1. JUST AN EXAMPLE FROM QUANTUM MECHANICS

When the curious and inquisitive people with different educational and professional backgrounds show an interest in my discovery concerning Lyapunov functions in the mathematical theory of stability, they often ask me the same question. How is the theory important to us and our social being? Maybe it has a quite narrow range of applications like the overwhelming majority of systems of ideas, they say. Despite having a good expertise in the theory of stability and extensive engineering and life experiences I always found it difficult to set forth the convincing arguments substantiating the fact that the concept of stability has an unique place among all other theories. Furthermore, in my personal opinion it is a core idea of our existence. You might say that this is a too bold statement. Today I will try to persuade all of you with one example.

The modern era, defined by computer and other various electronic technologies, takes its origin in quantum mechanics that was born in 1900 due to the Planck’s postulate of the quantum nature of atomic world with the aim "to prevent ultraviolet catastrophe from happening". The alternative motivation for the creation of quantum mechanics is the need to explain the stability of the structure of atom, namely why negatively charged electrons do not crash in positively charged nuclei. This is the most fundamental question of our existence and it has not been answered yet even by quantum theory. Why? Because the theory does not explain the stability of the structure of atom. The one just postulates it. See a good explanation of it to my eye given at the link below https://www.amazon.com/gp/review/R1F8RI0MXBZQF3?ref_=glimp_1rv_cl

All around us including ourselves consists of atoms being ones of the basic elementary bricks of the matter. Thus, if we cannot understand why the atoms have many stable forms of existence and do not collapse immediately after their creation, then it is highly likely that we understand a little properly about ourselves and the world we live in. In other words, we just think that we understand much more complicated formations of the matter but our understanding might be inadequate.

This simple example foregrounds two obvious and important points, namely it

• shows how easy the concept of stability can undermine our faith in the dogma of modern knowledges;

• explains the ubiquity and universality of the property of stability in the cosmos with the omnipresence of atoms as its building blocks that spread this intrinsic feature throughout it all.

2. THE NONPAREIL PHENOMENON OF THE PROPERTY

The stability of any physical entity can be defined as the intrinsic ability of the one to return to its previous state by itself after being forced out of it under the influence external or internal causes. We deal with stability every moment of our lives, from birth to death. And there is no other chance to live. Moreover, the Universe exists only because the matter is mostly stable. Some examples of the remarkable actions of the property of stability, which we take for granted, are given below.

• If you have a bone fractured, the stability of your organism functioning ensures that its ends will coalesce soon. In general, if you sick, then your recovery happens only because of the stability provided by your immune system. This means to continue to live a healthy life for you. Even the process of aging can be mathematically formulated as a problem of stability.

• If you fly a plane in the condition of air turbulence, the stability of the aircraft ensures the return to the trimmed (balanced) condition if it is disturbed. This means a safe flight for you.

• If you drive a car on a slippery road, then the car’s dynamic stability control prevents you from a loss of steering control. This means a safe ride for you.

• If you have tripped over something, then your brain using vestibular sense detects it and sends the corresponding commands to your body to maintain the balance. This means to avoid the fall and possible injury for you.

• If the operational system of your computer has become completely unresponsive, then what do you usually do? Correctly, you restart the computer and the good operational system tries to fix the glitch by means of returning to its previous healthy state. This is an instance of a good man-made imitation of Mother Nature miraculous design pattern.

3. ANCIENT WRITTEN LANGUAGES

Sir Isaac Newton is famously known, first of all, for his Philosophiæ Naturalis Principia Mathematica written in Latin, the international scientific language in the Age of Exploration. Today modern English has successfully replaced Latin in this role. But not too many people know that he is an author of a number of good works in theology and linguistics. Isaac Newton even wanted to create an universal language on the basis of English, which he considered so imperfect that he was afraid for its future among other European languages. This may cause a smile but the truth is that such kind of Cosmic Irony can toy even with the mighty minds of the greatest mortals. There are the written language sciences with a long history rooted in the very distant eras of Mesopotamian, Ancient Egyptian and Minoan, etc. civilizations. What conclusion have these sciences led us to? Any language can become extinct with time. Moreover, the one can disappear almost without traces in the next generations of languages. It means it will not modify, merge with or give rise to other languages like Latin. No. It will just vanish off the face of the earth. This is the death of the language and it is usually very difficult to predict which modern language will disappear and which will continue its life in another form. The situation with languages can be also formalized as a problem, extremely complicated one, of stability of the active use of languages. But the pith in the example with languages is not stability. The pith here and in general is in the difficulty to dig out the more or less adequate knowledge about the real facts, properties, etc., including the factor of stability, and their future. All we know is just some approximation of the reality reflected in our mind in some still unknown to us way and no more. We call this reflection understanding or knowledge. It can be initial or advanced. It differs from other understandings by limitations of its applications, degrees of adequacy, the forms of representation, etc. but it always remains only an approximation of the reality, not the reality per se. It is not rare to make an initial well-adequate approximation of a new specific knowledge equals to accomplish a feat. And the main reason of it often is the lack of necessary technological tools, research techniques, mastery and gift of scholar, sometimes a lucky concurrence of circumstances and a full set of the elements or pieces of the required knowledge. The process of creating the initial approximation of this new knowledge is similar to assembling a jigsaw puzzle with oddly shaped interlocking and tessellating pieces. If some pieces are missing or misshapen then the whole puzzle cannot be complete properly. Of course, the one can be “forcibly” assembled in a wrong way but presented in a credibly looking and prepossessing manner to pass it off as the genuinely correct assembly. We will dismiss such cases out of hand because of obvious reasons.

Now let us turn our attention to the front image of the post. It is of the Phaistos disk that is “a fired clay disk, probably of Minoan origin, measuring some 16cm in diameter and impressed on both sides with 242 symbols set in a spiral arrangement. As yet, this unique archaeological find remains an undeciphered enigma … The disk is now generally accepted as Cretan in origin and therefore is probably a representation of the Minoan language in use during the period at which scholars date the disk - from 1850 to 1550 BCE … The fact that the symbols are arranged in a spiral is also given as evidence supporting the Minoan (or at least Aegean) origin.” Cartwright, M. (2012, June 28). Phaistos Disk. Ancient History Encyclopedia. Retrieved from http://www.ancient.eu/Phaistos_Disk/. The many facts about the disk have been hotly debated among scholars almost immediately since it was unearthed in 1908 including authenticity, dating, origin, symbols, etc. A number of scholars have claimed deciphering the disk but the scientific community has stayed skeptical. The reason is simple: too little material of this lost language presented with artifacts is at scholars' disposal in order to be able to conduct thorough comparative analysis. Here we encounter the typical and quite frequent case of missing jigsaw puzzle pieces.

4. EARTH'S CLIMATE STABILITY AND HYPOTHESIS OF GLOBAL WARMING

The alarming signs of climate change are evident: sea level rise, changes in climate extremes, Arctic sea ice decline, glacier retreat, etc. Most initial causes-factors of temperature change are believed to be known well: greenhouse gases, aerosol and soot produced by volcanoes and human-made pollutants, solar activity, etc.

However, the following questions then arise:

• How significant is contribution share of each above-mentioned factor?

• Which factors are major and which are minor?

• Is the list of the aforesaid factors quite complete? Are there not missing some very important ones but still unknown?

• Is the period of a hundred year of the well registered and documented observations of climate change sufficient to make long-term predictions?

• How well adequate are the global mathematical models of Earth's climate confirming these predictions?

• Is Earth's climate a stable physical phenomenon and what do the mathematical models tell us about its stability?

We will only discuss questions concerning the mathematical models and the factor of stability that are in the field of author’s expertise.

First, if Earth's climate has not been well stable and robust, the life on our planet stopped existing many thousands years ago because of planetary and cosmic cataclysms that from time to time were happening to Earth. In the mathematical theory of stability the term of robust means the stability when the parameters of a system under study itself change. Sheer stability involves only the change of initial conditions of the system and external disturbances.

Second, to construct a well adequate mathematical model of Earth's climate is a tremendously complicated problem. In my opinion, it should be governed by a high-dimensional system consisting of essentially nonlinear partial differential equations, ordinary differential equations and functional equations with uncertain or stochastic parameters and unpredictable external and internal disturbances. What do we mean when we say well adequate mathematical model or theory? It means that the difference between the results of experimental measurements and the results predicted by the model or theory is acceptably small to be neglected. For comparison with the well adequate theory see the prediction of the value of Dirac constant made by Quantum Electrodynamics: the experimental value of 1.00115965221 versus the theoretical value of 1.00115965246. (The Strange Theory of Light and Matter by Richard P. Feynman, 1988). As we have said before to construct such a complicated model is terribly difficult problem but what is much worse is to investigate the stability of this model. This problem is one hundred times harder than the previous one. Cherishing hopes for “omnipotent” computer technologies (hardware and software) that will help get us out of the difficult situation will be disappointing. The output of computer simulation strongly depends on its input. If you have a badly designed or wrong algorithm that processes your equations or bad input data, you will definitely receive bad, practically useless or nonsensical output data, if any. Furthermore, computer simulation is not so reliable and credible as it seems to be. It transpires that the computer software based on discrete mathematics does not always preserve the very important or even fundamental characteristics of real (continuous) time dynamical systems. For instance, the one might turn conservative systems into dissipative ones, break limit cycles, not be able to finish the process of the integration of differential equations to an acceptable extent due to weak convergency that makes the results of simulation uninterpretable, etc. Thus, computer simulation cannot be done successfully without good preliminary theoretical analysis. Researchers should foresee its possible results to some degree before starting simulating. They should understand well what they do. “There is nothing more practical than a good theory.” said James C. Maxwell. However, here is the stumbling-block called a good theory. It has yet to be developed for such complicated mathematical models!

But there is good news. Basing on multiple empirical studies and our history, we can say with a full certainty that

• The physical phenomenon of Earth’s climate is definitely well stable and robust. There are explicit manifestations of this fact revealing that stability of the structure of Earth’s climate is organized through the complex network of multiple local and global negative feedback loops covering the globe. Our planet is deftly designed to harbor and protect various forms of life including Humankind. Can people inflict the fatal damage on the planet and its climate resulting in the total disappearance of all living organisms and making Earth unfit for human habitation any longer? It is very unlikely at least today. What our civilization is able to do now is to destroy itself. But our place on Earth will be taken by another civilization of human race. Nature abhors a vacuum. Our foolproof planet is supposed to get rid of bad and unintelligent ones in order to ultimately preserve the most valuable thing in the Universe, the life.

• We have to deal with stability of the natural phenomenon that has an intrinsically oscillating complexion with occasional considerable fluctuations of the quantities describing it in space-time.

• Humanity should make all the possible efforts to minimize the deleterious effect of its activity on Earth's climate.

5. CONCLUSION

To sum up, we can say that God created the world infused with stability but not all formations and forms of the matter are so blessed to be endowed with it. However, the following observation definitely reflects the reality: His divine intervention often manifests itself through the astonishing activation of this supernatural property.

P.S. All the said above is the personal opinion of the author. The objective of this post is not to support or refute any theories, statements, ideas, and hypotheses. The only goal, the author has pursued here, is to make the concept of stability taken seriously not only by international scientific communities but any reader too.