Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.

The coherent state representations of the group G = W1 ⊗ G0 (where G0 = SU(2),SU(1,1)) are used in computer simulation of the dynamics of single two-level atom (G0 = SU(2)) interacting with a quantized photon cavity mode- the Jaynes- Cummings model (JCM) without the rotating wave approximation and, in general, nonlinear in photon variables). The second case (hyperbolic Jaynes- Cummings model (HJCM), G0 = SU(1,1)) corresponds to the quantum dynamics of quadratic nonlinear coupled oscillators (the parametric resonance on double field frequency and a three- wave parametric processes of nonlinear optics). Quasiclassical dynamical equations for parameters of approximately factorizable coherent states for these models are derived and regimes of motion for ”atom ” and field variables are analyzed.

Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the n-body problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.