Nersessian, N. J. (1997) Abstraction via generic modeling in concept formation in science. In Idealization and Abstraction in Science. M. R. Jones and N. Cartwright (eds.). Amsterdam: Editions Rodopi, 1997.

@InCollection{Nersessian1997,
  author =       "N. J. Nersessian",
  year =         "1997",
  title =        "Abstraction via generic modeling in concept formation
in science",
  booktitle =    "Idealization and Abstraction in Science",
  editor =       "M. R. Jones
                  and N. Cartwright",
  publisher =    " Editions Rodopi",
  address =      "Amsterdam",
}

Author of the summary: Jim Davies, 1999, jim@jimdavies.org

Cite this paper for:

• generic modeling
• Maxwell got his equations from the vortex-fluid model. (p5)
• Maxwell got the vortex-fluid model through an analogy with continuum mechanics. (p5)
• Maxwell used idealization. (p6)
• Maxwell made generic models. (p6)
• Models can be hybrids from multiple source domains. (p7)
• Cross-domain analogies can occur. (p7)
• Maxwell's model, properly understood, accounts for all but one of the errors in the papers he wrote. (p11)
• Idealzation is used to simplify a system to a point where mathematics can be applied to it. (p17)
• Models can remain generic while getting less ideal.(p18)
• One can use a model, and then make equations out of it that no longer really apply to one of the analogues you used to make the model in the first place. (p20)
• At one point Maxwell thought that the vortex model might be true. (p6)
• The imaginary model was necessary for the creation of the theories. (p12)

Abstract:

Summary:

For example, in physics you learn that a pendulum is one kind of harmonic oscillators. Chi et al 1981 and Clement 1989 found that in problem solving, people look for an abstract model from which to get the preliminary mathematical relationships. Thus though Maxwell is complex, studying him will provide insights about more common usage.

Constructive modeling: employing analogical and visual modeling as well as thought experimentation (mental simulation) to create source models where no direct analogy exists.

This analysis focuses on Maxwell's paper "On Physical Lines of Force." In this paper he first provided a unified representation of the transmission of electic and magnetic forces, and calculated their speed of propogation. He did this by transforming the problem from one of analyzing the production and transmission of emag forces into a problem of analyzing potential stresses and strains in a continuum-mechanical medium. That is, stresses and strains in the aether. So examining his procedures will shed light on how old representations play a role in the creation of new.

The two main ways to analyze in physics were 1. action at a distance and 2. continuum mechanics. Some thought that the apparant action at a distance was actually a macro-levl effect of some continuum mechanics. Maxwell thought that emag (electromagnetic) actions were continous transmissions through the aether. Maxwell probably got this idea from William Thompson.

In this paper Maxwell calls his method "physical analogy." It "allows the mind at every step to lay hold of a clear physical conception, without being committed to any theory founded on the physical science from which the conception is borrowed." This employs generic modeling. In Maxwell's first paper he took a fluid-dynamical system as his analogical source and made certain idealizing assumptions such as making the fluid incompressible. He treated processes of the fluid generically: "flow" instead of "fluid flow."

In the second paper he used continuum mechanics and machine mechanics as source domains, with emag constraints to make an imaginary system from which you could abstract the mathematical structure.

Stress comes when there are pressures in different directions on the same point. Force is the direction of the greatest pressure, and tension is the direction of the least pressure.

maybe I'll finish this later..

Claims and Evidence

Claim: Maxwell got the vortex-fluid model through an analogy with continuum mechanics. (p5)
Evidence:

Claim: Maxwell used idealization. (p6)
Evidence:

• At first the friction between vortices is ignored. (p6)

Claim: Maxwell made generic models. (p6)
Evidence:

• In part I the model satisfies constraints form both magnetism and continuum mechanics. (p6)
• Maxwell showed a lack of concern for multiplicitave factors when appropriating a formula from an earlier paper. This shows that he was thinking about the model in generic terms. (p14)
• Generic modeling is used to derive equations in physics problems. See Giere (1988).

Claim: Models can be hybrids from multiple source domains. (p7)
Evidence:

• In part II, the model used is a hybrid of fluid and machine mechanics. (p)

Claim: Cross-domain analogies can occur. (p7)
Evidence:

• Maxwell notes that the "Siemens governor for steam-engines" have idle wheels. He places idle wheels in his model. This is a mechanical device being used to help a fluid dynamics problem. (p7)

Claim: Maxwell's model, properly understood, accounts for all but one of the errors in the papers he wrote. (p11)
Evidence:

• Nersessian 1984 a, b (p11)

Claim: Idealzation is used to simplify a system to a point where mathematics can be applied to it. (p17)
Evidence:

• (p)

Claim: Models can remain generic while getting less ideal.(p18)
Evidence:

• At different stages friction and elasticity were added to Maxwell's models. (p18)

Claim: One can use a model, and then make equations out of it that no longer really apply to one of the analogues you used to make the model in the first place. (p20)
Evidence:

• "The abstract laws, when applied to the class of electro-magnetic systems yield the laws of a dynamical system that is non-mechanical; that is, one that cannot be mapped back onto the mechanical domains used in their construction." (p20)

Claim: At one point Maxwell thought that the vortex model might be true. (p6)
Evidence:

• Maxwell contrasts part I, where he thought the vortices might actually exist, with part II, where they are used merely as a tool for understanding. (p6)

Claim: The imaginary model was necessary for the creation of the theories. (p12)
Evidence:

• Without the physical model in mind, there is no reason to think of the moving idlewheels as a current. (p12)

Claim: Maxwell made his generic abstraction by focusing on the salient properties, relationships and processes. [p16]
Evidence:

Summary author's notes:

• this summary was made from the Georgia Institute of Technology Cognitive Science Technical Report series version GIT-COGSCI-94/22. So the page numbers are off.