Monday, April 30, 2007

spring

It finally feels like spring has arrived here in Worcester. The flowers are blooming from the trees, in great white poofy and pink blossoms. After my first winter here on the East Coast, it feels glorious to stand outside and just soak in the sun.

This semester is finally over. I still feel a little unsatisifed with my performance in Dan's logic class; the simplest things trip me up. Ever time I do a logic session, I come out feeling mentally pummeled. Brain squish just like grape! But not because the material's necessarily difficult, but just that I come in with so much mental confusion.

For example, I got confused with the concepts of Skolem Hull and the Herbrand universe, which are different concepts. The Skolem Hull submodel only contains points that are interpretations of all the nameable elements of a language. A Herbrand universe, on the other hand, is a set containing only the nameable terms themselves. A hash collision.

We talked about models that include "junk" (elements that can't be named by terms) and "confusion" (named terms that go to the same element). It's funny, though, how the terms of logic are adopted by other subcultures, things like "compactness" and the "no junk, no confusion" properties, and in ways that are totally different from the definitions in mathematical logic.

I should probably spend a few more days in the sun and try to weed out the junk and confusion in myself, the ill-formed and redundant thoughts.

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