The knowledge modality of idealisation

As discussed in chapters two and three, idealisation and modelling are extensively used in the sciences and engineering sciences as they engage with the world. Idealisation is described in the literature as intentional and sometimes selective distortion of reality for various purposes. It involves the deliberate employment of assumptions about phenomena (for example

simplification or approximation) that may not be accurate in a strict understanding of the real- world phenomena, in order to be able to explain phenomena, make predictions or solve problems (including the design of artefacts). A view of models (in both the sciences and the engineering sciences) as epistemic tools and independent ‘concrete’ objects (Boon & Knuuttila, 2009) that have been constructed for a particular epistemic purpose, could be substantiated in some of the examples of the data discussed in chapter five (see for example control volume

27 _{The notion of coding the engineering sciences’ emphasis on devices as towards ‘particulars’ has to be} qualified: the level at which the devices are discussed in the engineering science texts is less specific than what would be required in a design task. For example, engineering science covers thermodynamic processes in generic power stations and turbines rather than a specific turbine or a particular generation or fleet of power stations. Nevertheless, in the context of comparing engineering science knowledge with knowledge in the sciences (rather than with engineering design), coding engineering science as

177 analysis in mechanical engineering, and harmonic oscillators in physics). Models as epistemic tools emphasise the functional properties of the models, and the way the modeller can manipulate and interact with the model as demanded by the particular requirements of a problem. The cognitive value of the model lies in the fact that this kind of interaction with the model is possible. Models do more than merely represent a target system.

In the data considered here, idealisation includes entities that are clearly identifiable models, such as the ideal gas model, but also simplifications or approximations of real processes and phenomena, such as treating real processes as quasi-equilibrium processes.

The modes developed for the idealisation orientation refer to the different purposes with the idealisation activity, and ultimately to the fundamental aims of the broader disciplinary fields of science and engineering: the idealisation enables thinking about the knowledge to be either towards abstract-ideal theorisation or towards physical realisability. The data analysis in chapter five demonstrates that in all cases considered for physics and chemistry the idealisation

remained at the abstract-theoretical level. This is seen most clearly in the use of the ideal gas in chemistry, and in the development of the statistical mechanical model in physics to describe the behaviour of matter. The models developed are detailed and able to explain and predict the macroscopic properties of matter.

One of the differences between the engineering sciences and the natural sciences is that knowledge production in the engineering sciences has the particular focus of “goal-oriented action based on that same knowledge” (Zwart, 2009, p. 633). This emphasis on action shapes the kind of modelling that takes place in engineering science, and therefore idealisation tends towards physical realisability. This is clear for mechanical engineering knowledge in the textbook: the summary of coding decisions in Appendix A indicates that for mechanical engineering, the idealisation orientation of all the data units discussed is towards physical realisability. The notion of the control volume is an example of a thinking tool exclusively used in engineering science (Pirtle, 2010; Vincenti, 1990). It is a virtual construct, conceived of purely for the purpose of solving open system flow problems, typical in engineering. In control volume analysis, the control volume is treated as black box with all extraneous properties removed. The focus is on fluid flow through an open, defined volume, conceived of in terms of inputs and outputs, with no concern given to the inner detail. Control volume analysis is clearly an example of a case where idealisation is used as an epistemic tool for solving problems of a particular kind.

Other examples of the use of idealisation in mechanical engineering include various cases of approximation, for example treating unsteady flow as steady flow and real gases as ideal gases.

178 The complexities of the ‘real’ world cannot be completely ignored in engineering problems even though full knowledge of a multitude of variables is often not possible. Approximation, when simplifying assumptions are made, then provides a way into ill-defined problems. The measure of satisfaction with the answer obtained by approximation is determined by the margin of error of uncertainty introduced by the approximation, which is therefore often stated explicitly in the mechanical engineering text. Physical realisability of a problem solution requires tolerance for approximation, provided the distortion so introduced does not compromise functionality and safety. Appropriate adequacy for functionality is therefore the practical outworking of physical realisability. This is seen in the mechanical engineering science data in the insistence on quantifying the error introduced by the use of approximation. Approximation is acceptable as long as it produces a solution that is fit-for-purpose required by the physical reality.

Another example of idealisation in the mechanical engineering textbook can be seen in the way the ideal Carnot cycle is used. Although the Carnot engine is covered in all the thermodynamics texts under consideration, in the mechanical engineering text there is an emphasis on using the ideal Carnot engine as a standard against which the efficiency of real heat engines is measured. The demands of the ‘real’ world and the need for physical realisability are therefore always present when idealisations are used in the mechanical engineering textbook.

Chemical engineering displays a weaker tendency towards physical realisabilty than mechanical engineering in all the cases discussed in chapter five, with one exception. Open systems are also treated as black boxes, but here a general non-specific balance equation is developed that is adapted across different generic types of systems. Although the chemical engineering textbook author emphasises the complexity of the physical world, he mostly deals with the needs of physical realisability via simplification by the use of specific assumptions, estimates and approximation in the face of incomplete information – a weaker commitment to physical realisability than was the case in mechanical engineering.

In spite of the weaker emphasis on physical realisability, it is also in the chemical engineering textbook that attention is drawn quite explicitly to the constraints of idealisation. The ideal gas model is a powerful idealisation used across all of the texts investigated in the study. However, for those fluids commonly used in (chemical engineering) industrial applications, the author points students to the detailed tables of empirical data available for calculations. The demands of physical realisability here overshadow the power of explanation offered by the model under ideal conditions.

There is one other interesting exception where the chemical engineering text displays a strong commitment to physical realisability. The idealisation employed in the tank-filling problem (see

179 5.4.2) is a completely utilitarian distortion of reality, engaged solely in the service of solving the problem at hand. The simplest way to solve the problem requires an approach using a distortion that not only violates reality, but also the theoretical model of ideal gas behaviour. The ideal gas model does not allow for identifying, at the start of the problem-solving process, the proportion of gas molecules left behind at the end of the process. It is therefore diametrically at odds with the type of theory building that idealisation is often used for in the sciences, and is employed here to find a way to solve a complex physical problem. The concept of idealisation as an epistemic tool (Boon & Knuuttila, 2009), here employed towards physical realisability (solving the real-world problem of tank-filling), is quite prominent. In a sense this is an example that illustrates that “physical realisability” is not the same as correspondence to “physical reality”. It is less a commitment to the “truth” Pirtle (2010) refers to, than a commitment to solving a problem, and in that sense dedication to physical realisability.

By contrast, the data from the chemistry textbook shows how the ideal gas model is infused throughout the textbook. Even though a macroscopic classical approach to thermodynamics is followed throughout, diagrams often show molecular detail to relate to macroscopic properties of pressure, temperature, volume and amount of matter. It is the underlying explanatory power of the model that is important in the chemistry text. This becomes abundantly clear when the chemistry authors discuss deviation from ideal behaviour exhibited by real gases. A very different approach from that of the two engineering texts follows. Whereas the engineering textbooks move swiftly to empirical data for real gases to facilitate the insistence on physical realisability, the chemistry text’s chief concern is to be able to explain the deviation from ideal behaviour under various circumstances. The authors express their uneasiness with following only the classic macroscopic approach, as it does not get to the bottom of the reasons for the deviations from ideal behaviour. They use changes in the potential energy between two interacting molecules that depend on the polarisability of the electron cloud of the two

molecules as they approach each other to explain the deviation. For the chemistry authors, it is most important to be able to give an explanation in terms of the ideal gas: real gas behaviour deviates from ideal behaviour, but the atomic/molecular model that encapsulates the ideal gas model is able to explain the deviations. This theoretical explanation in terms of the main theory accounts for the empirical observation of real gas behaviour, and the theory is in fact

corroborated because of the evidence that it can deal with empirical behaviour. The idealisation most prized here is one that leads to building and affirming abstract-ideal theorisation.

The two physics textbooks follow a very different approach from the other three textbooks: instead of the classical macroscopic approach, a statistical mechanical approach is followed. The first year textbook authors describe the role of modelling as a central aspect of science for the

180 purpose of predicting and explaining behaviour. Their description of modelling mirrors

Weisberg’s (2007a) Galilean idealisation: phenomena are stripped of “messy complexities” (Chabay & Sherwood, 2011, p. 82) to enable patterns to become visible and understand factors that impact on these. These patterns lead to revision and elaboration of the model. The third year textbook author demonstrates this in his discussion of the ideal gas model that starts off with just a single gas molecule. He builds an explanation of the behaviour of the molecule that links the kinetic energy of the particles with the ideal gas equation.

However, it is ultimately the way the statistical mechanical approach allows the physics texts to deal with explaining fundamental aspects of the Second Law of thermodynamics that

demonstrates the commitment to the abstract-ideal theorisation mode of idealisation. (By contrast the engineering texts’ starting point is the fact of the irreversibility of some

macroscopic processes: heat flows from a hotter to a colder object, a ball dropped to the ground bounces lower each time it hits the ground, etc.). Using combinatorics and factorials to calculate the likelihood of a particular distribution of energy for large numbers of particles, the physics authors use arguments from statistical mechanics to explain why macroscopic thermodynamics processes are irreversible. The physics texts apply probability theory to large numbers of particles to demonstrate how energy is distributed amongst particles in large systems, why objects reach thermal equilibrium, and ultimately develop a theorised understanding of the meaning of temperature. Particles are modelled as idealised harmonic quantum oscillators that store energy in different macrostates corresponding to different numbers of microstates (ways of distributing quanta of energy across oscillators). Although all microstates are all equally likely, some macrostates are more probable than others: the macrostates with the largest number of corresponding microstates. The ability to predict and explain the macroscopic behaviour of matter is highly valued in the physics texts, and their orientation to idealisation is therefore towards the abstract-ideal theorisation.

The empirical data from the textbooks illustrates quite vividly how idealisation is approached in different ways in the disciplines for distinct purposes. The scientific concern for generalisable theoretical explanations places no constraints on the amount of idealisation employed, hence Cartwright’s (1983) reference to the “lying laws of physics” (Laymon, 1989b, p. 353).

Cartwright’s argument is that the fundamental physical laws (which involve idealisation in order to apply broadly) are powerful explanatory tools, but that these come at the cost of a loss in “descriptive adequacy” (p. 3). On the other hand, the demand for physical realisability in the engineering science knowledge implies that the distortion brought about by idealisation cannot stray too far from the complex demands of the real world (presented in the data, for example in the quantification of error introduced by approximation). This confirms Hansson’s (2007)

181 suggestion that the engineering sciences make use of “less far-reaching idealizations” (p. 526), and Pirtle’s (2010) argument that models in engineering ultimately have to “tell the truth” (p. 95), with ‘truth’ here referring to a closer correspondence with reality.

Houkes (2009) suggests something slightly different (but still illustrating engineering science knowledge’s strong allegiance to solving ‘real’ problems), namely that the engineering sciences might employ idealisation for pragmatic purposes of finding a solution to a problem. In

principle, it is therefore possible to use a method or an approach that is not strictly speaking ‘true’ or accurate, but gives an acceptable answer to a complex problem. Houkes suggests that this method or approach will not be taken up in the sciences, as it counters the kind of detailed explanatory knowledge valued in the sciences. The data discussed in chapter five offered two instances of this kind of idealisation: the control volume analysis prominent in mechanical engineering is not taken up in the sciences (see paragraph 5.2.1), and the tank-filling problem in chemical engineering offers a simple solution involving a ‘model’ that contradicts the ideal gas laws and theory (see paragraph 5.4.2).

In all of these examples, the influence of engineering’s field of practice (to use Bernstein’s term) in engaging with physical realisability required for problem solving is evident. See the further discussion under 7.6 later in this chapter.

In view of the fact that the modalities are conceptualised as continua, it becomes possible to represent the idealisation modality in Figure 7-2.

The diagram indicates strong inclination towards abstract-ideal theorisation of the science disciplines in the physics (PHY) and chemistry (CHE) idealisations, as well as the tendency towards physical realisability in the engineering science knowledge. The weaker engagement with physical realisability evident in the chemical engineering text (CEng) when compared to the mechanical engineering (MEng) knowledge is also evident on the idealisation continuum.