Hi,
(1) The Moebius strip is a 3-dimensional object while a rectangle is a
2-dimensional one which can be made into the 3-dimensional Moebius strip by
(i) twisting one end of the rectangle by 180 degrees relative to the other
end, and (ii) bending the strip into a twisted cylinder and gluing the ends
together.
The following properties of the Moebius strip are of interest:
"The recto and the verso are the two opposite sides of a 2-dimensional
rectangle (022415-1)
that lose meanings when the 2-D strip is made into a 3-dimensional Moebius
strip
where recto and verso fuse into one surface."
Statement (022415-1) is equivalent to the following:
"The recto and the verso sides are evident only when a Moebius strip is
viewed (022415-2)
locally: When viewed globally, no such distinction can be made."
(2) I defined complementarity as follows in 1995 (reviewed in [1]):
(i) Exclusivity: A and B are mutually exclusive.
(ii) Essentiality: A and B are essential for C.
(iii) Transcendentality: C transcends the level where A and B have
meanings.
(3) I suggest that the Moebius strip can be used as a geometric
representation of the principle of complementarity if the following
attributions are accepted:
(i) A = rector; B = verso, of either the 2-dimensional rectangular
strip or the local view of the 3-dimensional Moebius strip.
(ii) C = the global surface of the 3-dimensional Moebius strip.
(4) To the extent that Peirce's logic is based on the irreconcilable
opposites of recto and verso, his logic may be represented on a
2-dimensional rectangular strip (which may be identified with his "sheet of
assertion" ?).
(5) To the extent that Peirce' logic admits of a third term that transcends
recto and verso, his logic may be represented on a 3-dimensional Moebius
strip and hence viewed as a complementarian logic.
Does anyone on these lists know of any of Peirce's writings that would
either support or negate Item (5) ?
With all the best.
Sung
Reference:
Ji, S. (2012). Complementarity.
<http://www.conformon.net/wp-content/uploads/2012/08/Excerpts_Chapters_2_complementarity_08192012.pdf>
In: *Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms,
and Biomedical Applications.* Springer, New York, pp. 24-50. PDF at
http://www.conformon.net under Publicaitons > Book Chapters.
--
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
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