Engineering Rigor and Its Discontents: Philosophical Reflection as Curative to Math-Physics Envy

Engineering Rigor and Its Discontents: Philosophical Reflection as Curative to Math-Physics Envy
David E. GoldbergIllinois Foundry for Innovation in Engineering Education
University of Illinois at Urbana-Champaign
Urbana, IL 61801 USA
deg@illinois.edu

Engineering Use of Term “Rigor”
Engineers, particularly academics, use interesting language.
“Rigor” as term of approbation.
“That’s a rigorous analysis” or “He had a rigorous education.”
Absence of “rigor” is bad: “Those leadership and teamwork classes are not sufficiently rigorous to be taught in the College of Engineering.”
“Soft” as synonymous with “not rigorous:” “We’ll accept those soft courses in a rigorous curriculum over my dead body.”
Usage is kind of informal demarcation by pejorative.
Critically examine these terms to
better understand different senses of usage,
uncover inconsistencies in usage, and
determine ways to move forward.

Roadmap
Rigor, the word & its conventional meanings.
A short history of rigor in engineering education.
Two senses of “rigor” in engineering:
In derivation.
In application of established scientific principles.
The economics of engineering modeling.
Reasonableness and reflective practitioners.
A third sense: “Rigor” as rite of passage.
Beyond informal demarcation: Rethinking the math-science death march.

Rigorous, the Word
Rigorous:
extremely thorough or accurate.
(of a rule, system, etc.) strictly applied or adhered to.
adhering strictly to a belief, opinion, or system.
harsh or severe: rigorous military training.
From the Latin rigor = stiffness.
Use rigor or rigorous (without quotations) in these senses & “rigor” as referring to the engineering usage of term.

A Short History of Engineering Rigor
Uses of rigor in technology are long and complex and in part justified:
Premodern technology had rigorous elements rooted in mathematics (a2 + b2 =c2)
Military engineering and origins of the notion of discipline. (Toulmin, 2001).
L’EcolePolytechnique as steeped in the best science of the time (Grayson, 1993).
Maxwell’s equations and the birth of electrical engineering (Layton, 1971).
Rigor as separating “engineering” from “craft.” (Davis, 1998).
Rigor as necessary to catch up with mathematicians and physicists post World War II (Grinter, 1955).
2types:
Rigor as necessary to task at hand.
Rigor as status enhancement device .

Early Uses of Rigor Largely Utilitarian
Premoderns used math because it was useful.
Surveying, architecture, military engineering relied heavily on geometry and trigonometry.
Heady days post-Newton/Leibniz power of calculus and physics simply stunning.
Injection of the best math in L’EcolePolytechnique continues that cultural tradition.
Electrical engineering as field essentially enabled by Maxwell’s equations.
Sir Isaac Newton (1643-1727)

Later Uses: Less Utility  More Status
Shift starts to take place with professional strivings.
Grand era of big artifacts (big bridges, structures, railroads, radio, steamships, & airplanes).
Big changes in science (relativity & quantum physics).
WW2: Physicists “won the war.” Engineers must “catch up.”
1955 Grinter report: Engineering as applied science to detriment of engineering, engineering education and engineers.

Two Senses of Engineering Rigor
Common types of engineering rigor:
Type 1: Mathematical rigor in derivation.
Type 2: Lawful scientific rigor.
Critically examine both.
Are they mutually consistent?
Are they self-contained tools of engineering thought?

Type I: Rigor in Derivation
Elements:
Start from a set of premises.
Use rules of logic.
Proceed to formally “correct” and “true” conclusion.
Good news and bad news: Nothing “added” to premises.
Conclusion follows directly from premises.
Toulmin: Not a good model of the full breadth of human argument. Return to that view in a moment.

Type II: Lawful Scientific Rigor
Elements:
Start from accepted equations of science (Newton’s laws, Maxwell’s equations, etc.)
Apply type I rigor.
Straightforward enough.
Problems:
Type I rigorist objection to type II rigor.
The plate tectonics problem.

Type II Inconsistent with Type I
Newton’s laws not a product of type I rigor.
Inverse square law in some sense a lucky guess.
Cartesians hated it.
Causation as merely “constant conjunction” (Hume).
No starting from premises.
No formal derivation: A curve fit to extant astronomical data.
A type I rigorist should object: Key elements of result (Newton’s laws) not the result of type I rigor.

Plate Tectonics: Type II Rigor Incomplete
Set inconsistency with Type I aside.
Type II rigorist insists on scientific laws in mathematical form.
What about plate tectonics?
Plate tectonics was revolution in geology.
Unified many qualitative geological phenomena from earthquakes to volcanoes.
Where are the equations?
Formal reasoning can proceed from linguistic propositions.
Type II rigorist rejects these as “merely words” and not “rigorous.”

Are These Straw Men?
Are these categories straw men?
Reasonable people would never insist on only being formal or only reasoning from mathematical laws.
But look at behavior.
Term “rigor” is used by engineering rigorists to
censor discussion (that’s not a proper model)
or reject teaching of certain topics (no “soft” stuff here).
They mean it!! Censorship or rejection of topic in classroom is sign of their seriousness.
Two answers in words & one answer in equations.

Reasonableness as Palliative
Toulmin argues that The Enlightenment made wrong turn.
Not all knowledge can or should aspire to mathematical form.
Earlier work (Uses of Argument) argued for relaxation of modus ponens in warrants with backing and qualification.
Understanding of lingua franca of reasonableness or reason giving.
Of course, philosophers hated book (called “anti-logic” book) originally on certain kind of philosophical “rigor” grounds.

Reflective Practice as Palliative
Related argument made in specific context of “professional practice” earlier by Schön.
Put math and science in their place as one of many tools.
Construct solutions creatively for clients using a variety of practices.
But rigorists unlikely to be convinced by words.

Not Curative: Not Convincing to Rigorists
These are reasonable arguments.
Unlikely to be persuasive to type I or II rigorists.
Those who live or die by symbolic formality or manipulation and application of equations want some red meat.
Can we make an argument in equation form to help change their minds?
Turn to an earlier argument from a different context.

An Economy of Models
Models live in plane of predictive power (error) and cost (complexity).
Scientists & mathematicians interested in new models.
Engineers & inventors interested in new technology.

Originally Invoked as Demarcation
Engineering demarcation problem: How to distinguish engineering model use from scientific?
Engineers perform in resource limited environments.
Subject to economic “laws.”
Marshallian analysis at the margins.
Marginal cost of modeling will tend to be less than or equal to marginal benefit of modeling (to the technology being developed).
ΔB ≥ ΔC

Implies a Spectrum of Models
Low cost, high error  high cost, low error.
Costs of proper derivation or proper use of science to the right.

Type I & Type II Rigor Often Uneconomic
Given state of the art (SOA) rigor may be too costly to be practical:
Formal derivation may be too complex.
Scientific laws may not exist.
Those demanding “rigor” in a bind.
Either they refuse to solve the problem, because of lack of rigor.
Or they relax demand for rigor.
Either way, inconsistent with professed beliefs.

Certain Kinds of Discussions Off Limits
How can type I or type II rigorist have discussion about engineering education?
What are the mathematical objects of engineering education to reason about in type I sense?
What are the equations of motion of engineering education to do proper type II rigor?
Like plate tectonics problem: Certain kinds of reasoning not permitted.
OK, type I & 2 debunked, but is there another sense of engineering “rigor” at work?

“Rigor” from Other Cultures
The Sambia of Papua, New Guinea
Initiate boys into adulthood in rigorous process of physical and mental hardship.
Similar to those that cults use to brainwash converts.
Involves ritual homosexuality between older and younger boys.
Engineering education enforces math-science death march, not ritual homesexuality (at UIUC anyway).
Sambian Nose Purge

Third Kind of “Rigor:” Rite of Passage
“I endured rigorous program with lots of math and science and they should, too.”
Rite of passage: Completion of an arduous or unpleasant task to gain membership in a social grouping.
Rites of passage are durable (hazing).
Common in professions (medical internship/residency & passing the bar).
Means to influence individual through commitment (Cialdini, 2001).

Modified Rite of Passage
Given importance in signaling social membership & commitment, should we eliminate? Probably no.
Can we modify rite of passage?
Something at the center of what it means to be an engineer:
Solve difficult design problem.
Demonstrate mettle in field.
Is there something practical that would be better than surviving the math-science death march?

Philosophy as Realignment Tool
Have been using philosophy here as tool for achieving conceptual clarity.
Other uses. Philosophy as
Response to crisis of a creative era.
Tool for category error diagnosis.
Pedagogy for teaching qualitative reasoning skills to engineers.
Competing form of rigor.
Status anxiety abatement device.
© David E. Goldberg 2009
Socrates (470-399 BCE)

As Pedagogy for Qualitative Reasoning

Elsewhere discuss the missing basics:
Question: Socrates 101.
Label: Aristotle 101.
Model conceptually: Hume 101 & Aristotle 102.
Decompose: Descartes 101.
Measure: Bacon-Locke 101.
Visualize/ideate: da Vinci-Monge 101.
Communicate: Newman 101
Overcome overemphasis on type I and type II rigor by teaching qualitative reasoning systematically.

Clinical Trials of Toulmin’s Model
Now using Toulmin’s model of argumentation in senior design.
Relaxed modus ponens:
if p then q (the warrant)
with qualification, backing, and exception.
Real data uncertain, limited trials, past or competitive practice.
Limited time and resources.
Tradeoff: improving certain/accuracy or investing elsewhere.

Competing Rigor & Status Anxiety
Wrong turn on rigor was to seek status.
Rotter’s distinction internal versus external locus of control:
Internal: Appropriate rigor to task.
External: Excess rigor to impress “betters.”
2 phase process:
Philosophy asmethadone for rigor junkies.
Philosophy as way to stop worrying about status and focus on being great engineers.

Summing Up
2 types of rigor: derivation & scientific:
Type II inconsistent with pure type 1.
Both type I & II incomplete.
3 arguments: Reasonableness, reflective practice, and economy of modeling.
3 type of rigor more interesting: Importance of rites of passage, substitution, not elimination.
Philosophy as realignment tool.
Code words as defense of paradigm, not an argument.
Welcome debate, just not interested in hearing “rigorous,” “not rigorous,” “soft,” as way to shut down discussion.

More Information
Slides: www.slideshare.net/deg511
iFoundry: http://ifoundry.illinois.edu
iFoundryYouTube: http://www.youtube.com/illinoisfoundry
iFoundrySlideShare: http://www.slideshare.net/ifoundry
TEE, the book. http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470007230.html
Engineering and Technology Studies at Illinois (ETSI) http://www-illigal.ge.uiuc.edu/ETSI
Workshop on Philosophy & Engineering (WPE)http://www-illigal.ge.uiuc.edu/wpe