Qualitative modelling for complex systems

E.E.Escultura

GVP Institute for Advanced Studies and Departments of Mathematics and Physics

GVP College of Engineering, JNT University, Madurawada, Visakhapatnam, AP India

The paper introduces qualitative modelling for analyzing complex systems and solving complex problems and explaining natural phenomena in terms of natural laws. Its power is demonstrated by its role in discovering the basic constituent of matter, the key to the solution of the gravitational n-body and turbulence problems. Qualitative modelling is applied to the equally difficult problem of development using a similar approach: discovering the relevant laws of society and production. The latter includes laws governing creation, accumulation, distribution and utilization of surplus. Then a theory of development is devised for formulating a strategy for development of underdeveloped countries. It notes that while the problem of underdeveloped countries is underproduction, i.e., scarcity of social surplus, the problem of developed countries is just the opposite: overproduction of commodities that cannot be disposed in the markets leading to periodic disruption in the global economy called recession or depression in its worst form. These opposites provide basis for symbiotic relationship that is availed of to devise a strategy for development of the underdeveloped countries based on advanced scientific knowledge provided by the Grand Unified Theory to generate appropriate technology.

For introduction we note.

One barrier to formulation of strategy for development is ambiguity of concepts. Development is ambiguous and means different things to different sectors of society and some movements oppose it at all costs. Another ambiguous concept is sustainable development and another barrier is lumping up environmental concerns with development. However, while they are distinct they are components of the same ideal: elevation of the human condition. Therefore, the correct strategy must deal with both but must also have a substrategy for handling their dichotomy to advance them together towards this ideal.

Another barrier is definition of complexity that has no bearing on strategy. Yet another source of devastating confusion is the erroneous belief that industrialization is bad for both ecology and environment because of the release of industrial waste. On the contrary, underdevelopment is the single most devastating factor that ravages the ecology and environment since it compels underdeveloped countries to rely on extraction of raw materials, e.g., mining and logging, to keep their economy afloat. Not only does it ravage the environment, it also robs them of valuable future industrial resource since raw materials are cheap and mainly for export and, therefore, massive extraction is required to provide basic necessities without bringing in substantial value and surplus. Many underdeveloped countries are now forced to impose logging ban which is too late and very difficult to enforce since it dislocates workers. In the face of this great devastation of the national patrimony they were compelled in the 70s to acquire loans initially for the purpose of supplementing the meager income from the extraction and export of raw materials and accumulating surplus for development. This wrong strategy has brought instead the opposite effect: they are now buried in the quagmire of foreign indebtedness. In the Philippines, for example, debt servicing reached a high of 33% of the national budget in the last 20 years compounded by the steady decline of the value of the Philippine currency relative to the US dollar by a total of 125% during the same period. Clearly, there is no light at the end of the tunnel, so to speak, for there is no tunnel at all in the first place. Given that ALL prescriptions for development coming from the World Bank, IMF and UNDP for more than half a century have not worked there is need for new direction and fresh start free from the fetters of traditions and old ideas that only bring the underdeveloped countries to the blind alley.

Initial statements.

Production is generation of commodities, i.e., objects that have exchange value. For purposes of development exchange value or value is the relevant concept although commodities are sold also for use by the purchaser. Some commodities have only exchange value, e.g., paper money, while others have both exchange and use value, the latter meaning that the purchaser can use or consume them, e.g., artwork and food. When the gold standard was in place gold had both exchange and use value. Development is the steady accumulation of surplus in society called social surplus coming from surplus (profit) contributed by various production centers. They are invested or kept in banks available for investment to generate more value and surplus or advance the intellectual and material infrastructure and improve support services. Surplus in a production center is what is left after all expenses of production have been cleared that include wages and salaries, taxes, utility bills, equipment cost or rental and overhead expenses. Marketing cost is borne by the buyer and goes to the marketing agency. The intellectual infrastructure includes educational and research institutions, scientists, engineers, inventors and managers and the material infrastructure includes factories and transportation and communication systems. Support services are also provided by educational and research institutions in terms of training and research and, in addition, banking systems, marketing centers and utilities, among others.

A complex system is a physical or mathematical system or process or socio-physical system (made up of people engaged in management of such systems and processes) whose motion, behavior and activity are not amenable to and, therefore, cannot be analyzed, understood and explained by computation and measurement alone. Some configuration and behavior of matter cannot even be described by computation and measurement, much less explained; examples are generalized fractal and chaos, the latter being mixture of order none of which is identifiable. All physical systems are complex and until the recent discovery of the superstring, the basic constituent of matter, which is a complex system, important physical concepts such as matter and energy were not known or defined. Not only is the superstring complex, it is dark (one of the two fundamental states of matter, the other visible or ordinary matter, i.e., not directly observable with present technology and known only through its effect on visible matter.

Present methodology of the natural sciences.

The present methodology of science that has its most advanced applications in physics is mathematical or computational modelling that describes physical systems or natural phenomena mathematically. Thus, it can only deal with appearances, its tools computation and measurement. Consequently, it has left unsolved and unanswered long standing problems and fundamental questions of physics such as the gravitational n-body and turbulence problems and what the basic constituent of matter and structure of the electron are. Their solutions required knowledge of how nature works. Consider the n-body problem that says: given bodies in the Cosmos at some initial time with known masses, positions and velocities and subject to their gravitational attraction find their positions, velocities and trajectories at later time, and the turbulence problem that essentially asks for conditions that lead to turbulence and how it develops so that, in some cases, e.g., tornado, it can be terminated. In both problems, the failure to solve them is due to two factors: (1) the ambiguity of concepts such as body, gravity and turbulence none of which can be defined by computation and measurement alone and (2) inadequacy of computational modelling. In both the n-body and turbulence problems the definition of the concepts requires the discovery of the basic constituent of matter which cannot be achieved by computation and measurement.

We start with a tentative definition: energy is motion of matter, tentative since matter is unknown unless the basic constituent is known. However, it tells us that matter and energy are never separate which helps our analysis. Flux is motion of matter with known direction at each point; turbulence is coherence of fluxes (flux is coherent fluxes) and chaos is mixture of order none of which is identifiable. Ambiguity of concepts and inadequacy of present methodology are even more acute in the social sciences where most concepts cannot be quantified. Therefore, for the most part social systems are complex and social science is inexact because of so many unknown variables such as human behavior and judgment which means that social science requires more sophisticated methodology. Thus, problem of development is complex.

Qualitative modelling and the basic constituent of matter.

The above discussion is needed to give a sense of how this most advanced natural science - physics - approaches complex problems, especially, since this new methodology that provides remedy to the inadequacy of computational modelling was first successfully applied to the solution of the n-body and turbulence problems and the resolution of its fundamental questions. Learning from this experience, we introduce the remedy: qualitative or non-computational modelling that, in contrast to computational modelling that describes natural phenomena mathematically, explains nature and natural phenomena in terms of the laws of nature. It certainly goes deeper than appearances and its two components are qualitative or non-computational mathematics and computation and measurement which are complementary.

What is qualitative mathematics? Imagine the daily activity of a mathematician or scientist: making conclusions, visualizing, guessing, thinking backwards, thought experimenting, engaging in creative activity, intuition and imagination, negating what is known to find an opening into the unknown, altering premises to draw out new conclusions and all other techniques that one brings into research to stamp it with his own style. Qualitative mathematics includes abstract mathematical spaces, foundations and the search for the laws of nature. In the solution of a physical problem it provides the explanation of the setting for the problem including the boundary conditions and the general solution and justifies the needed computation while the latter provides details and the concrete solution. The main computational mathematics for the n-body problem was the integrated Pontrjagin maximum principle. Its qualitative solution in 1997 required the discovery of the initial 11 laws of nature of the Grand Unified Theory that was then called the Flux Theory of Gravitation.

Now, we demonstrate how this new methodology resolved the 5,000-year-old search for the basic constituent of matter. Observation by the Hubble telescope reveals the steady formation of cosmic dust that gets entangled in cosmological vortices and collect at their cores as stars at the rate of one star/minute (there are star nests and nurseries in the Cosmos that release stars rapidly. In view of the energy conservation law that says, among others, that matter and energy cannot be created or destroyed the premise of the theory of relativity that other than gases and cosmological bodies the Cosmos is empty collapses. The only reason such matter is not observed directly is it consists of pieces of matter so small they are not detected by our medium for observation - light. This leads to the discovery of another natural law that says: There exist two fundamental states of matter: visible and dark; the former is directly observable the latter is not and is known only by its impact on visible matter.

With this natural law that insures the existence of dark matter we now raise this question: what does it consist of? The answer is: the superstring. This resolves the 5,000-year quest for the basic constituent of matter discovered in 1997 to solve the gravitational n-body problem. For now it is just a name but we shall embellish it with structure, properties and behavior by the laws of nature using qualitative modelling.

We recall that in the last 50 years the search for the basic constituent has intensified and physicists have devised more and more powerful atom smashers in search of it. Each time they raised the power of the smasher they found new generation of so called elementary particles but none of them qualifies as basic constituent since they all vanish, most in split second. The basic constituent must be indestructible, otherwise, our universe would have collapsed. On the contrary, it has existed for 8 billion years. What the physicists missed is this important question: what structure or configuration makes the superstring indestructible?

Imagine an eggshell that contains an egg shell that contains an eggshell, etc., ad infinitum. This is called nested fractal sequence. If we hit it by a hammer can we destroy it? No; a finite number of shells, perhaps, but not all since the tail sequence being so small will get inside the hammerhead and remain intact as nested fractal sequence of eggshells. This is the structure of the superstring that makes it indestructible. In a generalized nested fractal sequence the second term is similar to and contained in the first, the third is similar to and contained in the second, etc., and the terms are at decreasing scale (properties or configuration not necessarily geometrical).

With known information on the impact of the superstring on visible matter and the requirement that it is nested fractal sequence of superstrings of similar structures and properties at decreasing scale and applying the energy conservation law and the energy conservation equivalence law that says energy conservation has different forms of which nested fractal is one we come up with the basic structure and properties of the superstring: the first term is a closed circular helix (i.e., a loop) that looks like a lady's spring bracelet; it contains a superstring called its toroidal flux traveling through its cycles at 7´10²² cm/s with similar structure and properties, that contains a superstring, its toroidal flux traveling through its cycles at the same speed and having similar structure and properties, etc. We have highlighted the superstring not only to illustrate the power and crucial role of qualitative modelling in its discovery but also because the superstring will play a central role in development in the new global situation.

Natural laws and laws of production for effective development.

We shall identify the relevant natural laws and laws of motion of society and production. The laws belonging to the second category may not be stated as formally and precisely as natural laws because of the nature of the subject matter. In fact, we have already introduced some forms of law of conservation of value.

In a free enterprise system the price of a commodity is roughly equal to its exchange value which is determined by the laws of production as well as the dynamics of competition. However, in a monopolistic situation the price is determined by how much the market can bear. Nevertheless it is still subject to the law of supply and demand of economics. Therefore, in both situations pricing is not arbitrary. Just as the energy conservation natural law has several equivalent forms so is the conservation law on surplus. One is that in a production center the cost of production includes wages and salaries, utility bills, cost or rental of equipment and supplies, taxes and incidental expenses. The cost of marketing is borne by the buyer and goes to the marketing agency or middlemen.

Human labor alone is not capable of creating surplus so that even pre-historic peoples needed tools for subsistence. Thus, the use of technology, especially, advanced technology (based on advanced science), intensifies creation of value and surplus. However, it is expensive since its value includes the aggregate costs of developing science institutions, training of scientists, inventors and engineers and production costs. From this alone one can see why the popular strategy in underdeveloped countries of development through technology transfer has not prospered for, where will those countries get the money to transfer technology? Many countries have been at it for half a century and they remain underdeveloped. Manufacturers promote reverse engineering, i.e., disassembling a piece of technology to study it and make improvement. That will, of course, increase their sale and, perhaps, the sale of needed parts for improvement as well but it will not contribute significantly to the generation of surplus no matter how much improvement one puts into it. For example, a car will still be a car and will not fly to make travel more efficient no matter how much improvement one puts on it.

We cite a new development that occurred in Southeast Asia: the emergence of countries and territories called newly industrializing countries (NIC) that developed relatively fast in the last few decades. They include South Korea and Singapore and the territories of Taiwan and Honking (now part of China). A late-comer, China, has now joined in, despite the disastrous political upheaval there in the fifties and sixties, and may surpass the US economically in a few years. Another new comer is Vietnam. Both of them rose from the rubble of war and destruction. How did they do it? We shall find out.

What are the parameters for effective development strategy? The key is rapid generation of value and surplus that cannot be achieved in an undeveloped setting because of the backwardness of everything related to production: technology, intellectual and material infrastructure and support services. At the same time, the main problem of the developed countries is the opposite: abundance of surplus that cannot be disposed so that they have to stop production periodically due to recession or depression while at the same time they have shortage of many things specially environment friendly technology for tapping abundant alternative and clean energy source, protection against natural disasters (e.g., tornadoes), easing traffic congestion on air, land and harbors and cleaning up heavily polluted lakes and rivers (e.g., the Great Lakes is now ecologically dead). On top of these, quality health care has become out of reach to most of the population of the world even in the most developed countries. This situation is part of the parameters for effective development strategy while it provides a clear basis for mutually beneficial symbiotic relationship between the developed and underdeveloped world, another parameter. The point is how to exploit it.

How do we partake of the huge social surplus in developed countries? In practical terms, we have to sell them powerful advanced technology that addresses these problems or technology that produces commodities rapidly to meet these needs, one for each underdeveloped country that can corner a huge chunk of the global market and draw in a large share of social surplus during the 20-year effectively of its patent. Powerful technology means there is a global demand for it or it produces commodities in global demand. This is what Taiwan did in the sixties and seventies with its monopoly of FAX machines and modems. South Korea developed advanced technology for the integrated steel industry (that includes the automobile, electronics and tire industries) and part of what is now called high technology based mainly on quantum physics. So did the other NIC in the area of high technology.

If advanced technology is expensive how can huge profit or surplus be generated. It is the contribution of advanced science that raises the efficiency of the technology to a very high level leading to the rapid accumulation of surplus even if the profit on each unit product is small. This has to be combined with global monopoly for suitable period Now, there is a new element in favor of the application of the new generation of technology that raises production to a qualitatively new level: the availability of abundant and inexhaustible raw material that exists everywhere in our universe which is, therefore, free to fuel the appropriate technology. This dubs in with the current world situation: high technology is not only crowded but also dominated by the developed countries and the NIC. Crowded areas are wrapped in a cloud of uncertainty aside from the problem of competition and their eventual stagnation and academic death. In mathematics, this is true of number theory and topology and group theory is also going downhill. In physics, the theory of relativity has not even contributed a piece of technology and most physics departments have folded up their relativity programs because there is hardly any paper on it getting published. Fortunately, there is the timely emergence of the new physics in the Grand Unified Theory that brings us, at the same time, to the threshold of a new technological Epoch based on conversion of latent or dark energy to visible or kinetic energy as well as dark to visible or ordinary matter conversion. Dark matter is not directly observable by our medium for observation - light - and is studied only through its impact on visible matter, the reason it is called dark. Its basic constituent, the superstring, is what mankind has sought for over 5,000 years and discovered only with the application of this new methodology. Dark matter pervades everything in our universe including our bodies the reason it converts to visible matter and energy everywhere at rapid rate: in the Cosmos and in the cellular membrane of living organisms.

We have already noted the configuration and some of the properties of the superstrings aside from indestructibility. Being dark, its toroidal flux has infinitesimal impact around it and, therefore, does not interact with other superstrings making dark matter stable and stationary and an absolute frame of reference for our universe that debunks the postulate of relativity.

The toroidal flux, as motion of matter, provides every superstring its latent energy, i.e., dark motion of matter, each cycle of which has the energy of Planck's constant, 6.64 ´ 10⁻³⁴ J. When suitably agitated, the superstring, i.e., its first term in the sequence, bulges to a primum, unit of visible matter, such as the electron and positive and negative quarks, or photon (unit of light). They also suitably couple to form proton and neutron. The latent energy density of vacuum (dark matter) has been calculated: 10²⁶ J/cu ft, according to De Broglie, or the equivalent of 10¹⁸ kg/cu m or 8.8´10⁸ volts/cm according to Seike Jr. It is the fractal configuration of the superstring that makes it not only indestructible that accounts for the stability of our universe but also the storage of staggering amount energy. Being everywhere, abundant and inexhaustible, dark matter is free.

It is accepted that the primum is a magnet; its magnetic flux the induced vortex flux around it; the electron is negative and its charge of −1 (1.6´10^-19 coulombs) is the unit of charge by convention.

Now, is this idea of devising technology that runs on dark matter just a dream? Not at all for we do not realize it but we have been using dark matter for over 300 years. The some Projects may be discussed. For instance: the magnetic train is powered by vortex fluxes of two magnets; electric power plants of any megawatts of power capacity that run on dark matter; project with magnetic levitation; project on that we can terminate or deflect a tornado away from city or farm or abort a forming tornado (up in the clouds 1.5 - 2 km above sea level); project with using genetic therapy, :

This unified methodology is providing the development of novel technology area; every underdeveloped country will receive huge advantages from the development of this technology. The imagination and creative abilities expand borders of opportunities, generated by using proposed modernization.