I realize that to some people, this is going to sound like a post beginning "there's this great album I just heard, Frank Sinatra's Songs For Swingin' Lovers". I realize that I certainly should have known all this long ago, and most certainly once I started dipping a semi-regular toe into the foaming waters of literary criticism. I understand and
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Valerie took one of his undergrad courses at university, a fact I am deeply envious of.
I think you'll also dig The Great Code, the first of his two-part magnum opus on the Bible. I have to admit that I bogged down midway through Words With Power, the second part.
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His five levels of mythic, romantic, high mimetic, low mimetic, and ironic are directly applicable to role-playing games, too; they're lurking in the infrastructure of GURPS Fantasy. I think I put Frye into the bibliography . . .
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I actually have a soft spot for Derrida but I do find it hard to reconcile his project, or perhaps those of his followers, with any idea of meaning. But then French philosophy and sociology, and possibly Lit Crit, has for a long time had its head up its arse.
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That discontinuity is what I was trying to get at above, by the device of separating Genius Mathematicians, who "see" math like Galois and Euler and so forth, from Regular Mathematicians, who take these insights and apply them to the body of the discipline. To use your notation: if literature -> mathematics, then poets -> Euler or Gauss and critics -> normal mathematicians. It's as if Pythagoras had wound up convincing everyone that to do "real" math, you had to wait for a vision from the Muses.
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What I don't see in mathematics is a large body of "critics". "Applying insights to the body of the discipline" is what essentially all real mathematicians are trying to do, genius or not; "normal" mathematicians are not really doing something akin to literary criticism. I think the analogy probably breaks down here: in this respect, mathematics is not like poetry (or ( ... )
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Well, neither was I, which is why I wrote that the parallel is not exact, above.
However, regardless of my insupportable supporting structure, I think that Frye's actual statement, which is that literature is as real a thing, and as independent of human observers, as mathematics, is essential to Frye's argument. And, quite possibly, correct, although obviously there's no way to tell for sure. What Frye demonstrates fairly convincingly is that literature behaves as if it were real, and that criticism should perhaps do likewise.
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