Worldviews Discussion Paper
Hubert Van Belle
The present technological evolution is characterised by the design and realisation of increasingly complicated, large-scale, flexible and agile technical-organisational systems. The implementation of these multidisciplinary systems is an answer to a global economy with a growing competition and uncertainty. The effective control of this rising complexity and the discovery of integral solutions for it are the main challenges for the modern technical-scientific thinking. In engineering sciences, very general and powerful theories, techniques, tools and methodologies are developed to solve the problems which are related to the design and control of complex systems, software, structures and organisations. These approaches are especially important for micro-electronics, information technology, robotics, business management, and many other fields which are confronted with increasing technical and organisational complexity. The fast paced developments in these fields are deeply changing the world.
Modern engineering involves several technical disciplines and integrates many different technologies. Mechatronic systems, for instance, consist of: mechanical, hydraulic, pneumatic, electrical and electronic subsystems. In the electronic subsystems, hardware as well as software has to be taken into consideration. The current trend is for hardware functions to be increasingly replaced by software. As a result, the man-machine interaction and the user-acceptance have to be taken more and more into account. Effective engineers operate in a very purposive and efficient way. They design, build and operate systems which have to meet the customer needs. Moreover, in doing this they must realise the economic and social objectives of their company. This implies that organisational and human aspects become important and that non-technical disciplines should naturally intervene. The modern technical-scientific thinking assumes a functional and organisational vision on the world and recognises purposive or normative systems not only in the technological and economic spheres but also on all levels of reality.
Engineering sciences provide general languages, models and methods which are developed especially to deal with complex and multidisciplinary problems. The computational methods are widely used to calculate the behaviour of complicated electrical networks and mechanical structures. An important example is the finite element technique which is used to guarantee the strength and stability of constructions and buildings. This typical engineering technique is also applied for continuum modelling in other disciplines. For control purposes, a very important element is the system theory and the state space formulation of this general approach. The bond graph method allows the modelling and simulation of multidisciplinary systems. The well-known thermodynamics can be considered as the first attempt to formulate a general technical system theory. The law of conservation of energy made it possible to link the different disciplines. All of these theories, which seem different at first glance, can be integrated relatively easily in a general network theory. The analogy between electricity, mechanics, thermodynamics, hydraulics, and many other fields also allows this generalisation. The energy-concept, Tellegens theorem and the properties of homogeneous energy functions are fundamental in this integration operation.
In examining the similarities between the different fields of exact and social sciences, we can find very convincing evidence that the applicability and results of the modern technical-scientific thinking are not limited to the technical world. The engineering sciences show us a possible way to unify different theories, disciplines and views. If a more general concept can be found for energy, it could be possible to bridge the gap between the exact sciences and social sciences. The general approaches can be used for the development of integrating world views and their successful application says something about the nature of reality. However, there exist a big wall between the worlds of engineering and philosophy. Action oriented engineers feel less attracted to philosophy and philosophers seem reluctant to accept technology as a reliable source of truth. The philosophy of technology is mainly interested in the negative effects that technology has on men, society and the environment and the ethical consequences of human interventions . The critical issue of the type of thinking which engineers exhibit and which has such a drastic impact on our life, is mostly not considered. For example, the system theory and modelling techniques as applied in engineering sciences deserve special attention (Van Belle, 1995). It is worth noticing that the modern technical-scientific thinking has its own unique characteristics which differs from the main aspects of the thinking in physics.
This article deals with the principles of modern technical-scientific thinking and defends an open exchange of ideas between the engineering sciences and philosophy, especially for the construction of world views. The first part deals with the conceptual framework of the (technical) system theory. Special attention is given to the blackbox-approach and the structured methods. The second part introduces the relevant energy and network concepts. Furthermore, Tellegens theorem and the analogy between the different branches of the engineering sciences are dealt with. An attempt is made to find a general concept that can take over the function of energy in social sciences as well as exact sciences. To conclude, questions are asked about the content of the system theory. For example, the question is raised as to whether or not the system theory is more than a general and successful but empty shell. Do the system and network theories say something essential about the structure of reality ? What are the principles of the technical-organisational world view ?
The system theory is based on a functional, analytical and reductionist view on reality. A system can be defined as a set of relationships. This web of relations establishes the connections in space and time between the attributes of the interacting entities. The world is considered as a system which consist of a number of interacting subsystems. Reality is consequently seen as a construction made up of interconnected building bricks. Besides, it is assumed that the relationships which characterise reality can be broken down into relations which describe separately the behaviour of the subsystems and their interconnections. This reductionist approach takes not only the parts of the system into account but also pays attention to their mutual influence. In the technical system theory, the surplus value of the whole with respect to its parts is completely attributed to the interactions. The interactions explain the creation or emergence of new properties. The interconnection relations give the physical systems a structure and coherence and allow the interplay and gearing of the elements.
The analytical method assumes the possibility to distinguish subsystems and to consider them separately. In this manner, subsystems also can be viewed as systems on their own. Examples of systems include: all kinds of structures, networks, organisms and organisations. As a result, a system can also be described as having a physical, technical or organisational structure, in which matter, energy and/or information are processed. An open system interacts with its environment, whereas a closed system is isolated from the outside world. An open system is affected by stimuli from its environment and reacts with signals to the outside world. The behaviour of an open system can be established by studying the interactions with the environment and making a model of the internal relationships. If the physical laws of the basic elements and their connections are identified, the open system is sometimes called a white box or clear box. The internal workings of a blackbox on the other hand are not known or are deliberately left out of consideration.
A blackbox is a part of the universe that interacts with its environment. The interaction actually occurs by means of incoming and outgoing matter, energy and information flows. The modern electronic appliances used at home are excellent examples of blackboxes. Most people know how to operate their radio, TV, video and PC but do not know their internal structure and workings. Conceptual blackboxes are also found in physics. For example, no further explanation has been found for elementary particles and their interactions. Nevertheless it proves to be possible to make some meaningful statements about reality without considering each of the underlying levels with their corresponding building components and their structure.
In the blackbox approach, the subsystems are delimited by a sealed boundary that separates the interior from the exterior. It is assumed that it is possible to distinguish what is part of the blackbox and what is part of the outside world. Blackboxes are influenced by the outside world and in turn they influence the outside world. The relevant part of the outside world that interacts with the blackbox is called the environment. A blackbox is consequently a part of the universe from which the interactions with the environment are studied from outside and without considering every detail. In this view, a system is built up by a number of blackboxes, which interact with one another and possibly with the outside world of the whole system. On the other hand, if a blackbox is forced open, a system consisting of interconnected blackboxes can usually be found.
The interaction between the blackbox and its environment can only take place via ports in the boundary line. The ports are the only known and observed input and output possibilities for matter, energy and information flows. The physical phenomena that affect the blackbox are called inputs and can be characterised by input variables while the response of the blackbox or outputs can be characterised by output variables. Hence the inputs and outputs are phenomena that link events inside and outside the blackbox. For example, the mechanical force acting on a vehicle can be considered as input and the resulting acceleration as output. A certain correlation exists between the inputs and outputs, which is characteristic for a blackbox. This more or less simple relationship can be modelled by studying the effect of input changes on the outputs. The behaviour of a blackbox without memory functions can be characterised by input-output relations. For a blackbox with memory or storage properties however, it is not enough to know the inputs at any particular moment in order to be able to correctly determine the outputs which correspond to that same instant. What the blackbox has remembered or retained from the past should also be taken into account. This is done by considering the internal states. The stopping distance of a car, for instance, depends not only of its brake force, but also on its initial speed and the corresponding kinetic energy. The momentum and kinetic energy can be taken in this case as state variables (or state functions).
Generally speaking, it is impossible to represent the behaviour of a blackbox fully and accurately without considering its internal states with the help of state variables. The behaviour of a system in the blackbox approach is modelled by a set of relations between input, output and state variables. The state space approach (Zadeh & Desoer, 1963) provides a very elegant mathematical description of this relation. The outputs of a blackbox are dependent on the inputs and the internal states. The internal states are themselves influenced by the inputs but are also partly determined by the previous internal states. The state variables characterise the internal entities that can play a part in the event. This is the free part of matter, energy and information that is present inside and available for the process. In abstract mathematical approaches, the internal states are regarded as the minimum information which, together with the inputs, fully determines the outputs. The concept of state variables is very important to understand the dynamic (time-dependent) behaviour of systems. The state variables represent the influence of the past on the present due to the memory properties of the system. The past influences the present via the internal states. It is important to notice that the blackbox approach reduces the influence of the outside world to the inputs from the environment and limits the effect of the past to the internal states.
In the analytical approach, an attempt is made to solve complex problems by splitting them up into sub-problems which are easier to manage and to solve, and which are then tackled one by one. When complex systems are being studied, this process is preferably done in several stages and in a hierarchically structured way. In breaking down problems, various levels of detail can be distinguished and there is a shift from macro to micro-scale. If, for example, we are analysing the operation of a company, we concentrate on the functions of the various departments, services and employees successively. This is a striking illustration of such a functional explosion. With the system approach, attention is not only given to the behaviour of the isolated elements, as is the case with the simple reductionist analytical methods, but also to the interconnection relations. Using the structured approach, the large number of relationships that characterise large scale and complex systems can be studied without losing the overall picture. In addition, the analysis phase is followed by a so-called synthesis phase, in which the interactions are taken into consideration again along with the interconnections. This process is very laborious and seems not at all efficient. However, the result is a system with a much higher level of quality than if this method was not followed. For this reason the structured method is applied very rigorously in the development of complex computer programs to automate complicated processes and companies. One speaks of top-down planning, bottom-up implementation. Reality as a whole can also be viewed in a structured way as a layered structure. When elementary particles rise to become social organisations, a number of successive layers, each with their own characteristics, are identified. Besides pre-material, material and biological layers, psychical, social and cultural layers can also be distinguished. Analogue models are used in the computer world. A clear distinction is made, for example, between hardware, system software and application software.
In the organisational branch of the system theory, purposive or normative systems are considered. The behaviour of the elements of these systems has a certain coherence and direction so that the system, considered as a whole, pursues an objective. This can occur by moving towards an ultimate goal and/or by optimising a performance criterion during developments. Even if there exists in reality no final cause, it is often possible to deduce, from the behaviour of systems, which objectives they have apparently in view. This extrapolation allows us to describe the global behaviour of a complex system in a very succinct manner. Purposes offer an economical way to characterise the overall behaviour of complex systems. Notice that having an endeavour to realise a goal, does not necessarily guarantee that this objective will be met. In most cases and broadly speaking, living beings, organisms and organisations seem to manifest themselves as purposive systems. The primary objectives are about perpetuation, continued existence, survival, growth and about acquiring the resources to achieve these aims. This applies both to individuals and complete organisations. Usually a hierarchy of objectives can be discerned, in which the objectives of the elements, subsystems and the whole system are geared to one another. By co-ordinating functions and tasks, a cohesive behaviour of the whole system can be realised. In many cases, the objectives of the system also need to be geared to its environment. The interests of the shareholders as well as the interests of the other stakeholders have to be taken into account. In modern companies, one of the main tasks of the management is to fine tune the internal and external objectives.
In the exact sciences, it is assumed that reality can be laid down in causal laws and that uncertainty plays an essential part. Stating a final intention as motive is fundamentally rejected and purposiveness is labelled as nothing more than a pretence. At best, purposiveness can be a broad manifestation of fundamental laws. Nevertheless, one has to at least accept that living organisations manifest a behaviour which is oriented towards survival. Everything that exists must have properties which allow it to last during a certain period. On each level of reality organisation structures can be distinguished which pursue their survival. Beings which are not able to defend their structure and to continue their existence, disappear. For that purpose they have to be robust against disturbances. Hence it is possible to find in each layer of reality feedback mechanisms which defend the integrity of the structure. Conveying information from the output back to the input of a system is called feedback and is characteristic of a control system. When a difference is found between the actual and desired behaviour, an adjustment is made. This is the case, for example, if a car deviates from its respective lane due to a disruptive influence, and the driver compensates by steering the car back into the correct lane. Feedback loops are not only responsible for stability but also for change. Feedback can explain the creation of patterns in space and time and the emergence of order out of chaos.
Many physical systems display a dynamic behaviour that can be called purposive. This is most evident in systems with feedback, which try to achieve the standard imposed on them. Any variances with respect to the standards fixed are determined in order to deduce the necessary corrective measures. This results in certain coherence in the behaviour of the elements and a trend in the evolution of the whole system. In many instances nature seems to lend itself to a simple description and often proceeds in the most economical way. This last principle was formulated by de Maupertuis as the law of least action. It was given a scientific basis by Euler, Lagrange and Hamilton. According to Hamiltons principle, a conservative mechanical system moves so that the integral of the Lagrange function, also called action integral, reaches an extreme value (usually a minimum). The Lagrange function of the system is equal to the difference between the kinetic and the potential energy (Spiegel, 1967). The criterion that the states of a system pass through and the path they have to follow is unexpectedly elegant in this formulation. The system seems to behave in a purposive way by optimising the action integral during the motion. Human beings are also able to be viewed as behaving as purposive systems. Men make plans, present dreams as objectives and pursue goals. They do not accept reality as a fact to be experienced passively and see the difference between what is real and what is desirable as a problem that has to be solved. This view, which is in fact a control engineers viewpoint, drives them to exert a systematic influence on the world, bend it to his will, bring it under control and improve it.
Networks are physical systems which are made up of a number of interconnected multiports. A multiport or n-port is a blackbox with different gates for interaction with its environment. Resistors, inductors and capacitors for instance, can be represented by electrical two-ports. Examples of networks are: electrical networks, electronic systems and even mechanical structures. Networks consist of active elements and passive elements. If the passive part of the network is considered as a blackbox, the active elements or sources correspond with inputs and outputs. The interaction between the network components and their environment is characterised by two types of variables which appear in pairs of variables. Each pair is assigned to a port. In case of electrical networks, pairs of currents and voltages occur. In the case of mechanical structures, pairs of forces and displacements, torques and angular rotations can be considered. Both kinds of variables can be taken as inputs or as outputs. The two types of variables are sometimes called through- and over-variables, trans- and inter-variables or efforts and flows. In a simple hydraulic analogy, these variables are seen respectively as the flow rate (a quantity per unit of time) and the level of a fluid. The occurrence of variables in pairs enables the concept of energy to be introduced with the product of both variables as the definition of power (or work). The energy concept makes it possible to characterise the behaviour of networks in a very compact way. With the help of internal energy for instance, it is possible to characterise globally the state of a system with only one figure that takes the different forms of energy storage into account. The energy concept which is defined in the different branches of the exact and engineering sciences is also important as the link between the different disciplines.
Two kinds of interconnection relations can also be distinguished which correspond with these pairs of variables. For electrical networks, the current and voltage laws of Kirchhoff apply. In mechanical structures, the equilibrium and compatibility conditions hold. The sum of the flow rates that converge in a node equals the total of the flow rates that emerge from that node. An interconnection brings the ports to the same level. These interconnection relations describe the continuity of the variables in space. So far as the interconnection relations are concerned, the independence of both types of variables is expressed too. Moreover, it is important to notice that interconnection relations are linear or can be put easily in a linear differential form. This property is the starting point for very general energy theorems such as Tellegens theorem and the similar theorem of virtual work. These theorems are oriented towards the interaction between the multiports and make as much as possible, an abstraction of the properties of these blackboxes.
In the analytical methods for the calculation of the behaviour of networks, the analysis phase is followed by a synthesis phase. The mathematical models for the separate elements and their interconnections are combined with each other and elaborated. The way the interconnection relations are modelled and introduced leads to two diverging formulations of the problem (El Naschie, 1990). In the non-energetic, vector approaches, the interconnection relations are directly applied to establish the differential equations of the problem. Historically, this method goes back to Newton and the laws of statics and dynamics. The energetic, scalar approaches follow from the work of Leibnitz, Lagrange and Euler and the variational branch of mechanics. The energetic methods are based on energy theorems such as the theorem of virtual work (Argyris & Kelsey, 1960). In engineering, this widely known yet little understood theorem plays an important part in the calculation of the stability of mechanical structures such as buildings and constructions. The analogous theorem of Tellegen (Tellegen, 1952), which was originally formulated for electrical networks, can be considered as the basic theorem for the energetic methods. This theorem is generalised for mechanical structures (Van Belle, 1974; 1976) and for all kinds of networks and structures with linear, adjoint and uncoupled interconnection relations. For further clarity it is worth noting that the notions adjoint and transpose of a matrix are related. The introduction of an abstract energy concept also made it possible to formulate Tellegens theorem for systems in general, as proven by Lee (1974).
Tellegens theorem is based on the interconnection relations for electrical networks: namely the current and voltage laws of Kirchhoff. No special requirements are imposed to the elements. The elements may be linear or non linear, time invariant or time variant, deterministic or stochastic, passive or active. Tellegens theorem shows that if the current and voltage distribution satisfy Kirchhoffs laws, the power supplied by the sources is completely absorbed by the passive elements. In fact, this theorem expresses the conservation of energy in space: or the principle of continuity of power. In this apparently evident theorem, it is proven that the quantities of energy are balanced and that no energy is dissipated in the interconnections. It is less straightforward that Tellegens theorem still holds, if the currents on a certain moment are considered but the voltages on a earlier or later instant are taken into account. This is also the case when the currents of a given network are combined with the voltages of another, adjoint network. The adjoint network can be widely different from the original network. It is required that the given and adjoint networks have the same topology, but the components can be completely changed. The validity of Tellegens theorem for situations at different moments and with modified networks, seem at first to be very strange, but can easily be proven. In these cases, we deal with the continuity of quasi-power instead of actual power. By the introduction of a well-chosen adjoint network it is possible to simplify the solution of some network problems considerably. The theory of adjoint networks offers, for instance, a very elegant and powerful method for the calculation of the influence of local element changes on the behaviour of the network, as a whole, for sensitivity and tolerance analysis purposes.
Tellegens theorem can be formulated in other forms. These formulations arise from the application of so-called Kirchhoff operators which do not affect the linearity of the interconnection relations. Examples are the differential and integral forms of the theorem. It follows, for instance, that Tellegens theorem holds for special energy definitions such as content and cocontent. The energy content of a (non-linear) resistor corresponds to the surface below the voltage curve in the current-voltage diagram and limited by the operation point. The cocontent is defined as the dual of the content. Another formulation of Tellegens theorem expresses the orthogonality of current vectors and voltage vectors. The orthogonality concept descends from geometry and indicates here that the two vectors are rectangular with regard to each other in the multidimensional space of currents and voltages. Their scalar product is always equal to zero under this condition. Consequently, it is clear that an invariance is expressed by Tellegens theorem. Since the orthogonal relation still holds after time shifts and element changes, one can speak about symmetries. Symmetries are more and more considered as a fundamental property of reality (Apostel, 1995; Van Belle, 1998). Orthogonality seems also to appear on many occasions.
Tellegens theorem can be used as starting point to deduce a large number of properties for networks (Penfield et al, 1970). For example, this is the case for the first law of thermodynamics or the law of conservation of energy. Energy does not appear out of nothingness and can not disappear into nothingness either. Tellegens theorem is, in the first place, oriented towards the energy distribution in space, while the conservation law stresses the changes of state in time due to energy storage. The increase of internal energy is equal to the difference between energy supply and heat dissipation. Besides, it should be noticed that the change of internal energy is not dependent on the path which is followed during the evolution from the original to the final state. The internal energy is a state function which is determined by the state variables only. This property follows from the integral form of Tellegens theorem and the mathematical properties of exact differentials. On the contrary, the terms which are related with the heat dissipation, cannot be integrated exactly and are thus dependent on the trajectory and a function of the elapsed time. If, for example, one climbs a mountain, the difference in height between the summit and the base camp and the associated increase in potential energy are not dependent on the route followed and the duration of the journey. This is certainly otherwise for the required effort (and perspiration).
In the process that determines the global behaviour of a network, four functions occurring in combination can be distinguished. These are the source, conservation, dissipation and transformation functions. Sources represent explicitly the boundary conditions of the system and are responsible for the energy exchange with the environment. They produce or annihilate power in the network. The conservation function resists change, tries to preserve the existing states and shifts the situation from the past via the present to the future. This function therefore implies retention, memory and storage properties. The conservation function ensures that network elements behave as reservoirs and initially absorb and subsequently possibly emit energy during the process. All kind of energy reservoirs such as masses, springs, capacitors and inductors, show these properties. Ideal storage elements are sometimes called energic elements. The second function represents the dissipative effect as a result of physical phenomena that can be associated with heat generation and losses. In practise, energy always seem to disappear from the internal process, become disseminated and no longer take part in the process itself. This happens in the case of energy leaks owing to friction, heat dissipation and real energy conversion processes. Dissipative elements, such as ideal resistors, are sometimes called entropic elements. The transformation function is responsible for the conversion of variables without any loss and storage. This kind of effect occurs, for example, in (ideal) mechanical levers and electrical transformers. All sorts of energy conversions can also be modelled with the help of transformation functions. If we look to the ideal case where no dissipation of energy occurs, the network seems to be able to exhibit a reversible behaviour. It is possible, as it were, to reverse the course of events, to achieve the original states once again and to emit entirely everything that was absorbed from the environment. The conservation and transformation functions can be associated with invariance and symmetry, the dissipation function indicates irreversibility and time asymmetry.
Tellegens theorem can also be useful to determine the natural evolution of the states of a network. It turns out to be possible to define a general entropy concept for networks and to derive the second law of thermodynamics or entropy law from Tellegens theorem. The entropy of a network without sources increases with the function of time. The stored energy spreads over the storage elements and the free part is dissipated. The internal potential energy pursues a minimum and the total entropy tends towards a maximum. The emission and absorption of energy by the reservoirs can be explained by the differences in level. Differences in level lead to flows through and between the elements of a network. The flows only cease if the differences in level disappear. In fact the flows try to neutralise the differences in level in the network and to equalise the levels. This is also the case for the flows of thermal energy from the dissipative network elements to their environment. Heat energy flows from a body at higher temperature to one at lower temperature. The natural tendency of energy to spread is in line with the law of entropy. It is further also possible to show that in networks the effect cannot precede the cause. The dissipation happens at the same moment or somewhat later than the input signals which are applied to the network (Penfield et al, 1970: 45-46). This proof could be an indication that asymmetries can be deduced from symmetries, at least for symmetry breakings which are related with dissipative effects.
As mentioned before, Tellegens theorem is proven starting from the interconnection relations. One can ask now if it is possible to derive the interconnection relations from Tellegens theorem. It is taken for granted that Kirchhoffs current law can be deduced from Tellegens theorem and Kirchhoffs voltage law. The voltage law on the other hand follows from Tellegens theorem and the current law. The introduction of a well chosen adjoint network makes it also possible to show, based on Tellegens theorem, that the interconnection relations are linear and in accordance with Kirchhoffs laws. This proof seems impossible without the introduction of an adjoint network and demonstrates that Tellegens theorem can be taken as a starting point for the development of network theories instead of the interconnection relations. The energy and non-energy approaches appear to be equivalent. They correspond to different views on reality but lead finally to the same results. In addition, Tellegens theorem can be considered as a postulate for networks. The continuity of power is in this case viewed as a leading principle.
It was already pointed out that the interconnections between the elements of a network can be modelled by linear relations. Moreover they are similar in the different fields of the engineering sciences and exact sciences. These remarkable analogies are used to extend the application of Tellegens theorem from electrical networks to other disciplines and to multidisciplinary systems. The general bond graph method is in fact based on this insight. There exists, for example, a similarity between the current and voltage laws of Kirchhoff and the equilibrium and compatibility conditions in mechanics. Currents can be considered as electrical analogues for mechanical forces and torques. Voltages can be seen as analogues for displacements and angular rotations. This formal analogy, called the Firestone analogy, is mostly used in structural engineering. In bond graphs, the physical analogy between currents and speeds and between voltages and forces is preferred. The question raises: Are these analogies a coincidence or do they follow from general principles ? Reality seems to impose general conditions of continuity which have to be satisfied by the interconnection relations. The flow rates and levels do not vary suddenly in a interconnection point and the conservation of power in space holds. The thermodynamic bond graph method relates the analogies to the properties of homogeneous functions (Breedveld, 1984).
A function F(x) is called a (first order) homogeneous function if for each scalar a and vector x:
F(a.x) = a.F(x)
The internal energy of storage elements in different physical domains can be expressed as a homogeneous function. Two equal masses which are in the same state for instance, are not interacting and do not require any energy transfer when they are connected with each other. This means that the state variables and internal energies are not influenced during this operation. They can be added together each to give the total status for the interconnected two masses. The properties of the homogeneous energy function can be used to define the pairs of network variables which play a part in Tellegens theorem and as a physical basis for the generalisation of this theorem from electricity to other fields. In the thermodynamic bond graph method, a homogeneous equation of extensive variables is applied. Extensive variables are state variables which are proportional to the extent of the element. Examples of extensive variables are the mass and momentum of a mechanical system consisting of a lumped mass. It can be easily shown that if the mass and the momentum are for instance, both doubled, the kinetic energy also doubles. The partial derivatives of the internal energy with respect to the extensive variables are called intensive variables or efforts. It is possible to show that these efforts are not proportional to the extent of the element. Moreover, the time derivatives of the state variables are defined and called flows. From Eulers theorem it follows that a (first order) homogeneous energy function for a storage element can be expressed as the scalar product of the state vector and the effort vector. It can also be proven that the power or rate of energy supply to an element is equal to the scalar product of the effort vector and flow vector. This brings us back to the definition of power in Tellegens theorem. Table I gives a survey of the state variables, efforts and flows and demonstrates the analogy between the different physical domains following the thermodynamic bond graph method (Breedveld, 1984: 50). These kinds of correspondence allow an extension and generalisation of the electrical network theories to other fields and multidisciplinary systems. The graphical representations of physical systems in the bond graph method are based on the existence of analogies.
|Physical domain||State Variable||Effort||Flow|
|- translationally potential||displacement||force||velocity|
|- rotationally potential||angular displacement||torque||rotational speed|
|- translationally kinetic||momentum||velocity||speed of momentum change|
Table I. Analogy between physical domains following the thermodynamic bond graph method.
The energy concept shows itself to be the key which relates, integrates and unifies the different disciplines of the exact sciences, including the engineering sciences. The degeneration of all types of energy by dissipative effects in heat and the energy equivalence expressed in the first law of thermodynamics are the base of this unification process. Heat energy can be considered as the Rosetta stone of the exact sciences. If, as mentioned before, a more general concept can be found for energy, it could be possible to bridge the gap between the exact sciences and social sciences. There is convincing evidence that the concept of purpose is able to take over, to a certain extent, the function of energy in the social sciences. The energy concept makes it possible to consider the behaviour of physical systems as purposive. The former law of least action and Hamiltons principle are already discussed. Mechanical systems, in an unforced situation, settle down and find a stable position if the potential energy reaches a minimum. Attractive and repulsive forces on each of the bodies are, for instance, in equilibrium. Under this condition, there is no longer any potential to change and the system becomes a fixed structure. A structure in a stable position is within some limits robust against disturbances. A stable system returns to its equilibrium position if the disturbances cease. Certain efficiency principles seem to be active in reality. It has been proven that for electrical networks with elements which show a positive behaviour, the energy content is minimum if the current and voltage distribution meet Kirchhoffs laws (Penfield et al, 1970: 37-41). An element is said to be positive if any increase of current is accompanied with an increasing or constant voltage. A dual theorem is valid for cocontents. Analogue properties hold in structural engineering and are applied to determine the stability of buildings and constructions. The tendency to minima plays an important part in energy methods. It is as if the physical systems behave in an energy-efficient and purposive way. This relates energy with more general concepts such as performance function, objective and purpose.
Technical systems are designed to satisfy some needs by performing certain tasks. The performance function is a measure of the extent in which the design specifications are met. This function attains a minimum if the system behaves as required. With the help of weight factors, it is possible to emphasise in the performance function the aspects of the system behaviour which are most important for an optimal functioning. The theory of adjoint networks provides an interesting method to calculate the sensitivity of performance functions for design changes (Director & Rohrer, 1969; Van Belle, 1976). Technical-organisational systems, such as manufacturing companies, have to deal with technical, economical and social objectives. The realisation of these objectives can be monitored by indicators which indicate, among others, the efficiency and profitability of the operations. Companies have to be profitable to survive and the financial aspects are vital. Money and value are the main issues in the business world. If one compares economical systems with mechanical systems, then one can view a minimisation of costs as analogous to a minimisation of energy. Consequently, the financial-economic aspect vision on the world and the energetic approach seem comparable. Survival is, without a doubt, a basic objective for all kinds of beings on each level of reality. Structural cohesion requires a certain gearing of the objectives of the subsystems to the objectives of the system, as a whole. For physical systems, energy plays an important part in this optimisation process. Purposes take over the function of energy in the higher layers of reality. Values can be seen as aspects or manifestations of these high level purposes. Beside perpetuation purposes, human purposes and transcendental purposes have an important influence on the behaviour of men and society. These higher level purposes are sometimes in conflict with the purpose to survive and seem to be uncoupled from the physical ground. The question arises: Can this purposive behaviour find a bottom-up explanation in physical laws, or does a top-down interpretation, based on general principles, need to be sought ? Or in other words, is the purposive behaviour the result of elementary laws only ? Or finally, is this behaviour determined by encompassing principles?
The successful application of the hydraulic analogy to understand phenomena in other disciplines is very remarkable. This analogy is successfully used in electricity and network theories. One speaks about electrical currents which flow, just as fluids, from a higher to a lower level. Since the discovery of electrons, we know that this model has also a physical basis. The electrons move however from minus to plus and not from plus to minus as was assumed before. In the Firestone analogy, which is mostly applied in the engineering world, mechanical forces are considered as analogues for electrical currents. The equilibrium conditions of the statics show a clear correspondence with the continuity principle of the fluid dynamics. This could be an indication that forces are transport phenomena in reality. This brings us to quantum physics and to force particles (gluons, photons, intermediate vectorbosons and gravitons) as carriers of the four fundamental forces of nature. Symmetries, especially gauge symmetries, are important in the standard model for the subatomic world of elementary particles and their mutual interactions.
In the previous pages, the rather mechanistic world view of the technical system and generalised network theories was outlined. The universe is seen as a web of relations with clusters of interactions which make a hierarchical view possible and significant. It is also possible to align blackboxes in each layer of the reality, to study them from outside, to limit the interactions with the outside world to inputs and outputs from the environment and to reduce the influence from the past to the state variables. Not everything seems directly and intensely related with everything. In addition, abstraction can also be made from the lower levels of reality and higher level models can be derived by identification techniques. For example, quantum physics had not yet been developed when the laws of mechanics and electricity were determined. The blackbox, state space and system approaches are very general but reductionist ways to model a part of reality. If variables occur in pairs of efforts and flows, a system can be considered as a network and the energy concept can be defined. The energy concept allowed the development of interesting methods which make abstraction of the characteristics of the network components. The very general theorem of Tellegen is only based on the linear and adjoint character of the uncoupled interconnection relations. Tellegens theorem stresses the distribution of energy over the network components and the continuity of power between these elements. This theorem expresses the orthogonality properties of the effort and flow vectors too. If adjoint networks are introduced, Tellegens theorem can be considered as a postulate which allows us to derive the interconnection relations, among many other things. The analogies between the variables in the different physical domains can be defined in a physical way with the help of the properties of homogeneous equations. Systems which can be modelled by homogeneous equations are additive with respect to their state variables and internal energies. The state variables and internal energy are not dependant on the position of a system in space. Continuity and invariance in space seem to be the important principles behind a physical network theory.
An important feature of the energy methods is the possibility to define global indicators, which characterise in a very compact manner, the status of the network as a whole. State functions, such as internal energy and generalised entropy, allow us to say something significant about the natural evolution of a network and the stability of a certain state. The tendency to extreme values, which manifests itself in physical systems, can be considered as a purposive behaviour. If this purposive behaviour is explained by physical network theories, it corresponds with an internal teleology (Soontiëns, 1993) which is resulting from the underlying physical laws. Perhaps, an explanation could also be sought in an efficiency principle which is imposed from outside. The organisational model of reality tries to combine both views and distinguishes internal and external purposes. In the organisational branch of the system theory, purposive or normative systems are introduced as a basic model which is applicable on each level of reality. A gearing process optimises the purposes and realises a cohesive and efficient behaviour of the system, as a whole, in its environment. In hierarchical as well as in heterarchical organisations, a mechanism is required to gear the objectives, to avoid chaotic situations and to arrive at a coherent behaviour. This organisational metaphor is less rigid and closed than the pure technical system theory and leaves space for autonomous human behaviour. In robotics, for example, holonic manufacturing systems are considered (Van Brussel, 1993). These flexible systems consist of holons. Holons are simultaneously part and whole. They are part with respect to the higher levels in the hierarchy and whole with respect to the lower levels. Holons can behave in a completely autonomous way, but try to combine their efforts to achieve an overall system goal. It should be noticed that the organisational and hierarchical views on reality imply highest level purposes as requirements imposed by the totality.
The behaviour of a network is determined by source, storage, dissipation and transformation functions. These basic functions can also be distinguished for other types of systems and on higher levels of reality. If the dimensions of the system are of importance, a transportation function should also taken into account. Not only energy but also matter and information can be gathered, stored, dissipated, transformed and transported. These five functions are responsible for the conservative, destructive and constructive forces in nature and the life cycles which are characteristic for organisation structures. The evolution process, with the emergence of the different layers of reality, can also be considered as the result of these forces. An explanation for stability, as well as evolution, can be found in feedback effects. The tendency to reach a minimum of potential energy can be attributed to negative feedback. Positive feedback, on the contrary, is an explanation for instability. This mechanism is also considered as the origin of order and allows the exploration of new structural and behavioural possibilities of reality. Reaction loops, due to autocatalitic processes for instance, can explain the creation of patterns in time and space. Feedback which is active on each level of reality and an efficient gearing of the actions imply purposive behaviour governed from higher levels. Efficiency in operations and robustness against disturbances are criteria for survival in a world with limited resources and intense competition. A connection is established between the evolution towards higher levels of reality and the purposes imposed from above. In this vision, emergence is considered as the manifestation of a purposive process which can be seen as the project of reality.
The technical-organisational vision on reality is based on the establishment of a structural and behavioural coherence. It is also assumed that the elementary physical laws are not (yet) able to completely explain reality, or that these explanations are much too complicated for practical applications. For example, quantum physics is not directly useful for a mechanical engineer or a factory manager. Even in the exact sciences it is accepted that indefiniteness due to bifurcations, chaos and catastrophic effects make reliable predictions impossible. In all cases the lower material layers of reality offer the conditions for the existence of the higher layers but it appears that the elementary laws do not determine the behaviour of complex organisations in a fully closed way. There seems to be some room for autonomous behaviour. However, governing principles also have to be taken into account. The jaws of an animal are not only determined by the laws of mechanics, but also by the necessity for effective gathering of food which is linked to the demand for survival. This effect is sometimes called downward causation.
Purposive behaviour is introduced alongside deterministic and stochastic behaviour allowing human beings to be able to model complicated organisations. The fundamental question arises: is this approach only a methodological solution ? Or, does it really correspond with the structure of reality ? There is convincing evidence that the co-operation of the laws of nature, which is necessary to realise the coherence of complex organisations, is impossible without certain preferences of the global framework. These preferences manifest themselves in forms such as values, external purposes and general principles and have a co-ordinating, orientating and governing effect. They are active alongside the elementary laws, they are hidden behind these laws and/or they interfere from above. Violation of these rules leads in many cases to destruction and self-destruction of individuals as well as communities. The totality limits the autonomy and independence of the individuals, making demands on robustness and pushing the evolution towards a higher degree of organisation (Van Belle, 1997).
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The author would like to thank Daniël H. Maslyn for reading the manuscript and suggesting improvements.
Presented at the International Conference on: The Interplay between Philosophy, Science and Religion: The European Heritage, K.U.Leuven , November 18-21, 1998.