Subject
On Symmetry II
From
Date
Body
Dear Jansy,
Thanks for your apology.
The essence of symmetry in the mathematical (as opposed to the
colloquial) sense is a non-identical 1-to-1 transformation of a
structured set onto itself in a way that preserves structure. So this
may include reflective, translational, dilatational and rotational
symmetry, but as Hermann Weyl says in his fascinating book "Symmetry",
"Straight line and circle are limiting cases of the logarithmic spiral,
which arise when in the combination rotation-plus-dilatation one of the
two components happens to be the identity."
So you're quite right that, for example, the shell of Nautilus, as Weyl
says, shows logarithmic spiral symmetry.
What I had in mind was that the Hegelian idea of dialectical reciprocity
is usually thought of as being debased by attempts to reduce it to
"symmetry". Just as Levinas objected that Buber's "I-Thou" relation was
too "symmetrical", and did not do justice to the utter otherness of the
other.
Best wishes,
Anthony
Search the archive: http://listserv.ucsb.edu/archives/nabokv-l.html
Contact the Editors: mailto:nabokv-l@utk.edu,nabokv-l@holycross.edu
Visit Zembla: http://www.libraries.psu.edu/nabokov/zembla.htm
View Nabokv-L policies: http://web.utk.edu/~sblackwe/EDNote.htm
Thanks for your apology.
The essence of symmetry in the mathematical (as opposed to the
colloquial) sense is a non-identical 1-to-1 transformation of a
structured set onto itself in a way that preserves structure. So this
may include reflective, translational, dilatational and rotational
symmetry, but as Hermann Weyl says in his fascinating book "Symmetry",
"Straight line and circle are limiting cases of the logarithmic spiral,
which arise when in the combination rotation-plus-dilatation one of the
two components happens to be the identity."
So you're quite right that, for example, the shell of Nautilus, as Weyl
says, shows logarithmic spiral symmetry.
What I had in mind was that the Hegelian idea of dialectical reciprocity
is usually thought of as being debased by attempts to reduce it to
"symmetry". Just as Levinas objected that Buber's "I-Thou" relation was
too "symmetrical", and did not do justice to the utter otherness of the
other.
Best wishes,
Anthony
Search the archive: http://listserv.ucsb.edu/archives/nabokv-l.html
Contact the Editors: mailto:nabokv-l@utk.edu,nabokv-l@holycross.edu
Visit Zembla: http://www.libraries.psu.edu/nabokov/zembla.htm
View Nabokv-L policies: http://web.utk.edu/~sblackwe/EDNote.htm