No worries. The maps are intended, actually, for folks who wouldn't necessarily recognize much beyond the big landmarks. E.g., for the rings, I'd imagine the interested non-mathematician would only recognize fields, rings, commutative rings, and possibly Boolean rings or Kleene algebras if they're computer scientists. In refining the maps since I started them, I learned a whole lot about non-associative algebra and about ring-theory proper (i.e., what lies between rings and fields). So while I started with more than the bare landmarks, even I didn't used to recognize everything there.
In addition to the terminological issues I mentioned in the first post, another goal is just to show the breadth of the world. Interested non-mathematicians tend not to explore the landscape very much. But is that due to lack of knowledge? or due to rating the received knowledge too highly, and not realizing they're allowed to explore on their own? I think, when people's horizons are narrow, the idea of expanding those horizons doesn't even emerge, or if it is conceived then it's something for the brave and adventurous to do. But as people's horizons grow wider, they begin to realize that it's okay to eschew the well-worn path between cities, and slowly they begin to wonder: what's beyond that next hill?
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Date: 2012-12-24 01:49 am (UTC)From:In addition to the terminological issues I mentioned in the first post, another goal is just to show the breadth of the world. Interested non-mathematicians tend not to explore the landscape very much. But is that due to lack of knowledge? or due to rating the received knowledge too highly, and not realizing they're allowed to explore on their own? I think, when people's horizons are narrow, the idea of expanding those horizons doesn't even emerge, or if it is conceived then it's something for the brave and adventurous to do. But as people's horizons grow wider, they begin to realize that it's okay to eschew the well-worn path between cities, and slowly they begin to wonder: what's beyond that next hill?