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TA107 (Rosen)

 

Response 5 (to Steven Bindeman, C6)

 

( KLEIN BOTTLE )
by Steven Rosen
19 June 2008, posted 28 June 2008

 

[1]
I appreciate Steven Bindeman’s thoughtful and thought-provoking comments on my target article.

In <2>, Bindeman asks if — in using the word “Crisis” in my subtitle, I was thinking of Husserl’s book, The Crisis of European Sciences and Transcendental Phenomenology.  Actually, I wasn’t, though I just as well might have been.  I was indeed trying to call attention to the bankruptcy of the empiricist view in physics.  Implicit in the paper is that the rationalist view also is suspect.  Empiricism and rationalism, each in their own ways, entail objectifications of the world that exclude concretely lived subjectivity and are therefore unequal to the challenge of contemporary physics, which at bottom requires including the subject in order to address the central problem of subject-object interaction.

[2]
As regards the Klein bottle, I agree with Bindeman that it is actually “
not conceivable under the objectivist framework of classical empiricist physical theory” <4>.  Of course, this does not stop conventional mathematicians and mathematical physicists from employing objectified versions of the Klein bottle, questionable though that may be (see footnote #2 of my target article).  I also agree that the reality of the Klein bottle “is impervious to our need to picture it as either one thing or another.”  In this respect, my own emphasis would lie not so much in the relativism that the Klein bottle conveys as in its paradoxical nature.  Yes, we can never pin the Klein bottle down by saying that it is definitely X as opposed to Y (current mathematical practice to the contrary notwithstanding).  But, for me, this is not primarily because we can only ever have a partial view of the Klein bottle.  I propose that a more complete experience of the Klein bottle is possible — not in the positive sense that it is X as opposed to Y, but in the dialectical sense that it embodies the interpenetration of X and Y wherein these terms are fully identified yet also entirely distinct !

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Steven Rosen
     e-mail <
StevenRosen (at) shaw.ca>