Natural Equilibrium

1. Intro
We have talked about Natural order, balance, adaptation and cyclic nature of things. How these processes can be explained in a more understandable way? Search for reaching equilibrium by responding, adjusting and adapting to stimulus, actions or interventions is nature’s way of doing things.
But before we begin, a distinction is required to separate static equilibrium from a dynamic one. The principle of static equilibrium is important in force mechanics to determine stability of resting objects, structures or restraints at any instant. In this principle, forces are resolved in distinct directions and balancing those yields the unknowns.
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2. Dynamic Equilibrium
Fluidity or dynamic equilibrium is the characteristic signature of Natural processes. Perhaps the best way to start is by taking a glimpse at the ancient wisdom of dependent origination, which in simple terms explains the principle of cause and effect, or action and reaction, or process and response. Cause and effect are intertwined – nothing exists without a cause, there is no cause without an effect. Of course, a cause has to be strong enough to have an effect. When a cause occurs on a system, it looks for ways to reach equilibrium by generating effects – and together, the twin represents the Universal Knot – the ever-evolving wheel of a natural system (image credit: anon). The effects can be adjustment and adaptation within the system and/or transmitted as a cause to a neighboring system. This search to reach equilibrium following a disturbance is the driving engine for grinding of the wheel.   
It took many centuries before this ancient wisdom was translated in a workable form by none other than Isaac Newton (1643 – 1727). This great genius, the father of classical physics proved and stated in his famous Third Law of Motion – that every action has an equal and opposite reaction. An analyst whether the individual is a scientist, an engineer or a social scientist, uses this law as an equation of variables representing actions and reactions, or forces and responses.
Equilibrium principle is also expressed as a conservation of momentum or energy-flux. And together with conservation of mass, the principle is another marvel of modern physics. Who could be a better person than Newton again to formulate this principle in a workable form? Conservation law of deterministic Newtonian physics tells us that what comes in is balanced by what goes out and the changes that occur within the system. In the context of momentum, the equilibrium principle essentially represents a force-response knot – the active and reactive forces on the one hand and the accelerating response on the other. An easily understandable schematic version of the equation is presented in my Encyclopedia Paper.
The variables in these balancing approaches representing certain parameters are conceived to change in time and space. As one changes, the equilibrium is broken until others change too in a defined pattern of processes balancing the equation – within a time frame known as the adaptation time. People often say that the left side of the equation knows what happens on the right.
What is the best way to apply equilibrium principle in a real-world problem? Scientists, for that matter any analyst or engineer, start by conceiving a model.
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3. Defining a Model
What is a model? I remember googling the term during the dawn of internet surfing. The search immediately came up with skinny images of fashion models. During that period, the search did not show the developments technical professionals looking for. The experience indicates how market demand overwhelms other things and that our non-technical colleagues are much more agile and active in reaping the benefit of technical innovation than ourselves.  
A model is generally conceived as a soft tool representing equilibrium inter-relationship among the essential elements of a system. A system is a closely dependent cause and effect entity separate yet connected to other neighboring systems. The key word for a model is soft. It signifies that a model represents simplification and approximation of a real case – and that its description and prediction are not expected to be exact. Despite dealing with real-world problems, simplification is a must to understand and solve a case as a manageable goal. In a model the weak causes and effects are sacrificed or approximated in favor of the dominant ones. However, as things move forward, sophistication is being developed to add to the robustness of modeling tools to account for more causes and effects.   
The workable form of a model can be concepts, ordinary language, schematics, figures and mathematics. A conceptual model is a non-mathematical representation of the inter-relationship of system elements. A mathematical model is the translation of a conceptual model in mathematical terms of variables and numbers.
I am tempted to spend a little time on mathematical models because of my experience in this field – in modeling hydraulics of tide, wave and tsunami, sediment transport-morphology, ship motion dynamics, etc. I intend to come back to the topic again in the Science & Technology section.
A mathematical model is not solvable in a digital computer right a way. When mathematical models become complex encompassing many variables, it becomes impossible to readily understand and solve them. The complication of the situation appears insurmountable as the models become dependent on calculus to describe processes. A model relating gradients of variables in space and time is such a calculus paradigm.
After a mathematical model is worked out, the next step is to translate it to a numerical model which basically involves transforming the mathematical model of calculus paradigm into algebraic equations. The numerical model also includes translating the algebraic equations into numerical codes so that it can be executed by digital processing of a computer. The art of applying a numerical model into the domain of a real-world case to replicate processes is known as computational modeling.         
For modelers, the challenges are to translate the continuum of space and time into the discretized domain of a model – such as: what to include, what to leave out, what to smooth out, and what are the consequences for such actions. How best to take account of practical constraints and describe forcing at the boundaries to be realistic but at the same time avoiding model instability. Reactive forces like frictional resistance are notoriously non-linear – therefore it is important to watch how parameterization of these forces affects results.
Because computational model results are expected not to be exact – some people question the predictability of a model. This doubt appears despite tuning, calibrating and validating a model to actual measured cases. The performance of a model depends on how sound and sophisticated the mathematical foundation is, and how skillfully the model is coded into algorithm and applied. It is often necessary to define a threshold so that some model results can either be accepted or discarded; that in itself is not an easy task however. Without going into the debate on predictability, it is safe to say that one of the most important aspects of model’s ability is simultaneity of its results – what happens at different places within its domain at any time due to boundary forcing, in natural conditions and when interventions are in place. This gives decision makers the opportunity to have a synoptic view of processes to compare situations with and without engineering interventions, and evaluate risks. Such a view is very important for decision making, and is not possible by any techniques other than a computational model. More in Water Modeling. 
Well, enough on models but with a note on sophistication. Digital processing in bits of 0 and 1 to process and store information is being infused by pioneering thinking of faster quantum computing in qubits of 0, 1 and combinations of 0 and 1. And computer codes of Artificial Intelligence are surging forward to conduct human functions. More in The Quantum World and Artificial Intelligence - the Tool of No Limit.
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4. The Single Most Characteristic of Nature
We talked about Nature’s single most characteristic cycle - the birth-growth-decay-death and birth again in my Natural Order blog. A circle – representing the slice of a sphere is perhaps the simplest two-dimensional visible form of this cycle. A circle, if laid out in space or time, takes the shape of a regular wave, a symmetry – the familiar sine or cosine curve – the rising and falling limbs representing disturbance-restoration dynamics of equilibrium.
Again in the end, it is all about humans and the responsibilities associated with human actions – either in applying the equilibrium principle to understand Nature and harness its resources, or in conserving and sustaining the beauty of natural canvas for the future. Human behavior – actions, reactions and associated uncertainties – is much more difficult to understand than physics of nature and its uncertainty. Ancient wisdom realized by religious leaders, and researches of modern psychologists shed some lights on the mysteries of human mind. Human mind is such that no two individuals act or react in the same way to identical stimulus. The approach then is to describe the poorly understood human behavior in terms of statistics – which by definition, is a generalization of numbers or information and is always marred with scatter. Two persons – let us say one with the qualities of loving kindness, compassion and empathy, and the other with none of those qualities – how can both be justifiably replicated by a single social scientists’ equilibrium paradigm? A serious mistake could occur labeling or stereotyping a person or a society in one way or the other. 
In the next article, I intend to focus on seeing definitions of Nature’s actions.
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Here is an anecdote to ponder:
The disciple asked the master, “Sir, I am afraid I am little confused. If the cause and effect are so intertwined – which is first, the chicken or the egg?”
The master looked at him and smiled, “You are like everybody else. It does not matter which is first, what matters is the fact that both exist.”  

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- by Dr. Dilip K. Barua, 5 May 2016

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