During the process of stepwise refinement, a notation which is natural to the problem in hand should be used as long as possible.
With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may, in effect, be used as a patient, precise, and knowledgeable "native speaker" of mathematical notation.
One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations.
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.
This ambiguity is another example of a growing problem with mathematical notation: There aren't enough squiggles to go around.
I often say that Bernhard, W. G. Sebald, and Javier Marías are my stylistic holy trinity, prose writers who amaze me with their notation of consciousness and voice.
All my paintings are usually done in drawing form, very small. I make notations in drawings first, and then I make a collage for color. But drawing is always my notation.
What happens with notation is that it reduces things to a language which isn't necessarily appropriate to them. In the same way that words do, you get a much cruder version of what was actually intended.
The process of writing has something infinite about it. Even though it is interrupted each night, it is one single notation.
It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour.
Saying directors don't write because they don't type is very wrong, it's like saying Dylan doesn't write music because he doesn't write notation.
It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot: but that hardly deserves the names of thought. It only becomes possible at all after the mathematical notation has, as a result of genuine thought, been so developed that it does the thinking for us, so to speak.
I wrote music as soon as I knew notation.
Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [. . . ] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [. . . ] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.
