Yes, but words are essential for mathematical definitions. The latter exist only within a very specific conceptual framework; words are just as much a part of math as they are of language, as far our conceptualization of it is concerned. (A life-long question I wonder is to what extent math is created vs discovered, but that's a separate discussion).
Not quite. Words form the base from which we ascend when doing math and descend when doing poetry -- in either case you have to start from words, but the two activities are reaching in different directions. Poetry is the art of abstracting subtle perceptions up to the level of conceptual articulation, while math is the science of abstracting concepts up to the level of form. The reason the former feels more like creation and the latter more like discovery is the difference in degrees of freedom -- there's as much idiosyncratic elbow room in poetry as there is variation in life experience and temperament, but math by definition tends toward unity.
"The reason the former feels more like creation and the latter more like discovery is the difference in degrees of freedom"?
Who said they feel like that? Maybe to you..
"but math by definition tends toward unity."
What do you mean by this? Unity in the sense that the mathematics community has generally agreed upon standards for what certain words mean? Sure, that's true enough; though they've ultimately seemed kind of arbitrary to me, like any construct (becomes more obvious when you do weird things like defining the real numbers from the ground up and talking about different kinds of infinities), and Goedel has quite a lot to say about the natural limitations of most types of axioms, i.e. incompleteness.
"the two activities are reaching in different directions."
Hmm..sounds like an awfully concrete judgment to make about two fields which are highly creative and can be very subjective :)
You say that like clearly articulating a thesis is a bad thing.
As for who says, patent law does for one thing. We can quibble over the correctness of IP law but the intuitions underlying what's patentable and what isn't are a fact, not something I'm making up.
Re: unity, I mean more than that. The notation is based on a combination of historical whims and practical functionality, but the operations and relations they stand for aren't -- quite the opposite, they're as constrained and timeless as anything known to man can be. That's why they're so useful, and why there's the need for agreement on semantics -- to enforce referential integrity and transparency, since the subject matter of math requires so much more precision than the usual sorts of objects natural language evolved initially to deal with.
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Who said they feel like that? Maybe to you..
"but math by definition tends toward unity."
What do you mean by this? Unity in the sense that the mathematics community has generally agreed upon standards for what certain words mean? Sure, that's true enough; though they've ultimately seemed kind of arbitrary to me, like any construct (becomes more obvious when you do weird things like defining the real numbers from the ground up and talking about different kinds of infinities), and Goedel has quite a lot to say about the natural limitations of most types of axioms, i.e. incompleteness.
"the two activities are reaching in different directions."
Hmm..sounds like an awfully concrete judgment to make about two fields which are highly creative and can be very subjective :)
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As for who says, patent law does for one thing. We can quibble over the correctness of IP law but the intuitions underlying what's patentable and what isn't are a fact, not something I'm making up.
Re: unity, I mean more than that. The notation is based on a combination of historical whims and practical functionality, but the operations and relations they stand for aren't -- quite the opposite, they're as constrained and timeless as anything known to man can be. That's why they're so useful, and why there's the need for agreement on semantics -- to enforce referential integrity and transparency, since the subject matter of math requires so much more precision than the usual sorts of objects natural language evolved initially to deal with.
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