Steven M. Rosen

This essay is written at the crossroads of intuitive holism, as typified in Eastern thought, and the discursive reflectiveness more characteristic of the West. The point of departure is the age-old human need to overcome fragmentation and realize wholeness. Three basic tasks are set forth: to provide some new insight into the underlying obstacle to wholeness, to show what would be necessary for surmounting this blockage, and to take a concrete step in that direction. At the outset, the question of paradox is addressed, examined in relation to Zen meditation, the problem of language, and the thinking of Heidegger. Wholeness is to be realized through paradox, and it is shown that a complete realization requires that paradox be embodied. Drawing from the fields of visual geometry and qualitative mathematics, three concrete models of paradox are offered: the Necker cube, the Moebius surface, and the Klein bottle. In attempting to model wholeness, an important limitation is recognized: a model is a symbolic representation that maintains the division between the reality represented and the act of symbolizing that reality. It is demonstrated that while the first two models are subject to this limitation, the Klein bottle, possessing higher dimensionality, can express wholeness more completely, provided that it is approached in a radically nonclassical way. The final question of this essay concerns its own capability as an essay. It is asked whether the present text is restricted to affording a mere abstract reflection on wholeness, or whether wholeness can tangibly be delivered.

The basic thesis is that the problem of infinity underlies the current dilemma in modern theoretical physics. The traditional and set-theoretic conceptions of infinity are considered. It is demonstrated that standard mathematical analysis is dependent on the complete relativity of the infinite. In examining the domains of modern physics, infinity is found to lose its entirely relative character and, therefore, to be less amenable to classical analysis. Complementary aspects of microworld infinity are identified and are associated with the equivalent features (inertial and gravitational mass) of Einstein's macroworld theory. The persisting effort to treat essentially non-classical phenomena in classical terms is critically discussed. A new attitude toward the infinite is recommended, one that might lead to establishing a second principle of the relativity of the infinite. The prospect for implementing the suggested approach through a "trans-analytic" meta-theory of dimensional generation is briefly entertained.

A dialectical, double-aspect model of general interaction is proposed as a means of visualizing existence. It is constructed from observation of the transformational properties of the Moebius surface, with hyperdimensional extrapolation to the Klein bottle. The interaction of systems is viewed as a process of circumversion (i.e. turning inside-out) whereby systems exchange relations, become mutually negated, then exchange identities. Interaction is discussed in the context of the PCT problem, symmetry, creation-annihilation, and uncertainty.