Duality via a view of Symmetry

Unity can only be manifested by the Binary. Unity itself and the idea of Unity are already two. 

- Gautama Buddha.

The numerical system is an amazing medium for the expression of reality. Numbers are remarkably congruent in translating the behavior of nature into a format that the mind can easily process for comprehension. The great device produced by Cartesian philosophy was the rigid grid of regularity, which could be superimposed over nature's curves and crevices to transform them into mathematical representations of some non-deified Order. This important historical development certainly made reality significantly palatable for the mind to grasp, without having the need to invoke complex feats of cryptic computation. At least for a while. It would take about another 300 years (and the invention of modern computers) for Benoit Mandelbrot to come along and reveal the squiggly infinity hidden in nature by transforming it into fractal dimensions on a computer screen. 

                   

Complex mathematics apart, the fundamental truth about Nature appears to be encoded in something relatively simple - duality. This property of nature can be illustrated through her many traits, which are observable in myriad natural phenomena. Around 460 BC, Democritus, the laughing philosopher, postulated that all matter is made up of indivisible particles called atoms. These atoms were later discovered to be composed of a finely tuned relationship between the positively charged  protons in the nucleus and the negatively charged electrons orbiting around it. Even though by the late 19th century it was determined that the atom was not indivisible as previously thought, the presence of electric charge, in terms of positive and negative polarities, had already unleashed the magical powers of electricity - the basic foundation of inventions to come. 

                Chiral molecules, sinister and dexter enantiomers with cis/trans type of configurations, optical isomers and zwitterionic forces, are symmetry motifs that form the foundation of some extremely potent chemistry. In biology, symmetry is evident in the complimentary properties of nucleotides in the DNA molecule. Adenine always pairs with Thymine and Cytosine always pairs with Guanine. Chromosomes usually come in pairs. Sex evolves primarily through the coupling between the male and female counterparts of a species - at all levels of anatomy, physiology, and psychology. There is a fine balance between apoptosis or programmed cell death, and cell proliferation, which is crucial for the sculpting of tissues and organs during embryonic development. 

                  

Meanwhile, to make matter more complicated the particle-wave duality pervades throughout the material universe, including light. Deeper dives into matters of matter in the late 20th and early 21st century, further exposed the tumultous tapestries of strings and super-symmetries that are thought to compose the basic fabric of the universe. The ancient symbolisms of yin-yang, the ‪Ardhanarishvara‬ dance between the feminine and masculine energies of the universe, the charming, and UP and DOWN flavors of quarks and antiquarks, the rising crests and dipping waves of unobservable uncertainties, were all suddenly integrated into a semiotic soup of quantum mechanics. Thankfully, these paradoxes of reality have some how found solace in terms of the complimentarity perspective. Nevertheless, the conundrums of continuity constantly continue and for ever. Space and Time, are supposedly two sides, of the same coin. 

              

Even our personalities are split between the left and right brained thinkers, the musicians and the logicians, the mathematicians and the wordsmiths, the abstract and the detailed, the scientists and the artists. Political parties segregate into polar world-views. Psychologists split between Jungians and Freudians. Reductionism thrives on the opposite side of the spectrum of Holism. 

              There is a past and a future. There is day and night. There is the Self and the Other. The black and white checkerboard of reality concatenates endlessly into greying areas of strings and SUSY. How then, can there be Symmetry without Duality? There is something strangely heartening about this particular complimentarity. Images invert to reveal the negativity situated so perfectly within the picture of reality. 

            

"Couples are wholes and not wholes, what agrees disagrees, the concordant is discordant. From all things one and from one all things." - Heraclitus, (the crying philosopher)