Content-Type: message/rfc822 Date: Fri, 29 Sep 2006 15:51:37 -0400 From: To: Subject: Re: [NABOKV-L] On symmetry II Mime-Version: 1.0 Content-Type: multipart/mixed; boundary="=__Part10344559.1__=" --=__Part10344559.1__= Content-Type: multipart/alternative; boundary="=__Part10344559.2__=" --=__Part10344559.2__= Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit In a message dated 29/09/2006 20:06:58 GMT Standard Time, jansy@aetern.us writes: I misread your statements and generalized what had been limited to a special context. Sorry. I had the impression you ascribed symmetry (and "obsessive patterning") mainly to VN's unreliable narrators and not to VN himself. Stadlen wrote: " VN did (in Strong Opinions, or was it Lectures on Literature, or Speak Memory, or perhaps all three?) praise the Hegelian-dialectical spiral as something that meant much to him. That is something different from either symmetry or circularity." I'm a bit confused with what the term "symmetry" means: If someone with mathematical abilities could correct me here: I don't think Symmetry only applies to mirror-like reflections or doublings. Wouldn't the regularities of, say, a spiral shell or caracole or any helicoidals represent one kind of "symmetry"? 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 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 --=__Part10344559.2__= Content-Type: text/html; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Description: HTML

In a message dated 29/09/2006 20:06:58 GMT Standard Time, jansy@aetern.us writes:

I misread your statements and generalized what had been limited to a special context. Sorry.
I had the impression you ascribed symmetry (and "obsessive patterning") mainly to VN's unreliable narrators and not to VN himself.

Stadlen wrote: " VN did (in Strong Opinions, or was it Lectures on Literature, or Speak Memory, or perhaps all three?) praise the Hegelian-dialectical spiral as something that meant much to him. That is something different from either symmetry or circularity."
I'm a bit confused with what the term "symmetry" means: If someone with mathematical abilities could correct me here: I don't think Symmetry only applies to mirror-like reflections or doublings. Wouldn't the regularities of, say, a spiral shell or caracole or any helicoidals represent one kind of "symmetry"?

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

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