Returning to the defense of the epistemic power of simulations, there are also grounds for rejecting the epistemological dependence thesis. As Parker (2009a) points out, in both experiment and simulation, we can have relevant similarities between computer simulations and target systems, and that's what matters. When the relevant background knowledge is in place, a simulation can provide more reliable knowledge of a system than an experiment. Acomputer simulation of the solar system, based on our mostsophisticated models of celestial dynamics, will produce betterrepresentations of the planets' orbits than any experiment.
Drawing explicitly upon Mayo's (1996) work, she argues thatwhat the epistemology of simulation ought to be doing, instead, isoffering some account of the ‘canonical errors’ that canarise, as well as strategies for probing for their presence.
The simulation hypothesis proposes that all of reality, ..
Both of the above definitions take computer simulation to befundamentally about using a computer to solve, or to approximatelysolve, the mathematical equations of a model that is meant to representsome system—either real or hypothetical. Another approachis to try to define “simulation” independently of thenotion of computer simulation, and then to define “computersimulation” compositionally: as a simulation that is carried outby a programmed digital computer. On this approach, a simulation is anysystem that is believed, or hoped, to have dynamical behavior that issimilar enough to some other system such that the former can be studiedto learn about the latter.
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Equation-based simulations are most commonly used in the physicalsciences and other sciences where there is governing theory that canguide the construction of mathematical models based on differentialequations. I use the term “equation based” hereto refer to simulations based on the kinds of global equations weassociate with physical theories—as opposed to “rules ofevolution” (which are discussed in the next section.) Equationbased simulations can either be particle-based, where there are n manydiscrete bodies and a set of differential equations governing theirinteraction, or they can be field-based, where there is a set ofequations governing the time evolution of a continuous medium orfield. An example of the former is a simulation of galaxyformation, in which the gravitational interaction between a finitecollection of discrete bodies is discretized in time and space. An example of the latter is the simulation of a fluid, such as ameteorological system like a severe storm. Here the system istreated as a continuous medium—a fluid—and a field representing itsdistribution of the relevant variables in space is discritized in spaceand then updated in discrete intervals of time.
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Serial multiscale methods are not effective when the different scalesare strongly coupled together. When the different scales interactstrongly to produce the observed behavior, what is required is anapproach that simulates each region simultaneously. This is calledparallel multiscale modeling. Parallel multiscale modeling is thefoundation of a nearly ubiquitous simulation method: so called“sub-grid” modeling. Sub-grid modelingrefers to therepresentation of important small-scale physical processes that occurat length-scales that cannot be adequately resolved on the grid sizeof a particular simulation. (Remember that many simulations discretizecontinuous equations, so they have a relatively arbitrary finite“grid size.”) In the study of turbulence in fluids, forexample, a common practical strategy for calculation is to account forthe missing small-scale vortices (or eddies) thatfall inside the grid cells. This is done by adding to the large-scalemotion an eddy viscosity that characterizes the transport anddissipation of energy in the smaller-scale flow—or any suchfeature that occurs at too small a scale to be captured by thegrid.
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In climate science and kindred disciplines, sub-grid modeling iscalled “parameterization.” This, again, refers to themethod of replacing processes—ones that are too small-scale orcomplex to be physically represented in the model— by a moresimple mathematical description. This is as opposed to otherprocesses—e.g., large-scale flow of the atmosphere—that arecalculated at the grid level in accordance with the basic theory. It iscalled “parameterization” because various non-physicalparameters are needed to drive the highly approximativealgorithms that compute the sub-grid values. Examples ofparameterization in climate simulations include the descent rate ofraindrops, the rate of atmospheric radiative transfer, and the rate ofcloud formation. For example, the average cloudiness over a 100km2 grid box is not cleanly related to the average humidityover the box. Nonetheless, as the average humidity increases, averagecloudiness will also increase—hence there could be a parameter linkingaverage cloudiness to average humidity inside a grid box. Eventhough modern-day parameterizations of cloud formation are moresophisticated than this, the basic idea is well illustrated by theexample. The use ofsub-grid modeling methods in simulation has important consequences forunderstanding the structure of the epistemology ofsimulation. This will be discussed in greater detail insection 4.