Subject: Re: [NABOKV-L] On symmetry II
From: <[email-masked]>
To: <[email-masked]>
Date: Fri, 29 Sep 2006 15:51:37 -0400

In a message dated 29/09/2006 20:06:58 GMT Standard Time,
[email-masked]  
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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