The book Synergetics is an unusually metaphysical treatise on geometry, as is shown by the many entries concerning twoness.
"The additive twoness derives from the polar vertexes of the neutral axis of spin of all systems. This twoness is the beginning and essence of consciousness:... consciousness of the other." (Synergetics 223.11)
This notion of the necessity of the other for the formation of the self, has been expressed by many thinkers, e.g. Dewey:
"The self is both formed and brought to consciousness through interaction with environment". (1934, p.282)
Fuller goes on to say that:
"The a priori otherness of comparative awareness inherently requires time. Early humanity's concept of the minimum increment of time was the second, because time and awareness begin with the second experience, the prime other ". (ibid.)
Very few references to other thinkers are made in Fuller's books, but what he says here is reminiscent of the intuitionist philosophy of mathematics:
"Intuitionist mathematics is an essentially language-less activity of the mind having its origin in the perception of a move of time, i.e. of the falling apart of a life moment into two distinct things, one of which gives way to the other, but is retained by memory. If the two-ity thus born is divested of all quality, there remains the empty form of the common substratum of all two-ities. It is this common substratum, this empty form, which is the basic intuition of mathematics ".
(Brouwer: Historical Background, Principles and Methods of Intuitionism, in South African Journal of Science, Oct.-Nov., 1952, and discussed by Körner, 1960, p.120)
There is another kind of twoness:
"The multiplicative twoness is inherent in the disparity of the congruent convexity and concavity of the system. The multiplicative twoness is because both you and I have insideness and outsideness, and they are not the same: one is convex and one is concave" (Synergetics 223.12)
The significance of this may be sought in the context of Fuller's notion of system.
Finally, let it be noted that the grand manoeuvre of Synergetics is the substitution of "the word tetrahedron for the number two", thus completing Fuller's "long attempt to convert all the previously unidentifiable integers of topology into geometrical accountability" (Synergetics 620.12).
© Paul Taylor 2001