TA107 (Rosen)


Commentary 2



by Donald Mender
27 May 2008, posted 31 May 2008




I am entirely in agreement with Steven Rosen's project of both "softening" physics and "hardening" phenomenology so that C. P. Snow's "two cultures" may extend to meet in a common middle ground.  I agree with Professor Rosen that a phenomenological re-working of the sub-Planck scale vital to the yet incomplete goal of unifying gravitation and quantum field theory holds the key to accessing that middle ground.    I am also on board with his ideas, respectively explicit and implicit, that 1) the incarnated subject, which non-transcendentally interpenetrates the "objects" of physics, is a perceiving subject, and 2) the "geometry" of that interpenetration cannot be subsumed by insufficiently generalized invariances under translational, affine, or diffeomorphic transformations.



However, with regard to 1) and 2) I must ask the following questions:


1)  Doesn't quantum physics require that the subject not only perceive but, more than that, ACT on physical "objects"?  That's why quantum observables are constituted not by mere variables but by operators, whether expressed as differential or matrix-mechanical symbols.   If so, then a quantum-oriented phenomenology will have to incorporate the notion of praxis directly into its rubric.  Husserlian constructs won't cut it here.  Even Merleau-Ponty alone won't do the job, though his propounding of subjective incarnation is a necessary first step.  Beyond that,  Heidegger's existentialism is required.


2)  Is geometrical abstraction to topology generalized enough to handle the conundra of self-referent paradox?  After all, these contradictions came to light historically through the doomed project of axiomatizing set theory, stripped even of constraints imposed by invariance under homeomorphic transformations.  Maybe topology is not a radical enough vantage point from which to address the big picture of subject/object interpenetration.  Perhaps some re-thinking of foundational set theory is needed.



Having raised these issues, I believe that Professor Rosen has unearthed some important leads pointing toward their resolution:


1)  The non-commutativity of uncertainty relations between canonically conjugate operators and hypernumbers may relate to each other in heretofore unexplored ways whose correspondences could yet prove theoretically redundant.  If so, a consolidating path toward wedding all quantum operators, both first- and second-quantizing, to the sub-Planck scale may thus be delineated.  This would afford the purveyors of quantum-gravitational unification and existentially phenomenological agency a comprehensive mode of mutual connection.


2)  The crucial role of Bose-Einstein and Fermi-Dirac statistics in the local supersymmetry of quantum gravity may indicate a possible means of reworking set theory to encompass the structural strengths of topology without requiring its overly specific recourse to explicit bicontinuity.  By re-working I mean an expansion of probability-valued logic in pure set theory to include also Bose-Einstein and Fermi-Dirac statistics.



If the measures outlined in the last two paragraphs were combined, one might thereby produce a sub-Planck mathematical structure weaving together quantum-subjective praxis and a pseudo-topologically elastic, potentially meta-paradoxical expansion of set theory.  This seems to me a worthy goal.




Donald Mender, M. D.

Assistant Clinical Professor of Psychiatry

Yale University School of Medicine

     e-mail < dmm87 (at) email.med.yale.edu >