|7. Systems Concepts
Many things in our nature, and probably everything, can be considered as systems and they can be analyzed using certain generalized principles. We show how the sigma law is used in these principles, and thereby show how the systems naturally obey the sigma law.
What is a System?
Every system has some components. In economic system for example, we may consider agricultural sector, commercial sector, financial sector, consumers, government, and banks as components. In our human brain we may consider, vision part of the brain, hearing part of the brain, body motion control part of the brain as the components. If you think analytically, you will find components in every system, however big or small.
We will also find that all these components are interconnected by some interfaces. The components are not isolated. In economic systems the components are connected by some financial transaction mechanism. Similarly, the human brain components are connected by some neurons and glial cells.
Finally, you may recognize that all systems have some purposes; they are created to perform some functions. For example, in the economic system, the purpose may be to sustain full population employment. In the brain system, the purpose may be to control harmoniously all physical organs inside the body.
That is, all systems have some coherency or consistency in them to make this purpose happen. Thus every system is composed of three things (a) components, (b) interfaces, and (c) objectives.
Through & Across Variables
All components have terminals. The terminals of two components are connected together to create the interfaces between components. As a result of these interfaces, the components form a network in the system.
All systems can be modeled using across and through variables. Across variable is measured across the terminals of the components. Similarly, the through variable is the quantity that flows through the terminals or through the interfaces into and out of the components. As an example for the economic system, the across variable may be the price and the trough variable may be the flow of goods. Similarly in a hydraulic system the across variable may be the pressure and the through variable may be the fluid flow rate, etc.
We are not suggesting writing down these equations of our systems. It is not practical to do that. What we are trying to show is that there is a possibility of creating a very large set of equations that will describe the totality of all systems. And we are also showing a constructive approach in producing that set (4.22). In addition we are using the sigma law as the foundation of this approach.
The feasibility of such an approach, and the existences of such a set of millions of equations in millions of variables that will describe the entire society and nature, should be understandable now. If we do that then there will be no unknowns anywhere, there will be no fuzziness in our knowledge. However, if we use a small set we will get only an approximate view; and there is a possibility that it may give a completely wrong view. This is because a local view cannot capture the global view, and the real truth may lie outside this local view. Thus the global space time (GST) view is absolutely necessary to find the real truth of nature.
Note that this idea of covering all objects of the entire universe is an attempt to combine the views of all local objects in a simultaneous, interactive, and dynamic way. This will prevent the possibility of remaining in the dark like the blind men and the elephant story. But can this modeling concept reveal the existence of soul and reincarnation? Definitely yes, if we cover all objects, all details, of all activities, over all time. It will show that a person dying in one place is coming back after some days, months, or years in another place, with the characteristics he had before. This model will represent the true knowledge or the existence of such knowledge. The idea should highlight the complexity of this model.
Solutions of DE
Once we have the equations, like in (4.22), then we can imagine their solutions. The mathematical theory of differential equations ensures the existence of a solution under fairly realistic conditions [Farlow].
It has also been shown that the solution is unique under a given set of initial conditions. The theory also says that the solution can be extended in both directions of the initial time t0, that is, from minus infinity to plus infinity on time scale. Thus the solutions can in theory, predict the past and the future. The solution is continuous. If a break happens, then it will start again at some other time, exactly from that break point in a continuous way. Better the model is better will be this prediction.
Thus the solution of the DE represents the memory of the system. This is because it shows how the system behaves in the past, at present, and in the future. This global time is also a key feature of the system theory based model of (4.22). This solution helps us to study the nature using the laws of nature.
The literature on the theory of relativity also talks about the predictability of future. It has been written in [Eddington, p. 46] “Events do not happen; they are just there, and we come across them”. Our view point, that the solution exists in the future, supports the above statement.
It seems the theory of relativity has not made any conclusive determination about the predictability of future. Some authors [Hogarth] say it is completely predictable and some say it is not possible [Manchak]. However our approach is different. We are considering a very large dimensional space as opposed to only four dimensions in the relativity theory; we are also considering very large set of simultaneous equations and relativity considers only a very limited number of field equations. The philosophy of our approach is also fundamentally different along with our definitions. Our focus is on the laws of conservation.
Although our view point is different, but there are many literature available on the internet on the subject presented in this section. Some concepts of general system theory have been discussed in the paper [Bertalaffy] and laws of nature in economic theory in [Halls].
It should be realized now that everything is a system. Our solar system is a very big system. Similarly, the model of our atoms is also a system, but a very small microscopic system. Since the derivative is a law of conservation, the differential equations represent the laws of conservation also. We have just shown that all systems can be represented by differential equations; therefore all systems follow the laws of conservation. Note that it is not that the models follow the sigma law; it is the real systems in nature that follow the sigma law. We can see that the collection of all systems, which is the GST, naturally follows the sigma law or the memory law.
We will discuss human memory in another chapter and in more details. We will give a generalized definition of memory there. But in this chapter we can also see some meaningful definitions of memory. The state variable x(t) at any time t represents the status of the universe at time t. Everything that you want to know about nature is included in the state. But when you find x(t) at some other time than present time t, say at time t1 , then the state x(t1) becomes the memory.
The theory of differential equations says that x(t) can be determined by the solution for all time t, both past and present. The solution can be used to find memory of the universe. Since these state equations are based on the conservation laws, this memory can never be lost. That is why we call it eternal memory.
It is obvious that DE theory does not allow us to actually find past or future memory. However, the theory confirms that the memory exists and its feasibility of finding them is also meaningful. All we need is a technology to get them. In the chapter on yogic power we will see that yogis can find such memories.