Engineers, Models & Thought David E. Goldberg Illinois Foundry for Innovation in Engineering Education University of Illinois at Urbana-Champaign Urbana, Illinois 61801 [email_address]

Engineers Think with Models Engineers think in terms of models. Many different types: physical models, visual models, mental models, and analytical models. Will Rogers theory of modeling: Never met a model I didn’t like. Will Rogers (1879-1935)

Engineers think in terms of models.

Many different types: physical models, visual models, mental models, and analytical models.

Will Rogers theory of modeling: Never met a model I didn’t like.

Engineers Use Models as Tools Engineer model usage is instrumental. Not an end in itself, but used for another end. Scientists and mathematicians build models as an end. Toolmakers to engineers. Engineers use math & science (and many other) tools as instruments or tools to make useful artifacts . Tool usage is subject to economics .

Engineer model usage is instrumental.

Not an end in itself, but used for another end.

Scientists and mathematicians build models as an end. Toolmakers to engineers.

Engineers use math & science (and many other) tools as instruments or tools to make useful artifacts .

Tool usage is subject to economics .

Economics of Modeling Error versus cost of modeling ε , Error C, Cost of Modeling Engineer/Inventor Scientist/Mathematician

Error versus cost of modeling

Spectrum of Models

Marginal Utility of Models Economic model usage: marginal cost less than or equal to marginal benefit to design.  C ≤  B If cost higher than advance in design, thinking is uneconomic. Maybe fun, maybe scientific. Does not advance technology enough to be worthwhile . Alfred Marshall (1842-1924)

Economic model usage: marginal cost less than or equal to marginal benefit to design.

 C ≤  B

If cost higher than advance in design, thinking is uneconomic.

Maybe fun, maybe scientific.

Does not advance technology enough to be worthwhile .

Economy of Thought Essential Terms “engineer” & “scientist” are used loosely. Sometimes “engineers” do science & “scientists” do engineering But economy of intellection helps understand which is doing what when. In real engineering, use thinking process balanced with design goals. Engineering thought is distinctive, partially because of this economic difference. www.ifoundry.uiuc.edu

Terms “engineer” & “scientist” are used loosely.

Sometimes “engineers” do science & “scientists” do engineering

But economy of intellection helps understand which is doing what when.

In real engineering, use thinking process balanced with design goals.

Engineering thought is distinctive, partially because of this economic difference.

Engineers, Models & Thought David E. Goldberg Illinois Foundry for Innovation in Engineering Education University of Illinois at Urbana-Champaign Urbana, Illinois 61801 [email_address]