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- 1. Engineering Rigor and Its Discontents: Philosophical Reflection as Curative to Math-Physics Envy<br />David E. GoldbergIllinois Foundry for Innovation in Engineering Education<br />University of Illinois at Urbana-Champaign<br />Urbana, IL 61801 USA<br />deg@illinois.edu<br />
- 2. Engineering Use of Term “Rigor”<br />Engineers, particularly academics, use interesting language.<br />“Rigor” as term of approbation. <br />“That’s a rigorous analysis” or “He had a rigorous education.” <br />Absence of “rigor” is bad: “Those leadership and teamwork classes are not sufficiently rigorous to be taught in the College of Engineering.” <br />“Soft” as synonymous with “not rigorous:” “We’ll accept those soft courses in a rigorous curriculum over my dead body.” <br />Usage is kind of informal demarcation by pejorative.<br />Critically examine these terms to<br />better understand different senses of usage,<br />uncover inconsistencies in usage, and<br />determine ways to move forward. <br />
- 3. Roadmap<br />Rigor, the word & its conventional meanings.<br />A short history of rigor in engineering education.<br />Two senses of “rigor” in engineering:<br />In derivation.<br />In application of established scientific principles.<br />The economics of engineering modeling.<br />Reasonableness and reflective practitioners.<br />A third sense: “Rigor” as rite of passage.<br />Beyond informal demarcation: Rethinking the math-science death march. <br />
- 4. Rigorous, the Word<br />Rigorous:<br />extremely thorough or accurate. <br />(of a rule, system, etc.) strictly applied or adhered to. <br />adhering strictly to a belief, opinion, or system. <br />harsh or severe: rigorous military training.<br />From the Latin rigor = stiffness.<br />Use rigor or rigorous (without quotations) in these senses & “rigor” as referring to the engineering usage of term.<br />
- 5. A Short History of Engineering Rigor<br />Uses of rigor in technology are long and complex and in part justified:<br />Premodern technology had rigorous elements rooted in mathematics (a2 + b2 =c2)<br />Military engineering and origins of the notion of discipline. (Toulmin, 2001).<br />L’EcolePolytechnique as steeped in the best science of the time (Grayson, 1993). <br />Maxwell’s equations and the birth of electrical engineering (Layton, 1971).<br />Rigor as separating “engineering” from “craft.” (Davis, 1998).<br />Rigor as necessary to catch up with mathematicians and physicists post World War II (Grinter, 1955).<br />2types:<br />Rigor as necessary to task at hand.<br />Rigor as status enhancement device .<br />
- 6. Early Uses of Rigor Largely Utilitarian<br />Premoderns used math because it was useful.<br />Surveying, architecture, military engineering relied heavily on geometry and trigonometry.<br />Heady days post-Newton/Leibniz power of calculus and physics simply stunning.<br />Injection of the best math in L’EcolePolytechnique continues that cultural tradition.<br />Electrical engineering as field essentially enabled by Maxwell’s equations.<br />Sir Isaac Newton (1643-1727)<br />
- 7. Later Uses: Less Utility More Status<br />Shift starts to take place with professional strivings.<br />Grand era of big artifacts (big bridges, structures, railroads, radio, steamships, & airplanes).<br />Big changes in science (relativity & quantum physics).<br />WW2: Physicists “won the war.” Engineers must “catch up.”<br />1955 Grinter report: Engineering as applied science to detriment of engineering, engineering education and engineers.<br />
- 8. Two Senses of Engineering Rigor<br />Common types of engineering rigor:<br />Type 1: Mathematical rigor in derivation.<br />Type 2: Lawful scientific rigor.<br />Critically examine both.<br />Are they mutually consistent?<br />Are they self-contained tools of engineering thought?<br />
- 9. Type I: Rigor in Derivation<br />Elements:<br />Start from a set of premises.<br />Use rules of logic.<br />Proceed to formally “correct” and “true” conclusion.<br />Good news and bad news: Nothing “added” to premises.<br />Conclusion follows directly from premises.<br />Toulmin: Not a good model of the full breadth of human argument. Return to that view in a moment.<br />
- 10. Type II: Lawful Scientific Rigor<br />Elements:<br />Start from accepted equations of science (Newton’s laws, Maxwell’s equations, etc.)<br />Apply type I rigor.<br />Straightforward enough.<br />Problems:<br />Type I rigorist objection to type II rigor.<br />The plate tectonics problem.<br />
- 11. Type II Inconsistent with Type I<br />Newton’s laws not a product of type I rigor.<br />Inverse square law in some sense a lucky guess.<br />Cartesians hated it.<br />Causation as merely “constant conjunction” (Hume).<br />No starting from premises.<br />No formal derivation: A curve fit to extant astronomical data.<br />A type I rigorist should object: Key elements of result (Newton’s laws) not the result of type I rigor.<br />
- 12. Plate Tectonics: Type II Rigor Incomplete<br />Set inconsistency with Type I aside.<br />Type II rigorist insists on scientific laws in mathematical form.<br />What about plate tectonics?<br />Plate tectonics was revolution in geology.<br />Unified many qualitative geological phenomena from earthquakes to volcanoes. <br />Where are the equations?<br />Formal reasoning can proceed from linguistic propositions.<br />Type II rigorist rejects these as “merely words” and not “rigorous.”<br />
- 13. Are These Straw Men?<br />Are these categories straw men?<br />Reasonable people would never insist on only being formal or only reasoning from mathematical laws.<br />But look at behavior.<br />Term “rigor” is used by engineering rigorists to<br />censor discussion (that’s not a proper model)<br />or reject teaching of certain topics (no “soft” stuff here).<br />They mean it!! Censorship or rejection of topic in classroom is sign of their seriousness.<br />Two answers in words & one answer in equations.<br />
- 14. Reasonableness as Palliative <br />Toulmin argues that The Enlightenment made wrong turn.<br />Not all knowledge can or should aspire to mathematical form.<br />Earlier work (Uses of Argument) argued for relaxation of modus ponens in warrants with backing and qualification.<br />Understanding of lingua franca of reasonableness or reason giving.<br />Of course, philosophers hated book (called “anti-logic” book) originally on certain kind of philosophical “rigor” grounds.<br />
- 15. Reflective Practice as Palliative<br />Related argument made in specific context of “professional practice” earlier by Schön.<br />Put math and science in their place as one of many tools.<br />Construct solutions creatively for clients using a variety of practices.<br />But rigorists unlikely to be convinced by words.<br />
- 16. Not Curative: Not Convincing to Rigorists<br />These are reasonable arguments.<br />Unlikely to be persuasive to type I or II rigorists. <br />Those who live or die by symbolic formality or manipulation and application of equations want some red meat.<br />Can we make an argument in equation form to help change their minds?<br />Turn to an earlier argument from a different context.<br />
- 17. An Economy of Models<br />Models live in plane of predictive power (error) and cost (complexity).<br />Scientists & mathematicians interested in new models.<br />Engineers & inventors interested in new technology.<br />
- 18. Originally Invoked as Demarcation<br />Engineering demarcation problem: How to distinguish engineering model use from scientific?<br />Engineers perform in resource limited environments.<br />Subject to economic “laws.”<br />Marshallian analysis at the margins. <br />Marginal cost of modeling will tend to be less than or equal to marginal benefit of modeling (to the technology being developed).<br />ΔB ≥ ΔC<br />
- 19. Implies a Spectrum of Models<br />Low cost, high error high cost, low error.<br />Costs of proper derivation or proper use of science to the right.<br />
- 20. Type I & Type II Rigor Often Uneconomic<br />Given state of the art (SOA) rigor may be too costly to be practical:<br />Formal derivation may be too complex.<br />Scientific laws may not exist.<br />Those demanding “rigor” in a bind.<br />Either they refuse to solve the problem, because of lack of rigor.<br />Or they relax demand for rigor.<br />Either way, inconsistent with professed beliefs.<br />
- 21. Certain Kinds of Discussions Off Limits<br />How can type I or type II rigorist have discussion about engineering education?<br />What are the mathematical objects of engineering education to reason about in type I sense?<br />What are the equations of motion of engineering education to do proper type II rigor?<br />Like plate tectonics problem: Certain kinds of reasoning not permitted.<br />OK, type I & 2 debunked, but is there another sense of engineering “rigor” at work?<br />
- 22. “Rigor” from Other Cultures<br />The Sambia of Papua, New Guinea<br />Initiate boys into adulthood in rigorous process of physical and mental hardship.<br />Similar to those that cults use to brainwash converts.<br />Involves ritual homosexuality between older and younger boys.<br />Engineering education enforces math-science death march, not ritual homesexuality (at UIUC anyway).<br />Sambian Nose Purge<br />
- 23. Third Kind of “Rigor:” Rite of Passage <br />“I endured rigorous program with lots of math and science and they should, too.”<br />Rite of passage: Completion of an arduous or unpleasant task to gain membership in a social grouping.<br />Rites of passage are durable (hazing).<br />Common in professions (medical internship/residency & passing the bar).<br />Means to influence individual through commitment (Cialdini, 2001).<br />
- 24. Modified Rite of Passage <br />Given importance in signaling social membership & commitment, should we eliminate? Probably no.<br />Can we modify rite of passage?<br />Something at the center of what it means to be an engineer:<br />Solve difficult design problem.<br />Demonstrate mettle in field.<br />Is there something practical that would be better than surviving the math-science death march?<br />
- 25. Philosophy as Realignment Tool<br />Have been using philosophy here as tool for achieving conceptual clarity.<br />Other uses. Philosophy as<br />Response to crisis of a creative era. <br />Tool for category error diagnosis.<br />Pedagogy for teaching qualitative reasoning skills to engineers.<br />Competing form of rigor.<br />Status anxiety abatement device.<br />© David E. Goldberg 2009<br />Socrates (470-399 BCE)<br />
- 26. As Pedagogy for Qualitative Reasoning<br /><ul><li>Elsewhere discuss the missing basics:
- 27. Question: Socrates 101.
- 28. Label: Aristotle 101.
- 29. Model conceptually: Hume 101 & Aristotle 102.
- 30. Decompose: Descartes 101.
- 31. Measure: Bacon-Locke 101.
- 32. Visualize/ideate: da Vinci-Monge 101.
- 33. Communicate: Newman 101
- 34. Overcome overemphasis on type I and type II rigor by teaching qualitative reasoning systematically.</li></ul>© David E. Goldberg 2009<br />
- 35. Clinical Trials of Toulmin’s Model<br />Now using Toulmin’s model of argumentation in senior design.<br />Relaxed modus ponens: <br />if p then q (the warrant) <br />with qualification, backing, and exception.<br />Real data uncertain, limited trials, past or competitive practice.<br />Limited time and resources.<br />Tradeoff: improving certain/accuracy or investing elsewhere.<br />
- 36. Competing Rigor & Status Anxiety<br />Wrong turn on rigor was to seek status.<br />Rotter’s distinction internal versus external locus of control:<br />Internal: Appropriate rigor to task.<br />External: Excess rigor to impress “betters.”<br />2 phase process:<br />Philosophy asmethadone for rigor junkies.<br />Philosophy as way to stop worrying about status and focus on being great engineers. <br />© David E. Goldberg 2009<br />
- 37. Summing Up<br />2 types of rigor: derivation & scientific:<br />Type II inconsistent with pure type 1.<br />Both type I & II incomplete.<br />3 arguments: Reasonableness, reflective practice, and economy of modeling.<br />3 type of rigor more interesting: Importance of rites of passage, substitution, not elimination.<br />Philosophy as realignment tool.<br />Code words as defense of paradigm, not an argument.<br />Welcome debate, just not interested in hearing “rigorous,” “not rigorous,” “soft,” as way to shut down discussion.<br />
- 38. More Information<br />Slides: www.slideshare.net/deg511<br />iFoundry: http://ifoundry.illinois.edu<br />iFoundryYouTube: http://www.youtube.com/illinoisfoundry<br />iFoundrySlideShare: http://www.slideshare.net/ifoundry<br />TEE, the book. http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470007230.html<br />Engineering and Technology Studies at Illinois (ETSI) http://www-illigal.ge.uiuc.edu/ETSI<br />Workshop on Philosophy & Engineering (WPE)http://www-illigal.ge.uiuc.edu/wpe<br />© David E. Goldberg 2009<br />

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