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August 22, 2005

The Hole

Part I: Mathematics and Narrative

Apostolos Doxiadis
on last month’s conference on “mathematics and narrative”–

Doxiadis is
describing how talks by two noted mathematicians were related to

“… a sense of a ‘general theory bubbling up’
at the meeting… a general theory
of the deeper relationship of mathematics to narrative….
“

Doxiadis says both talks had “a big hole in the middle.”

“Both began by saying something like: ‘I
believe there is an important connection between story and mathematical
thinking. So, my talk has two parts. [In one part] I’ll tell you a few
things about proofs. [And in the other part] I’ll tell you about
stories.’ …. And in both talks it was in fact implied by a variation
of the post hoc propter hoc, the principle of consecutiveness implying
causality, that the two parts of the lectures were intimately related,
the one somehow led directly to the other.”
“And the hole?”

“This was exactly at the point of the
link… [connecting math and narrative]… There is this very
well-known Sidney Harris cartoon… where two huge arrays of formulas
on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’
And one of the two mathematicians standing before it points at this and
tells the other: ‘I think you should be more explicit here at step
two.’ Both… talks were one half fascinating expositions of lay
narratology– in fact, I was exhilarated to hear the two most purely
narratological talks at the meeting coming from number theorists!– and
one half a discussion of a purely mathematical kind, the two parts
separated by a conjunction roughly synonymous to ‘this is very similar
to this.’ But the similarity was not clearly explained: the hole, you
see, the ‘miracle.’ Of course, both [speakers]… are brilliant men,
and honest too, and so they were very clear about the location of the
hole, they did not try to fool us by saying that there was no hole
where there was one.”

Part II: Possible Worlds

“At times, bullshit can only be countered with superior bullshit.”
– Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

“The concept of possible worlds dates back to a least Leibniz who in his Théodicée
tries to justify the apparent imperfections of the world by claiming
that it is optimal among all possible worlds. Voltaire satirized
this view in his picaresque novel Candide….
Borges’ seminal short story El jardín de senderos que se bifurcan (“The Garden of Forking Paths“) is an early example of many worlds in fiction.”

“Il faut cultiver notre jardin.“– Voltaire

Background:

Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole

Part III: Modal Theology

“‘What is this Stone?’ Chloe asked….
‘…It is told that, when the Merciful One made the worlds, first of all He created that
Stone and gave it to the Divine One whom the Jews call Shekinah, and
as she gazed upon it the universes arose and had being.’”

— Many Dimensions, by Charles Williams, 1931 (Eerdmans
paperback, April 1979, pp.
43-44)

“The lapis was thought of as a unity and therefore often stands
for the prima materia in general.”

— Aion, by C.
G. Jung, 1951 (Princeton paperback, 1979, p. 236)

“Its discoverer was of the opinion that he had produced the
equivalent of the primordial protomatter which exploded into the
Universe.”

— The Stars My Destination, by Alfred
Bester, 1956 (Vintage hardcover, July 1996, p. 216)

“We symbolize
logical necessity

with the box ()