Engineering Thinking and Rhetoric

John A. Robinson

Faculty of Engineering and Applied Science

Memorial University of Newfoundland

St. John's, NF, Canada

Engineers seek optimal solutions to problems. Often, though, the constraints of the problem and the solution criteria are of several, qualitatively different types, and there is no formal way to find the best trade-offs. Nevertheless, engineers make judgments and provide explanations to justify their choices. Engineering thinking and rhetoric is the development of such explanations that identify and validate a particular solution as the best. Engineering thinking involves analogical reasoning as well as deduction. This implies that in teaching engineering, descriptive case-based examples are important to the student as source analogs for problem solving.

William Wordsworth, in The Prelude [1], writes:

Scientists and engineers would agree that Wordsworth got it wrong. He was talking about engineering. Science is our glory, the scientists would say, because it is a proven road to discovery. By framing questions and seeking answers in a formal and consistent way without fear or favor, science enables us to know the truth about the world. While the scientists happily strike out "Science" from Wordsworth's first line, the engineers just as happily insert "Engineering", because that discipline is all about service. Being "a prop to our infirmity" is a noble enough cause for engineers.

Perhaps because they see their work in servanthood terms [2], engineers are reluctant to claim it is intellectually profound. Memorial University's library has several hundred books on the philosophy of science and not one on the philosophy of engineering. Engineers deal with complicated and difficult problems that admit many possible solutions but few good ones; they have theories and methodologies, some of which can be applied very broadly; but they shy away from advertising their way of thinking as something distinct and valuable in its own right.

On the other hand, engineers argue that the creative aspect of their thinking cannot be analyzed completely. "Engineering judgment", the ability to make sound design choices based on experience and intuition, cannot be summarized in a list of rules. This may be true, but for scholars of the discipline in a University, engineering judgment is something that should be analyzed. To understand knowledge, and in particular, to educate engineers, academics should attempt to explain, as clearly as possible, what engineers do intuitively.

Consider the question: "If there were no practical use for engineering, what could be said about the way engineers think as an alternative to the way (for example) mathematicians, physicists, anthropologists and historians think?" A good answer will mark out the intellectual dimension to engineering which draws on and can contribute to other areas of scholarship. It will identify the academic role of engineering education. A good answer will also show what kind of argument or rhetoric is appropriate for explaining engineering decisions. This paper attempts a preliminary answer, and identifies the central role of analogy in engineering thinking.

The Oxford English Dictionary [3] defines an Engineer as "one who contrives, designs or invents; an author, designer; also an inventor, plotter, a layer of snares". Delightful though this definition is, it does not capture why or how an engineer works. The Encyclopaedia Brittanica has "engineering [is] the application of scientific principles to the optimal conversion of natural resources into structures, machines, products, systems and processes for the benefit of mankind" [4]. Cambell Martin succinctly identifies the "essence of the engineering approach" as "using models to make proper decisions" [5]. I offer the following five-point description of engineering as a synthesis:

The above definitions include the key issues of problem solving, the reliance on science and math, and methodology. However, they do not say much about how engineers think. What can be added to express the intellectual root of engineering? I suggest the following:

This supplementary definition builds on the idea of optimal problem solving already suggested in the earlier definitions, but it emphasizes explanation. The idea is that engineering has a rhetoric, or a mode of argument to justify what it does. Indeed, there are at least two modes of argument, and these depend on what the word "best" means for a particular problem. For some problems, which here will be termed "simple problems", best means the solution which can be proved optimal through mathematical analysis or other deductive reasoning. For other problems, here called "compound problems", it is not possible to find such an analytic optimum, and best means the solution which is judged the most suitable tradeoff. That judgment is made, and justified, through "engineering thinking".

In simple problems, the constraints and criteria for evaluating the solution are all qualitatively similar. Even difficult problems in computational terms can be simple according to this definition. The traveling salesman problem, which involves working out the shortest path to visit a number of cities, is computationally hard, but because it has a single evaluation criterion (distance) it is a simple problem. Many other engineering optimization problems are simple in this sense. Designing a circuit that has to meet its specification with the minimum number of devices is a simple problem, because two solutions can be compared and the better one selected.

The explanatory framework of simple problem solving is deductive. Engineers solving such problems are thinking more like mathematicians than scientists (science is fundamentally inductive). The similarity should not be overstressed however. In many branches of math, optimally is not essential. For a mathematician, finding any proof is often a triumph. Engineers, by contrast, are not satisfied with existence proofs. Getting something to work is inadequate; it has to work well according to parameters of the problem. Even in simple problem solving, the engineer looks for evidence that the space of possible solutions was properly searched, and the chosen solution correctly proved to be optimal.

In compound problems, the evaluation criteria are not qualitatively similar and cannot be jointly optimized. Engineering jobs which require the balancing of cost, safety and aesthetics are compound. Most systems engineering jobs are compound. Wherever there are choices of materials, subsystems or methods that emphasize one or another property, the problem is compound. The engineer can now apply several strategies:

Strategy 1 sometimes has to do. For example, it may be impossible to say how the aestheics of a bridge are to be measured. However, if a criterion like aesthetics is rejected, there may still be some implicit lower limit on ugliness. It is part of the job of engineering, as an intellectual discipline, to understand how immeasurable but implicit criteria are to be dealt with.

Strategy 2 is important. Cost-benefit analysis uses money as the common currency of diverse constraints and criteria. When engineers do this, they are acting like economists, and must answer the same economic (and philosophical) questions about attributed value. But engineers have a wider gamut of mappings between qualitatively different constraints. Speed/accuracy and speed/size are common tradeoffs. When the engineer chooses a tradeoff, a judgment is being made about relative value, and that must be explained.

Strategy 3 is pervasive. Almost all real engineering projects are decomposed into subproblems which are then solved almost independently. Explaining why the problem has been decomposed is usually easy: The problem would be insoluble otherwise. But engineers should also be able to explain why a particular decomposition has been chosen, to justify the belief that the aggregate of optimal subproblem solutions will be the best overall solution, or, at least, close to it. Usually a project-wide goal, for example use of existing components, re-usability of new designs, or localizing properties and features into modules, guides the decomposition. Such a goal is really an evaluation criterion, and engineering rhetoric should explain why it is weighted so highly.

Compound problems include simple problems and their solution is therefore partly deductive. But trading off between qualitatively different domains requires a different kind of thinking. It has much in common with legal reasoning. In law, some decisions are made by the interpretation of legislation; some are made by developing earlier case decisions. These two routes to a decision are different: the first is the application of an abstract rule to a particular instance, the second is dealing with a particular instance according to similar previous instances. The first is a top-down theory-to-application route, while the second is a sideways precedents-to-application route. Compound problem solving uses the same two routes. Abstract rules are applied when the relative values of different courses of action can be measured and compared. This is not usually the case in design, so exemplars (previous designs) have to be applied too. By analogy with these precedents, compound problem solving decides on a best solution.

Practicing engineers probably make use of analogy as often as practicing lawyers. Reference to previous jobs, identifying similarities and differences, making linkages between contexts, are all regular habits. In many cases the analogies will be simple and direct, but, especially in systems engineering, the linkage can be between two very different domains. The ability to see analogical situations, particularly in balancing the values of different criteria, is central to engineering judgement. The ability to explain these analogies, and argue their relevance, is engineering rhetoric.

Engineering solves problems using physical science and mathematics. Its links to those disciplines are clear. Yet, in terms of engineering thinking and rhetoric, its dependence on them is really accidental rather than essential. Engineering's goal (problem solving) and its method (deduction and analogy) is much closer to medicine and ethics than to science. Its rhetoric (justifying its analogies) is close to law, and perhaps to economics. Table 1 summarizes three approaches to thinking, which groups engineering with these disciplines. While this classification is very tentative, I find it helps in introducing students to the academic place of engineering (see below).

Engineering does differ from other disciplines that rely on analogical reasoning. For medicine and law it is usually very easy to define the terms of success. Not so for engineering, which must begin its search for solutions by demanding clarity on what sort of solutions will do, and how they will be measured. The criterion question, "How will I know I have succeeded?", is the first step in design, and uncovers user requirements, presuppositions, physical limitations, and values. Defining criteria requires systematic analysis, and again draws on both analogy and deduction.

Engineering students should be taught both simple and compound problem solving. Because the modes of thinking are different, the teaching methods will also be different.

Simple problem solving is deductive. It may be taught normatively; that is, students are told what they should do. Method, theory, its application, heuristics, are all appropriately taught with rigor. Illustrative examples do not validate concepts in simple problem solving; the concepts stand in their own right, derived from theory. Examples simply help students to master the application of those concepts.

Compound problem solving relies on analogy. Normative teaching is still important, but there should also be teaching which recognizes the role of analogy. This will be of two types -- how to think analogically, and case-based descriptive teaching of particular engineering topics. Courses on critical thinking are useful for alerting students to the dangers of reasoning based on patterns (including analogies) alone. However, they rarely incorporate insights about how to use analogy effectively. This subject is now beginning to be taught in philosophy departments alongside traditional reasoning courses (see, for example [6][7]), and engineering students could be a prime audience. Learning to use analogy effectively and reliably is a worthwhile complementary studies component in any engineer's program. The second type of analogy-based teaching is in the engineering discipline itself. In learning new engineering subjects, students should be told what has been done in a variety of past situations. Practical examples now take on a much more fundamental role -- they do not merely illustrate concepts, they contribute to them.

In the teaching of analogical reasoning, engineering educators can learn from other disciplines which make heavy use of analogy. Foremost among these is law, but literature, rhetoric and philosophy have contributions to make too. More important, they are taught how to find, adapt and apply previous cases to new situations.

To see how the understanding of compound problem solving affects teaching, consider design methodology. Because design is common to all kinds of engineering, it has often been understood, researched and taught as an abstraction. In teaching, the abstraction is illustrated through real design projects for students to tackle. This mode of teaching reflects the normative stance of simple problem solving -- develop a common theory, apply it to examples. But if the understanding of compound problem solving as analogical judgment is correct, then design methodology teaching should also include case-based teaching. Rather than learning to solve problems by following a generic recipe, students should be learning to solve problems by getting as much information as possible on analogous previous problems, their solutions, and their solution processes, and then applying this information skillfully. This does not mean there is no place for teaching design in the abstract -- but it does mean that the sideways links between different instances of design must be taught and exploited too.

In teaching courses in digital systems engineering and software engineering, I have introduced students to the subject with a discussion of analogy in engineering design and in the particular subdiscipline. The introductory lecture invariably excites a small portion of the class who seem not to have either a common ability level or a shared special interest within engineering. For these students, seeing the relationship of engineering to other disciplines is highly motivational, and occasionally leads to further study of engineering education and philosophy. My purpose in writing this paper is to stimulate similar interest among the professoriat.

Engineering problems involve interacting, but qualitatively different, constraints. Engineering solutions must be justified by explaining the weights given to qualitatively different criteria. The impact of technology on its problem domain, on the business developing it, and on society are important management, historical and ethical questions. But they logically depend on deeper philosophical and psychological questions about what justifies the arguments, what validates the method, what makes explanations plausible and why. This is engineering thinking.

In making decisions concerning qualitatively different constraints and criteria, the engineer draws on similar previous problems and solutions. Analogical reasoning is thus at the heart of Engineering Thinking. Therefore engineers should be trained in the use of analogy, and given a rich set of source analogs from which to reason.

Engineers are not alone in facing the problems of technology, society and values, but they have a special responsibility. If they are well trained in both simple and compound problem solving, they will also have special expertise. With training in finding solutions subject to qualitatively different constraints, engineers will have the tools and experience for meeting situations where costs must be balanced, but there are ambiguities about relative value. Understanding engineering thinking therefore leads to better training of engineers as society's servants