Dualisms and dualities apply to both the physical world of matter and the non-physical realm of ideas.
Many dualisms can be understood in a dialectical or Hegelian (thesis-antithesis) sense.
The dialectical method of Socrates and the deconstruction techniques of Derrida can be utilized to uncover the components in dualistic types of relationships.
If two concepts are dualistic in nature and form a well-defined system, then they can be used to draw analogies with other dual systems.
If two concepts have the dualism characteristic, then each component can be used as a theoretical basis for investigating the system as whole (as is the case in the Heisenberg discrete & Schrodinger continuous equations).
Rowlands' formalism of the Dirac equation effectively nullifies the possibility of finding a unified field that describes all fundamental forces. This does not mean that a theory unifying electromagnetism and gravity is an impossibility. It only means that if a unifying force field is discovered physically or derived mathematically then a dual force field must also exist because "a fundamental principle of duality acts to preserve a zer0-totality in our description of nature." Rowlands, P., The Nilpotent Dirac Equation and its Applications in Particle Physics, arXiv:quant-ph/0301071, 2003, pg. 10.