Wednesday, November 17, 2010

Church Narrative

Filed under: General,Geometry — m759 @ 2:22 AM

Thanks to David Lavery for the following dialogue on the word "narrative" in politics—

"It's like – does this fit into narrative?
It's like, wait, wait, what about a platform? What about, like, ideas?
What about, you know, these truths we hold to be self-evident?
No, it's the narrative."

"Is narrative a fancy word for spin?"

Related material —

Church Logic (Log24, October 29) —

  What sort of geometry
    is the following?

IMAGE- The four-point, six-line geometry


"What about, you know, these truths we hold to be self-evident?"

Some background from Cambridge University Press in 1976 —


Commentary —

The Church Logic post argues that Cameron's implicit definition of "non-Euclidean" is incorrect.

The four-point, six-line geometry has as lines "all subsets of the point set" which have cardinality 2.

It clearly satisfies Euclid's parallel postulate.  Is it, then, not  non-Euclidean?

That would, according to the principle of the excluded middle (cf. Church), make it Euclidean.

A definition from Wikipedia that is still essentially the same as it was when written on July 14, 2003

"Finite geometry describes any geometric system that has only a finite number of points. Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points…."

This definition would seem to imply that a finite geometry (such as the four-point geometry above) should be called non -Euclidean whether or not  it violates Euclid's parallel postulate. (The definition's author, unlike many at Wikipedia, is not  anonymous.)

See also the rest  of Little Gidding.

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