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adpoe | 8 years ago
It's the same difference between writing mathematical proofs as systems of equations vs. proof by drawing a diagram, or making a visualization.
Proofs can be written using both methods, but if you have a strong command of the written/symbolic vocabulary, it is faster and more succinct.
Put another way: I can describe the landscape of a lush, green Tuscan Countryside--with rolling hills, morning dew, and and crisp feeling of the first rays of sun cutting through the mist--in just a few lines. You get a picture in your head, and it is likely very similar to what was in mine.
Imagine now, that we can't use words. We have to draw pictures. It will take much longer to get the same point across. Language--for certain purposes--is more efficient, and more information dense.
That's my hypothesis/feeling.
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