Saturday, January 6, 2007

Saturday January 6, 2007

Filed under: General,Geometry — m759 @ 10:31 AM

An Epiphany
for the Birthday
of E. L. Doctorow,
Author of
City of God

(Doctorow wrote about
New York. A city more
closely associated with
God is Jerusalem.)


On the morning of January 2 this year, inspired by Sambin’s “basic picture,” I considered an entry dealing with Galois lattices (pdf).  This train of thought was halted by news of the death earlier that morning of Teddy Kollek, 95, a founder of the Israeli intelligence service and six-term mayor of Jerusalem. (This led later to the entry “Damnation Morning“– a reference to the Fritz Leiber short story.)

This morning’s entry reboards the Galois train of thought.

Here are some relevant links:

Galois Connections (a French weblog entry providing an brief overview of Galois theory and an introduction to the use of Galois lattices in “formal concept analysis“)

Ontology (an introduction to formal concept analysis linked to on 3/31/06)

One motive for resuming consideration of Galois lattices today is to honor the late A. Richard Newton, a pioneer in engineering design who died at 55– also on Tuesday, Jan. 2, the date of Kollek’s death.  Today’s New York Times obituary for Newton says that “most recently, Professor Newton championed the study of synthetic biology.”

A check of syntheticbiology.org leads to a web page on– again– ontology.

For the relationship between ontology (in the semantic-web sense) and Galois lattices, see (for instance)

Knowledge Organisation and Information Retrieval Using Galois Lattices” (ps) and its references.

An epiphany within all this that Doctorow might appreciate is the following from Wikipedia, found by following a link to “upper ontology” in the syntheticbiology.org ontology page:

  • There is no self-evident way of dividing the world up into concepts.
  • There is no neutral ground that can serve as a means of translating between specialized (lower) ontologies.
  • Human language itself is already an arbitrary approximation of just one among many possible conceptual maps. To draw any necessary correlation between English words and any number of intellectual concepts we might like to represent in our ontologies is just asking for trouble.

Related material:

The intellectual concepts
mentioned by Richard Powers
at the end of tomorrow’s
New York Times Book Review.
(See the links on these concepts
in yesterday’s “Goldberg Variation.”)

See also Old School Tie.

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