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- 1. Engineering & Models:Hint: Real Engineers Use More than Just Equations<br />David E. GoldbergIllinois Foundry for Innovation in Engineering Education University of Illinois at Urbana-ChampaignUrbana, Illinois 61801 USAdeg@illinois.edu<br />
- 2. Engineering Modeling: Education vs. Practice<br />Math-science march in first two years of engineering education is misleading.<br />Imples: Meaningful models come from math & science alone.<br />Young engineers confused on first jobs.<br />2 problems:<br />Don’t use appropriate models.<br />Don’t think they’re doing engineering.<br />Need better understanding of types & breadth of engineering modeling. <br />
- 3. Roadmap<br />What is a model?<br />Legacy of Newton: equations versus words & images.<br />Matching models to problems.<br />What are models used for.<br />Tech visionaries as broad spectrum modelers.<br />Toulmin’s model of arguments as unifying approach.<br />Return to flour physics.<br />
- 4. What is a Model?<br />A model is a system that represents one or more facets of some other system.<br />Typical model facet combinations:<br />Drawing or solid model geometry.<br />Prototype geometry & operation.<br />Graph variation of variable with independent variable(s) (time, space, etc.).<br />Equilibrium equation select state variables at steady state.<br />Dynamic equation variation of select state variables with time.<br />Computer simulation similar to equations.<br />
- 5. Models & Engineering Knowledge<br />Models capture what engineers know about what exists or could exist.<br />Study of knowledge: Epistemology.<br />Study of existence: Ontology.<br />What engineers know and how they know it? <br />Walter Vincenti’sbook takes examples from aeronautical history.<br />Discusses distinctions between engineering knowledge and scientific-mathematical knowledge.<br />
- 6. Newton & Engineering Models<br />Invented calculus (so did Leibniz).<br />In 1687 published PhilosophiaeNaturalis Principia Mathematica.<br />Changed world.<br />Remarkable agreement between equations & measurements.<br />Many engineering models use his equations (F=ma) directly.<br />Represents an ideal of scientific knowledge that others attempt to emulate.<br />Highest status accorded to those who use these kinds of models.<br />Does status = efficacy?<br />Sir Isaac Newton (1643-1727)<br />
- 7. Words, Language and Engineering Models<br />Newton-style models dominate engineering equation.<br />Engineers often use natural language in modeling.<br />Many first models are verbal.<br />Types of verbal models:<br />Single word or noun phrase.<br />Description of an object/process.<br />Feature list.<br />Dimension list.<br />Set of engineering specifications, standards, or claims.<br />
- 8. Images and Engineering Modeling<br />History of drawings and visual representations of engineered objects is long.<br />Downgrading of engineering visualization and drawing since Cold War.<br />Ferguson’s book argues this was/is educational mistake.<br />
- 9. Connection to the Napkin<br />Diagrams can be models.<br />Drawings can be models.<br />The Back of the Napkin connects visual thinking and verbal thinking in important way.<br />
- 10. How to Match Models to Engin Problems<br />What characterizes an appropriate model in engineering?<br />What do you think?<br />Take out a piece of paper and write down 3 attributes that suggest you have a good model.<br />2 minutes.<br />
- 11. An Economy of Models<br />Engineers think in terms of models.<br />Have many models with different precision-accuracy and different costs.<br />Can we distinguish appropriate engineering model usage from that of scientist?<br />The economics of modeling. <br />Engineers use models in economic context model usage must support objectives within available resources.<br />
- 12. Fundamental Modeling Tradeoff<br />Engineer/Inventor<br />ε, Error<br />Scientist/Mathematician<br />C, Cost of Modeling<br />Error versus cost of modeling<br />
- 13. Spectrum of Models<br />
- 14. What Are Models Good For?<br />Many uses for models:<br />Description: describe the ways things are (were).<br />Prediction: describe the ways things will be.<br />Prescription: describe the way things should be. <br />Key variables: time and change.<br />Usually assumes have extant object to model.<br />
- 15. Research on Tech Visionaries as Clue<br />Helpful to look at extreme exemplars of success.<br />Price, Vojak, & Griffin have done work on tech visionaries (TVs).<br />TV creates bottom line revenue from new products & services.<br />TVs are consummate broad-spectrum modelers.<br />Use qualitative-quantitative models as necessary to bring monster products/services to market.<br />Ray Price<br />
- 16. Key Distinction: Imagined vs. Existing<br />Modeling of imagined or desired objects versus extant objects (recall category creatory vs. enhancer).<br />To model imagined or desired objects, what can we draw upon?<br />Existing objects that fail in some regard.<br />Similar or related objects.<br />Analogically related objects.<br />Creatively concocted objects.<br />Problem of the tabula rasa: How to model that which does not exist.<br />In category creation, more modeling will be to the left (qualitative versus quantitative).<br />Category enhancement: improvements require more precision. More modeling to the right (quant over qual).<br />
- 17. How can we model the burnt-flour-as-mold problem?<br />Newton’s laws?<br />Need framework to tie different models together.<br />Back to the Tortilla Factory <br />17<br />
- 18. Help from Argumentation Theory<br />1958 book by philosopher Stephen Toulmin formed basis of argumentation theory.<br />How do people really make arguments?<br />How do people give reasons for what they think or do?<br />Form of reasoning ties together formal and informal engineering reasoning.<br />
- 19. Formal Reasoning: Logic<br />Modus ponens (modus ponendo ponens: mode that affirms by affirming): <br />if pthen q<br />pis true<br />thereforeqis true<br />Method of mathematical logic & formal reasoning.<br />Note: Once premises and rules in place, formal logic derives conclusions mechanistically.<br />Aristotle (384-322 BCE)<br />
- 20. Toulmin: Elements of a Human Argument<br />Like modus ponens:<br />Claim. A single statement advanced for the adherence of others.<br />Grounds. A statement about persons, conditions, events, or things that says support is available to provide a reason for a claim.<br />Warrant. A general statement that justifies using the grounds as a basis for the claim<br />Backing. Any support (specific instance, statistics, testimony, values, or credibility) that provides more specific data for the grounds or warrant.<br />Qualifier. A statement that indicates the force of the argument (words such as certainly, possibly, probably, usually, or somewhat).<br />Warrants can be generalizations, cause, sign, analogy, authority.<br />Backing can be anecdote, stats, testimony, credibility, and values.<br />Rieke, R. D & Sillars, M. O. (1997). Argumentation and critical decision making. New York: Longman.<br />
- 21. Back to the Tortillas: Burnt Flour Model<br />Grounds. Dusting flour is spread onto the moving dough on a continuous tortilla line.<br />Claim. Burnt black flour deposits is mistaken for mold, resulting in quality complaints<br />Warrant. Excess flour can become airborne and burn in the oven, deposit on tortilla.<br />Qualifier. Sometimes<br />Backing. Client story & increased flour results in increased spot problem.<br />
- 22. Tradeoff: Improve Backing or Solve Problem<br />In resource limited environment, often face decision:<br />Should you improve warrant and backing?<br />Or should you work on solving the problem?<br />Difficult choice: If you assume correctness of warrant/backing & you are wrong, will it prevent you from solving problem. <br />In tortilla problem students took explanation as true because it didn’t affect investigation.<br />
- 23. Summary<br />Engineering students are convinced that math and physics are the main (only?) tools of engineering.<br />Real engineers use a spectrum of models from qualitative to quantitative.<br />Economy of modeling separates engineering from scientific practice.<br />Toulmin’s model of arguments introduced & example from flour physics given.<br />
- 24. Bottom Line<br />Modeling is critical engineering activity, but don’t let emphasis on math-science mislead you.<br />Great engineers and tech visionaries are broad-spectrum modelers.<br />Use simplest models that will advance design objectives (economy of modeling).<br />Unify models by using Toulmin’s model of arguments & use explicitly to tradeoff model improvement vs. design.<br />

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