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Raise your level of abstraction
A lot has been written on the differences between Craftsman and Engineer. Recently I came across a simple example by Hofstadter & Sander, that nicely shows the basic difference in thinking. We start with a little exercise:
“Draw a square, a rectangle, a rhombus, and a parallelogram.”
Some people draw a solution as in (a), some draw solution (b). Both are perfectly acceptable in their way:
The latter is an abstraction by constructing the structure of concepts (formally: the concept lattice). Imho, being able to 'navigate' this structure of concepts - that of course looks much more complex for real world subject areas - is what separates the thinking of Engineer and Craftsman.
So long
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yes, think applying math principles plays a central role. Esp. relational maths and logic.
Yes, this sums up much of my opinion as well. Craftsmen are much better at putting things together with what they have in their toolbox. However, many of them have difficulty in leaving the area of their toolbox. Engineers are much more comfortable with moving forward without a toolbox because they have deep conceptual understanding of the domain. I think this deep domain understanding is largely created using abstraction via mathematical principles.
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