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by pnathan
4052 days ago
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Ah, this one again! At the specific level, I don't consider this strongly useful information being presented: the examples are generally more useful when represented in math in the usual abstractions. At the meta level, I remain of the belief that this class of activity privileges the concrete over the abstract, and the instance over the general. Having specific examples is useful, but they remain specific. I remain persuaded that symbolic analysis via mathematics and the written word beat all other forms of communication in ability to express complex concepts. |
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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.