable role in our understanding
  •  289
    Emergence, Singularities, and Symmetry Breaking
    Foundations of Physics 41 (6): 1031-1050. 2011.
    This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world
  •  209
    Falling cats, parallel parking, and polarized light
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (4): 527-557. 2003.
    This paper addresses issues surrounding the concept of geometric phase or "anholonomy". Certain physical phenomena apparently require for their explanation and understanding, reference to toplogocial/geometric features of some abstract space of parameters. These issues are related to the question of how gauge structures are to be interpreted and whether or not the debate over their "reality" is really going to be fruitful.
  •  163
    This paper concerns the scale related decoupling of the physics of breaking drops and considers the phenomenon from the point of view of both hydrodynamics and molecular dynamics at the nanolevel. It takes the shape of droplets at breakup to be an example of a genuinely emergent phenomenon---one whose explanation depends essentially on the phenomenological (non-fundamental) theory of Navier-Stokes. Certain conclusions about the nature of "fundamental" theory are drawn.
  •  162
    Critical phenomena and breaking drops: Infinite idealizations in physics
    Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2): 225-244. 2004.
    Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to…Read more
  •  146
    Defining chaos
    Philosophy of Science 60 (1): 43-66. 1993.
    This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of …Read more
  •  24
    Chaos and algorithmic complexity
    with Homer White
    Foundations of Physics 26 (3): 307-336. 1996.
    Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define “chaos” in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in…Read more
  •  54
    This paper aims to draw attention to an explanatory problem posed by the existence of multiply realized or universal behavior exhibited by certain physical systems. The problem is to explain how it is possible that systems radically distinct at lower-scales can nevertheless exhibit identical or nearly identical behavior at upper-scales. Theoretically this is reflected by the fact that continuum theories such as fluid mechanics are spectacularly successful at predicting, describing, and explainin…Read more
  •  82
    A ‘Modern’ Attitude Towards Scientific Understanding
    The Monist 83 (2): 228-257. 2000.
    In a recent book on applied mathematics A. C. Fowler offers the following description of what is involved in mathematical modeling
  •  111
    Asymptotics and the role of minimal models
    British Journal for the Philosophy of Science 53 (1): 21-38. 2002.
    A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.