題(compound problems)，并重點論述了復合問題的解決步驟。作者認為工程師應重點掌握“類比”的思維方式。原文摘錄如下，內容有一點艱澀，我自己也理解地不是很好。
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E- l8 m5 @7 O8 B l6 @' FEngineering Thinking and Rhetoric
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John A. Robinson
, n; E& q: S( ~ M, V" }. SFaculty of Engineering and Applied Science
: [7 }, X/ V$ B2 hMemorial University of Newfoundland
& ?9 Q- K2 L$ ~9 g7 ZSt. John's, NF, Canada
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Abstract
3 U6 I" s# @- q! b0 h$ YEngineers seek optimal solutions to problems. Often,though, the constraints of the problem and the solution criteria are ofseveral, qualitatively different types, and there is no formal way to find thebest trade-offs. Nevertheless, engineers make judgments and provideexplanations to justify their choices. Engineering thinking and rhetoric is thedevelopment of such explanations that identify and validate a particularsolution as the best. Engineering thinking involves analogical reasoning aswell as deduction. This implies that in teaching engineering, descriptivecase-based examples are important to the student as source analogs for problemsolving.
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Introduction
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William Wordsworth, in The Prelude [1], writes:
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Science appears as what in truth she is, 1 w: D# b7 q9 T6 [; w
Not as our glory and our absolute boast,
7 b& U; T$ F8 @+ A0 [; {. lBut as a succedaneum, and a prop : L) e8 t4 S" F3 H7 C
To our infirmity.
- H# p+ }" s. n5 u% dScientists and engineers would agree that Wordsworthgot it wrong. He was talking about engineering. Science is our glory,the scientists would say, because it is a proven road to discovery. By framingquestions and seeking answers in a formal and consistent way without fear orfavor, science enables us to know the truth about the world. While thescientists happily strike out "Science" from Wordsworth's first line,the engineers just as happily insert "Engineering", because thatdiscipline is all about service. Being "a prop to our infirmity" is anoble enough cause for engineers.
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Perhaps because they see their work in servanthoodterms [2], engineers are reluctant to claim it is intellectually profound.Memorial University's library has several hundred books on the philosophy ofscience and not one on the philosophy of engineering. Engineers deal withcomplicated and difficult problems that admit many possible solutions but fewgood ones; they have theories and methodologies, some of which can be appliedvery broadly; but they shy away from advertising their way of thinking assomething distinct and valuable in its own right.
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On the other hand, engineers argue that the creativeaspect of their thinking cannot be analyzed completely. "Engineeringjudgment", the ability to make sound design choices based on experienceand intuition, cannot be summarized in a list of rules. This may be true, butfor scholars of the discipline in a University, engineering judgment issomething that should be analyzed. To understand knowledge, and in particular,to educate engineers, academics should attempt to explain, as clearly aspossible, what engineers do intuitively.
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Consider the question: "If there were nopractical use for engineering, what could be said about the way engineers thinkas an alternative to the way (for example) mathematicians, physicists,anthropologists and historians think?" A good answer will mark out theintellectual dimension to engineering which draws on and can contribute toother areas of scholarship. It will identify the academic role of engineeringeducation. A good answer will also show what kind of argument or rhetoric isappropriate for explaining engineering decisions. This paper attempts apreliminary answer, and identifies the central role of analogy in engineeringthinking.
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What Engineers Do
& {; P: {* n" l/ YThe Oxford English Dictionary [3] defines an Engineeras "one who contrives, designs or invents; an author, designer; also aninventor, plotter, a layer of snares". Delightful though this definitionis, it does not capture why or how an engineer works. The EncyclopaediaBrittanica has "engineering [is] the application of scientific principlesto the optimal conversion of natural resources into structures, machines,products, systems and processes for the benefit of mankind" [4]. CambellMartin succinctly identifies the "essence of the engineeringapproach" as "using models to make proper decisions" [5]. Ioffer the following five-point description of engineering as a synthesis:
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• Engineering is applying scientific knowledge andmathematical analysis to the solution of practical problems.
$ H- Y* e1 O2 G, h• It usually involves designing and buildingartifacts.
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• It seeks good, and if possible, optimum, solutions,according to well-defined criteria.
~( E) C; O: F8 S! t; J {• It uses abstract and physical models to represent,understand and interpret the world and its artifacts.
3 f" k U8 N$ r7 ?( ?# f2 D h• It applies well-established principles and methods,adapts existing solutions, and uses proven components and tools.
5 u' e- Z' i4 o! J5 `' U$ R. VThe above definitions include the key issues ofproblem solving, the reliance on science and math, and methodology. However,they do not say much about how engineers think. What can be added to expressthe intellectual root of engineering? I suggest the following:
) J3 H' B3 N3 O. N• Engineering is the development of an explanatoryframework that identifies and validates a particular solution to a problem asthe best.
8 I2 l5 `: R- W" j( BThis supplementary definition builds on the idea of optimalproblem solving already suggested in the earlier definitions, but it emphasizesexplanation. The idea is that engineering has a rhetoric, or a mode of argumentto justify what it does. Indeed, there are at least two modes of argument, andthese depend on what the word "best" means for a particular problem.For some problems, which here will be termed "simple problems", bestmeans the solution which can be proved optimal through mathematical analysis orother deductive reasoning. For other problems, here called "compoundproblems", it is not possible to find such an analytic optimum, and bestmeans the solution which is judged the most suitable tradeoff. That judgment ismade, and justified, through "engineering thinking".
0 d2 s! O( |' i1 KHow Engineers Think
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Simple Problems
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In simple problems, the constraints and criteria forevaluating the solution are all qualitatively similar. Even difficult problemsin computational terms can be simple according to this definition. Thetraveling salesman problem, which involves working out the shortest path tovisit a number of cities, is computationally hard, but because it has a singleevaluation criterion (distance) it is a simple problem. Many other engineeringoptimization problems are simple in this sense. Designing a circuit that has tomeet its specification with the minimum number of devices is a simple problem,because two solutions can be compared and the better one selected.
+ _! u. {2 }9 ~The explanatory framework of simple problem solving isdeductive. Engineers solving such problems are thinking more likemathematicians than scientists (science is fundamentally inductive). Thesimilarity should not be overstressed however. In many branches of math,optimally is not essential. For a mathematician, finding any proof isoften a triumph. Engineers, by contrast, are not satisfied with existenceproofs. Getting something to work is inadequate; it has to work well accordingto parameters of the problem. Even in simple problem solving, the engineerlooks for evidence that the space of possible solutions was properly searched,and the chosen solution correctly proved to be optimal.
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Compound problems
; c) m8 Y) E+ uIn compound problems, the evaluation criteria are notqualitatively similar and cannot be jointly optimized. Engineering jobs whichrequire the balancing of cost, safety and aesthetics are compound. Most systemsengineering jobs are compound. Wherever there are choices of materials,subsystems or methods that emphasize one or another property, the problem iscompound. The engineer can now apply several strategies:
X& B; F9 b' N3 b, y1 Disqualify (ignore) criteria that cannot bemeasured.
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2 Express relative values of criteria based on someevidence, then try to reduce the problem to a simple one.
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3 Divide the problem into parts which can beindependently solved as simple problems.
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Strategy 1 sometimes has to do. For example, it may beimpossible to say how the aestheics of a bridge are to be measured. However, ifa criterion like aesthetics is rejected, there may still be some implicit lowerlimit on ugliness. It is part of the job of engineering, as an intellectualdiscipline, to understand how immeasurable but implicit criteria are to bedealt with.
1 e7 L) j! [6 RStrategy 2 is important. Cost-benefit analysis usesmoney as the common currency of diverse constraints and criteria. Whenengineers do this, they are acting like economists, and must answer the sameeconomic (and philosophical) questions about attributed value. But engineershave a wider gamut of mappings between qualitatively different constraints.Speed/accuracy and speed/size are common tradeoffs. When the engineer chooses atradeoff, a judgment is being made about relative value, and that must beexplained.
* e0 d3 b, Z9 J; j) B! hStrategy 3 is pervasive. Almost all real engineeringprojects are decomposed into subproblems which are then solved almostindependently. Explaining why the problem has been decomposed is usually easy:The problem would be insoluble otherwise. But engineers should also be able toexplain why a particular decomposition has been chosen, to justify the beliefthat the aggregate of optimal subproblem solutions will be the best overallsolution, or, at least, close to it. Usually a project-wide goal, for exampleuse of existing components, re-usability of new designs, or localizingproperties and features into modules, guides the decomposition. Such a goal isreally an evaluation criterion, and engineering rhetoric should explain why itis weighted so highly.
- f- u& H1 M' g/ r& g- V p+ P3 w6 ~Compound problems include simple problems and theirsolution is therefore partly deductive. But trading off between qualitativelydifferent domains requires a different kind of thinking. It has much in commonwith legal reasoning. In law, some decisions are made by the interpretation oflegislation; some are made by developing earlier case decisions. These tworoutes to a decision are different: the first is the application of an abstractrule to a particular instance, the second is dealing with a particular instanceaccording to similar previous instances. The first is a top-downtheory-to-application route, while the second is a sideways precedents-to-applicationroute. Compound problem solving uses the same two routes. Abstract rules areapplied when the relative values of different courses of action can be measuredand compared. This is not usually the case in design, so exemplars (previousdesigns) have to be applied too. By analogy with these precedents, compoundproblem solving decides on a best solution.
' P w5 g8 t+ R3 M; n7 [: N. FPracticing engineers probably make use of analogy asoften as practicing lawyers. Reference to previous jobs, identifyingsimilarities and differences, making linkages between contexts, are all regularhabits. In many cases the analogies will be simple and direct, but, especiallyin systems engineering, the linkage can be between two very different domains.The ability to see analogical situations, particularly in balancing the valuesof different criteria, is central to engineering judgement. The ability toexplain these analogies, and argue their relevance, is engineering rhetoric.
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Links with other disciplines
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Engineering solves problems using physical science andmathematics. Its links to those disciplines are clear. Yet, in terms ofengineering thinking and rhetoric, its dependence on them is really accidentalrather than essential. Engineering's goal (problem solving) and its method(deduction and analogy) is much closer to medicine and ethics than to science. Itsrhetoric (justifying its analogies) is close to law, and perhaps to economics.Table 1 summarizes three approaches to thinking, which groups engineering withthese disciplines. While this classification is very tentative, I find it helpsin introducing students to the academic place of engineering (see below).
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| Aim | Method | Argument |
| Science | To explain | Observe\Hypothesize\Test | Falsifiable hypothesis has been corroborated and not refuted |
| Humanities | To interpret | Collect\Critique\Synthesize | Interpretation is coherent and revealing |
| Engineering | To solve | Specify\Design\Verify | Design is optimal analytically or by analogy |
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Engineering does differ from other disciplines thatrely on analogical reasoning. For medicine and law it is usually very easy todefine the terms of success. Not so for engineering, which must begin itssearch 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 Ihave succeeded?", is the first step in design, and uncovers userrequirements, presuppositions, physical limitations, and values. Definingcriteria requires systematic analysis, and again draws on both analogy anddeduction.
1 v; F( I% _/ H: x( `' @Teaching Engineering
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Engineering students should be taught both simple andcompound problem solving. Because the modes of thinking are different, theteaching methods will also be different.
/ ~* D" l- {. J) ISimple problem solving is deductive. It may be taughtnormatively; 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; theconcepts stand in their own right, derived from theory. Examples simply helpstudents to master the application of those concepts.
; Y0 Y& U8 j8 x& A1 pCompound problem solving relies on analogy. Normativeteaching is still important, but there should also be teaching which recognizesthe role of analogy. This will be of two types -- how to think analogically,and case-based descriptive teaching of particular engineering topics. Courseson critical thinking are useful for alerting students to the dangers ofreasoning based on patterns (including analogies) alone. However, they rarelyincorporate insights about how to use analogy effectively. This subject is nowbeginning to be taught in philosophy departments alongside traditionalreasoning courses (see, for example [6][7]), and engineering students could bea prime audience. Learning to use analogy effectively and reliably is aworthwhile complementary studies component in any engineer's program. Thesecond type of analogy-based teaching is in the engineering discipline itself.In learning new engineering subjects, students should be told what has beendone in a variety of past situations. Practical examples now take on a muchmore fundamental role -- they do not merely illustrate concepts, they contributeto them.
+ _2 J% f8 h3 A& x6 m7 z- e3 n( LIn the teaching of analogical reasoning, engineeringeducators can learn from other disciplines which make heavy use of analogy.Foremost among these is law, but literature, rhetoric and philosophy havecontributions to make too. More important, they are taught how to find, adaptand apply previous cases to new situations.
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To see how the understanding of compound problemsolving affects teaching, consider design methodology. Because design is commonto all kinds of engineering, it has often been understood, researched andtaught as an abstraction. In teaching, the abstraction is illustrated throughreal design projects for students to tackle. This mode of teaching reflects thenormative stance of simple problem solving -- develop a common theory, apply itto examples. But if the understanding of compound problem solving as analogicaljudgment is correct, then design methodology teaching should also includecase-based teaching. Rather than learning to solve problems by following ageneric recipe, students should be learning to solve problems by getting asmuch 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 -- butit does mean that the sideways links between different instances of design mustbe taught and exploited too.
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In teaching courses in digital systems engineering andsoftware engineering, I have introduced students to the subject with adiscussion of analogy in engineering design and in the particularsubdiscipline. The introductory lecture invariably excites a small portion ofthe class who seem not to have either a common ability level or a sharedspecial interest within engineering. For these students, seeing therelationship of engineering to other disciplines is highly motivational, andoccasionally leads to further study of engineering education and philosophy. Mypurpose in writing this paper is to stimulate similar interest among theprofessoriat.
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Conclusion
6 X- a2 d2 t2 l- a$ p5 K9 f' ~Engineering problems involve interacting, butqualitatively different, constraints. Engineering solutions must be justifiedby explaining the weights given to qualitatively different criteria. The impactof technology on its problem domain, on the business developing it, and onsociety are important management, historical and ethical questions. But theylogically depend on deeper philosophical and psychological questions about whatjustifies the arguments, what validates the method, what makes explanationsplausible and why. This is engineering thinking.
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In making decisions concerning qualitatively differentconstraints and criteria, the engineer draws on similar previous problems andsolutions. Analogical reasoning is thus at the heart of Engineering Thinking.Therefore engineers should be trained in the use of analogy, and given a richset of source analogs from which to reason.
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Engineers are not alone in facing the problems oftechnology, society and values, but they have a special responsibility. If theyare well trained in both simple and compound problem solving, they will alsohave special expertise. With training in finding solutions subject toqualitatively different constraints, engineers will have the tools andexperience for meeting situations where costs must be balanced, but there areambiguities about relative value. Understanding engineering thinking thereforeleads to better training of engineers as society's servants
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發表于 2012-10-23 16:36:00
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