[avmich]

> this class of activity privileges the concrete over the abstract

Agree, however here are other considerations.

Symbolic analysis won over words for tasks like x^2+10x=39 , so advantages like these are not absolute.

Math notation continue to evolve - e.g., APL language invention attempted strict inline notation. I'd say instead of written "word" a generic form of communications is free-form drawing - including schemas, diagrams, graphs, blueprints. Of course here we use pen and paper, and smart computers would be careful not to get in the way of what we can do "with the speed of thought". E.g., the oscillator schema which Bret displayed and then analyzed had to be first created, and to "record a thought" scribbling on paper a shape of a transistor is likely faster than, say, dragging it from an electronic components library, which first has to be ready for that.

When you don't know a symbolic method, you use specific numbers in specific examples, look into many examples and then generalize - moving to symbols. When you already know an appropriate symbolic method, you can switch gears and instead of "specific" numbers use "specific" symbolic manipulations.