Equilibrium pursuits of natural processes are subtle most of the time. The subtlety lets us feel that everything is guaranteed that nature has to offer. But when nature’s actions become disruptive and destructive we look at nature in awe and realize the enormity of its power. Nature’s forces – the powers of earthquakes, volcanoes, tsunamis, floods, landslides, hurricanes, and storm surges are no match to our limited power – in our scale of thinking and doing things.
Some of these forces are so powerful and so extensive that they make us feel small and helpless – we start saying one cannot argue with Mother Nature. Structures and monoliths however strong they may appear, are destabilized and crumbled like toys, essentially flowing like fluid. The destructive power of nature tells us to know our limits and work responsibly within it – that nature needs room to stretch and wake up now and then to relieve some of its stresses.
Our memories are still fresh with the devastation of the 2005 Hurricane Katrina, the 2004 and 2011 tsunamis in Indonesia and Japan (Japan tsunami image, credit: anon). Now we have better ideas of how these types of forces are caused, but in ancient times the events have inspired people to think of them as actions of super-natural beings.
Scientists tell us that apart from their disruptive sides, these types of violent actions have been responsible for the development of atmosphere, and the birth and evolution of bio-chemical lives – plants and animals. The continuity of life is ensured with plants absorbing Earth’s nutrients like sponges, and animals developing webs of eating habits in the myriad layout of food chain.
Perhaps this means all that happens has a purpose; nothing is lost in the wide canvas of life and existence. Does this imply that nature’s violent actions are to be mimicked by humans? The answer is definitely no. The reason is that the human scale of things – life cycle and tolerance thresholds is much smaller than nature’s. Therefore for humans, small is beautiful and sustainable. The sustainability and beauty can be explained and interpreted from all different perspectives in order to achieve reasonable goals. But one thing is sure and it is the fact that our prosperity should not be considered as something dependent on upsetting nature to cause irreparable damage – rather working with it within limits. It is not a wise policy to create cases of human-made potential disasters to add on top of natural disasters.
How are nature’s actions required to turn the wheel of equilibrium conceived in a workable form? Let us try to revisit the concepts and definitions we know.
In simple considerations, all physical actions are described in terms of four inter-related parameters - energy, force, work and power. Energy is the ability to do something. We all have different physical energy depending on our health, body structure, strength and acquired skill level. Similar can be said about our mental energy which again depends on on mental health, education, caliber and experience. When given to work, we all perform differently depending on this potential energy.
Force is the measure of applied energy to do work in a certain direction for a unit measure of change in position. Work is the total accomplishment of the applied force and is equivalent to the applied energy. Power is the work done in unit lapse of time. Also fundamental to the concept is the mass, which according to Einstein’s (1879 – 1955) famous Theory of Relativity is equivalent to stored energy. We will have more occasions to explore the extraordinary brilliance of Einstein – one of the greatest minds in the history of mankind.
Perhaps a practical example would illustrate the meaning of these parameters better. A pole-vault thrower applies his body strength and skill level to throw a pole. The impact the pole has on the ground is the measure of force – and is the product of the mass of the pole and its rate of change of velocity. The average force multiplied by the distance traveled by the pole is the measure of the applied energy or work done. The power of the athlete is measured by the time taken by him. The faster the pole strikes the ground the more powerful is the energy applied by the athlete.
Now while the pole races throw air, some of the applied energy is lost through friction. The lost energy is proportional to the density and viscosity of the medium, and the force applied on the pole. For example, if the same pole is thrown in water with the same force, more energy will be lost, because water is more dense and viscous than air. According to conservation principle, energy or equivalent mass-energy can neither be created nor destroyed implying that the lost energy must transform into heat and sound.
Physicists see all natural forces as four fundamental types – the gravitational force, electromagnetic force, strong nuclear force and weak nuclear force. Einstein’s theory of mass-energy equivalence in its most demonstrated form represents the strong nuclear force – where an atom is split to transform its mass into energy. Weak natural force is the radiation of radio-active materials. Most of the natural actions are forced by Newtonian gravitational force, or in macro-scale thinking, by Einstein’s accelerating force in the space-time curvature of the mass-energy field.
Propagating energy distorts the medium to a wave form – like we see in ocean waves. Most energy propagates through a medium, except electromagnetic and gravitational radiations which do not require a describable medium to propagate energy. It seems the requirement of a medium becomes redundant as energies propagate at the very high speed of light – 671 million miles per hour. The product of energy and its speed of propagation is known as energy flux – that we have talked about on earlier occasions.
In addition to the equilibrium quests of natural processes, there are many connotations of propagating energy in life and social interactions. But, for now let us think about two important aspects in the context of human interventions on natural processes. Firstly, are human ambitions driving all to take unmanageable risks to create interventions in catastrophic proportions? Secondly, is it at all possible to protect ourselves from extreme catastrophic events?
We have answered the first question somewhat earlier. We all know that the more we become confident of ourselves, the more we tend to become ambitious to build larger and larger thus entering into the unpredictable or poorly understood areas of risks. The risks that we take are like creating a time capsule that is destined to bust – if not now, may be sometime in the future. Safeguards and precautions that we think adequate now, may prove to be blindsided by ambitions and arrogance in later times.
Fortunately, the growing awareness of the problems in recent times is helping all to appreciate the necessity of steering the wheel in the right direction by working on the development of smarter methods and sophisticated risk management tools. No seemingly smart method is full-proof however.
The relevancy of the second question knocks our door each time we think about the devastation of natural disasters. While facilities destroyed by the Indonesia tsunami could be understood because there were hardly any existing infrastructure for protection against extreme events of such magnitudes. The same cannot be inferred about protection facilities destroyed by Hurricane Katrina storm-surge flooding in USA, and the Japan tsunami. The facilities in these two developed countries were supposedly adequate or assumed to be somewhat sufficient to protect lives and properties.
Therefore one may argue that there might be a gap in our understanding and characterization of some extreme events. One likely flaw is that we treat an extreme event as an extrapolation of some other lesser events assuming that all of them have comparable characteristics. Unfortunately, this assumption has the risk of overlooking high randomness and non-linearity of extreme events, and their loadings on and reactions from structures we build.
Let me reinforce this by highlighting a warning from the US Army Corps of Engineers as described in the Coastal Engineering Manual. It answers the second question partly referring to our misconception of rare weather events or combination thereof: “It is important to bear in mind that the most extreme record of event may not merely be an intensified version of lesser extreme events. . . Often the catastrophic event arises from an unusual interaction between several major weather features. The Halloween Storm that occurred in the northwestern Atlantic Ocean in October 1991 is a good example. Three significant meteorological systems, including a hurricane and an intense winter storm, combined to create very strong winds over an extremely long fetch, which lasted for a period of days. This type of event is difficult to anticipate, but it should be recognized that such things can occur. They may appear as outliers in extreme data distributions.”
In a lighter vein let us take a glance at Murphy’s Law, anything that can go wrong, does go wrong. Is it certainty or uncertainty?
In my next posting I will be talking about the Fluidity of Nature.
Here is an anecdote to ponder:
The disciple asked the master, “Sir, I wish to defy gravity and levitate to float in air.”
The master thought for a while and laughed loud, “Good, my dear! Try to slow down and decelerate.”
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- by Dr. Dilip K. Barua, 12 May 2016
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.
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 modern 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.
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.
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.
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.
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 blog, I intend to focus on seeing definitions of nature’s actions.
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