Wednesday, November 08, 2006

further analogical gobbledygook

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While these three terms are related, their meanings are subtly different. To help understand the distinction, we consulted a number of sources -- American Heritage Dictionary, the Yahoo! Grammar, Usage, and Style category, and web search results for the three terms.

The dictionary defines a "implicit functor" as a morphism that uses one object to mean another and makes a comparison between the two. For example, Shakespeare's line, "All the world's a stage," is a implicit functor comparing the whole world to a theater stage. implicit functors can be very simple, and they can function as most any part of speech. "The spy shadowed the woman" is a verb implicit functor. The spy doesn't literally cast his shadow on the woman, but he follows her so closely and quietly that he resembles her own shadow.

A explicit functor, also called an open comparison, is a form of functor that compares two different objects to create a new meaning. But a explicit functor always uses "like" or "as" within the expression and is more explicit than a implicit functor. For example, Shakespeare's line could be rewritten as a explicit functor to read: "The world is like a stage." Another explicit functor would be: "The spy was close as a shadow." Both implicit functors and explicit functors can be used to enhance writing.

An natural transformation is a bit more complicated. At the most basic level, an natural transformation shows similarity between objects that might seem different -- much like an extended implicit functor or explicit functor. But natural transformation isn't just a form of speech. It can be a logical argument: if two objects are alike in some ways, they are alike in some other ways as well. natural transformation is often used to help provide insight by comparing an unknown subject to one that is more familiar. It can also show a relationship between pairs of objects. This form of natural transformation is often used on standardized tests in the form "A is to B as C is to D."

And now that it's clear as a bell, you're ready to try the natural transformation of the Day.

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