Duality and Multiplicity in Nature

1. Intro
In the Ocean Waves blog on this page, I have briefly talked about the composition of a visible Natural wave with many invisible component waves – in other words with the Multiplicity of diverse waves. Ocean waves, for that matter all Natural wave phenomena are spectromatic and asymmetric with the visible Duality of highs and lows. As one practical example, I have also mentioned in that page how some tidal waves are defined by the superimposition of many high harmonic shallow-water tides. Let us try to explore more to see how the systems of Duality and Multiplicity work exactly.
The phenomenon of Duality is somewhat obvious – in the most visible manifestation of the top wave crest and the bottom wave trough. Duality does not mean that there are just the two of something – but that the two are the inseparable and complementary components of the unity - union of the two opposites combined together in the pursuits to reaching the symmetry of stability. Duality should be understood as the incremental motions of the opposites geared toward achieving agreement and dynamic equilibrium. It cannot be described by a divisive phrase like either/or, but rather by a unity phrase of Multiplicity like this, that, and the others.
Before going further, I am tempted to briefly explore some of the ancient Eastern thoughts on this topic. In one of the simplest ways of explaining the Buddha - The Tathagata's Perfection of Wisdom Discourse, Buddhist scholar Nagarjuna (150 – 250 CE) at an earlier informal establishment of the world’s second earliest University at Nalanda (427 – 1192CE) stated: That which is the element of light is seen to exist on account of darkness; that which is the element of good is seen to exist on account of bad; that which is the element of space is seen to exist on account of form. In a similar platform of thoughts, the Duality principle is expressed as the union of the opposites – Yin and Yang in the Buddhist philosophy.
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2. Duality and Multiplicity in Waves
Coming back to the Natural waves, it is interesting to see how the crest and trough are related to each other within the framework of elastic resistance to deformation – the trough is forced by the flow of energy to work up to the phase of the crest, while the gravitational pull drags the crest to work down to the phase of the trough. The process is associated with a forward motion and a compensating reverse motion of the medium particles required to completing the loop. This balancing act between the excitation energy and gravity indicates that the crest and trough work together to attain stability and equilibrium.
As the Natural waves and these ancient thoughts tell us, the Duality of the opposites in a society should be interpreted as something convergent – not something divergent. Duality and Multiplicity are not chaos, but rather Nature’s way of responding to the excitation in order to propagate and dissipate the gained energy. Perhaps one relevant lesson from the Duality principle is that, a democratic rule can only prove meaningful and stable if the oppositions and others are truly accommodated in governance. We can talk about this more in the SOCIAL INTERACTIONS page at some other time.
Let us turn our attention to the Multiplicity in waves. To help us understand better, I have constructed a simple image showing four sinusoidal or symmetric waves of different amplitudes and frequencies. In the shown image, the horizontal x-axis is time normalized by the period of the first wave, and the vertical axis is water level in meter with reference to mean or still water level (SWL). These four monochromatic waves when superimposed, added to the asymmetric and spectromatic wave shown as the envelope. In addition to losing the symmetry, the envelope has amplified at some phases and reduced at others. While this fundamental principle holds in all cases, one needs to understand that a Natural wave in the open ocean is much more complex with the superimposition of many spectral waves coming from all different directions.
Perhaps one more example would clarify things. We all know about the illumination of light – that it is composed of a spectrum of seven distinct colors. Most Natural waves – be it light, sound, electromagnetism or any other mechanical waves such as those we have described – are characterized by the Duality envelope of the crest and trough, but within which exists the Multiplicity of component waves. This Multiplicity is the building block of the Duality. 
The suggestion that Multiplicity is the building block of the Duality indicates that a monochromatic wave is not sustainable in Nature for long. Why is that? To find the answer we have to turn to Isaac Newton (1643 – 1727) again, to his famous Third Law of Motion – that every action has an equal and opposite reaction. As soon as a monochromatic wave is formed, it invokes reactive waves from the boundary. The resulting superimposition of the active and reactive waves turns an original monochromatic wave into a spectromatic one. In a near ideal case, when the reactive wave is reflected perfectly, the superimposition causes what is known as the standing wave – with the depressed high-current nodes and high-amplitude anti-nodes. A standing wave is the perfect example of a stalemate. 
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3. Duality and Relativity
Why are all these discussions important? Perhaps seeing a wave and pondering about its components are very helpful in unraveling many of the Natural and social mysteries. It is because of the fact that excitation always distorts the medium to a wave form. It is how the medium attempts in time to return back to its non-excited tranquil stage by balancing itself through the processes of transmission, absorption and losses of energy. But to keep our understanding in true perspective, it is important to note however that for the electromagnetic waves and gravitational radiations traveling at the very high speed of light, no medium is necessary to transport energy.
Now I like to turn my attention to a different question. Is the Duality we have described same as Relativity? Although the two appear to indicate the same meaning, I would argue that while the Duality is real, the concept of Relativity is subjective, resulting from our differences in perceptions of things. However the Duality and Relativity could converge at some points or levels when our perception approaches the reality of Duality, or when the Duality can be stressed or extrapolated to explain something that could approach the level of Relativity. For example, light and darkness represent the reality of Duality, but the perception of the good relative to the bad could only mean Duality, if the definitions of and the difference between good and bad are well-established and accepted across the board. Nagarjuna’s explanation includes both the reality of Duality and the concept of Relativity.      
Let us try to clarify the concept of Relativity further through the mind of a champion thinker. Albert Einstein (1879-1955) – the pioneer of the General Theory of Relativity – described it in an attractive but understandable way for non-scientists: When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it's longer than any hour. That's relativity. Scientists often explain a simple phenomenon like lightning thunder; and how it is perceived differently. One standing at the platform will perceive the phenomenon differently than the one riding the speeding train. This different perception of the same event by different persons depending on their states of motion is Relativity.
Or we can think about our own change of perceptions – things were tall and long when we were little, but the same things appeared shorter and shorter as we grew up. All these arguments lead us to say that the truth of things is nothing but the subjective perception one experiences. In other words, in our perception or measurement, nothing is absolute – time is not absolute, space is not absolute, our social interactions are not absolute. This raises the issue that there are two basic types of truths – absolute and relative. Let us get back to this concept at some other time in the future.  
Do the Duality and Multiplicity of the same phenomenon continue to remain the same as they evolve in space and time? In analogous with the transformation of propagating waves, the Duality and Multiplicity of the same phenomenon at one place and time are not the same in different places and times. This means that a downstream phenomenon can be traced to the upstream source, but they are not the same.
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Here is an anecdote to ponder:
The disciple asked the master, “Sir, how come I continue not seeing things as described.”
The master took a pause and looked at the disciple and laughed, “Aha! Aha! That is because you are standing in the dark. Stand in the sunlight and watch how your shadow changes shape and size as the daylight passes.”

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- by Dr. Dilip K. Barua, 14 July 2016

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