The retina works best at a certain intensity of illumination. In bright light the nervous system contracts the pupil, and in dim relaxes it. Thus the amount of light entering the eye is maintained within limits.

When dry food is chewed, a copious supply of saliva is poured into the mouth. Saliva lubricates the food and converts it from a harsh and abrasive texture to one which can be chewed without injury. The secretion therefore keeps the frictional stresses below the destructive level.

Many more examples could be given, but all can be included within the same formula. Some external disturbance tends to drive an essential variable outside its normal limits; but the commencing change itself activates a mechanism that opposes the external disturbance. By this mechanism the essential variable is maintained within limits much narrower than would occur if the external disturbance were unopposed. The narrowing is the objective manifestation of the mechanism's adaptation.

1. A rule or procedure for solving a recurrent mathematical problem.
    
   
2. A complete, unambiguous procedure for solving a specified problem in a finite number of steps. (Richard Dorf)
    
   
3. Deterministic ALGORITHM: Given the same input information, will always produce the same output information, when applied correctly. (John Warfield)
    
   
4. Stochastic ALGORITHM: Given the same information, will not necessarily produce the same output information, even though applied correctly. (John Warfield)
    
   
6. Any mechanical or recursive computational procedure (Dictionary).

1. correspondence in some respects, especially in function or position, between things otherwise dissimilar.
    
   
2. a form of logical inference, or an instance of it, based on the assumption that if two things are known to be alike in some respects, then they must be alike in other respects.

1. A branch of philosophy dealing with values, i.e., ethics, aesthetics, religion. Based on the Greek for "worth."
    
   
2. The study of the nature of types of and criteria of values and of value judgments, especially in ethics (John Warfield)
    
   
3. The general theory of value; the study of objects of interest. (Lotze)

1. any sequence of states of a system. (Ashby, Handout, 1961)
    
   
2. The behavior of a system is overt and thus manifested in input-output relationships, whereas state trajectories are covert and must either be inferred or must be obtained by "opening the black box". (Michael Arbib)

1. The science of communication and control in animal and machine.
    
   
2. Perhaps because the field is still young, there are many definitions of cybernetics. Norbert Wiener, a mathematician, engineer and social philosopher, coined the word "cybernetics" from the Greek word meaning steersman. He defined it as the science of communication and control in the animal and the machine. Ampere, before, him, wanted cybernetics to be the science of government. For philosopher Warren McCulloch, cybernetics was an experimental epistemology concerned with the communication within an observer and between the observer and his environment. Stafford Beer, a management consultant, defined cybernetics as the science of effective organization. Anthropologist Gregory Bateson noted that whereas previous sciences dealt with matter and energy, the new science of cybernetics focuses on form and pattern.
    
   
3. A way of looking at things and a language for expressing what one sees (Margaret Mead)

1. an organism with a machine built into it with consequent modification of function;
    
   
2. an organism which is part animal and part machine. Since some theorists regard organisms as biological machines, we must define our terms further. An animal will be defined as a creature whose elements are the result of "small loop autopoiesis." That is the creature creates itself but the parts are the result of localized processes. Mind is not involved in the production of the parts. Mind results from the functioning of the parts but is manifested in the external behavior of the organism. A cyborg, then, is a creature composed of some parts constructed without the benefit of mind and some parts constructed with the benefit of mind. Furthermore the parts must be of greater than molecular size. A creature with aspirin in its body is not a cyborg. A creature with an artificial heart is a cyborg. Under this definition, animals with donated hearts, kidneys or retinas would also be cyborgs. (Umpleby)

1. A group communication structure used to facilitate communication on a specific task. The method usually involves anonymity of responses, feedback to the group as a whole of individual and/or collective views and the opportunity for any respondent to modify an earlier judgment. The method is usually conducted asyncronously via paper and mail but can be executed within a computerized conferencing environment. At the essence of the method is the question of how best to tailor the communication process to suit the situation. The Delphi method was originally developed at the RAND Corporation by Olaf Helmer and Norman Dalkey. (Murray Turoff)
    
   
2. A technique to arrive at a group position regarding an issue under investigation, the Delphi method consists of a series of repeated interrogations, usually by means of questionnaires, of a group of individuals whose opinions or judgments are of interest. After the initial interrogation of each individual, each subsequent interrogation is accompanied by information regarding the preceding round of replies, usually presented anonymously. The individual is thus encouraged to reconsider and, if appropriate, to change his previous reply in light of the replies of other members of the group. After two or three rounds, the group position is determined by averaging. (IIASA)

1. As a term in economics, demand means the amount of a commodity (good or service) that would be purchased at a given price. An associated term is [DEMAND FUNCTION,] which presents the demand-versus-price relationship. A demand function for a given commodity is compared with a corresponding [SUPPLY FUNCTION] to determine the EQUILIBRIUM PRICE: a price at which the supply offered matches the demand.
    
   
2. In another usage, demand means the amount of a commodity required for a certain purpose. It often relates to the future, as in: "the world energy demand in the year 2030 will be 35 terawatts." Implicit in this statement is that the price of energy as well as other economic conditions will be such that 35 terawatts will be consumed (purchased) if technically available. (IIASA)

     Present value =       X
                         ------
                         (l+i)n

1. In SYSTEMS ANALYSIS, the effectiveness of an ALTERNATIVE is usually represented by an aggregative expression approximating the totality of output or performance aspects of that alternative that are relevant to goal attainment. Ideally, it is a single quantitative measure that can be used to evaluate the performance level achieved in attaining the OBJECTIVES. (IIASA)
    
   
2. An absolute measure of performance. (Turoff)

1. Program A is said to be more efficient than program B if, for a given cost, a chosen aggregated measure of its positive results (such as EFFECTIVENESS or BENEFIT) is greater than that for program B. (IIASA)
    
   
2. A ratio scale measurement of a measure of performance to resources expended to obtain the level of performance. (Turoff)

1. of or relating to a process in which a sequence or sizable sample is equally representative of the whole (as in regard to a statistical parameter);
    
   
2. involving or relating to the probability that any state will recur, especially having zero probability that any state will never recur. (WEBSTER'S DICTIONARY)

1. A process of continuous change from a lower, simpler, or worse, to a higher, more complex, or better state; a process of change in some direction. (Webster's)
    
   
2. The coming into being of a new and higher order process. (Laszlo)
    
   
3. The development of each species from different, usually simpler ancestral forms. The more similar are two species, the closer in time are they likely to be to a common ancestor. (Arbib)
    
   
4. history of change in the realization of an invariant organization embodied in independent unities sequentially generated through reproductive steps, in which the particular structural realization of each unity arises as a modification of the preceding one (or ones) which, thus, constitutes both its sequential and historical antecedent. (Maturana and Varela, 1979)

1. Metaphor, that image which determines another image. (Rogers)
    
   
2. An association of a certain object(s) from one set with each object from another set (mathematics). (Rogers)
    
   
3. The normal or characteristic action of a system of entities, generally in time. (Iberall)
    
   
4. The variation of some magnitude that depends upon the variation of some other magnitude. (Iberall)
    
   
5. a notion that arises in the description made by the observer of the components of a machine or system in reference to an encompassing entity, which may be the whole machine or part of it and whose states constitute the goal that the changes in the components are to bring about. (Maturana and Varela, 1979)

In game theory one usually makes the following assumptions:

1. Each decision maker ["PLAYER"] has available to him two or more well-specified choices or sequences of choices (called "PLAYS").
    
   
2. Every possible combination of plays available to the players leads to a well-defined end-state (win, loss, or draw) that terminates the game.
    
   
3. A specified payoff for each player is associated with each end-state (a [ZERO-SUM GAME] means that the sum of payoffs to all players is zero in each end-state).
    
   
4. Each decision maker has perfect knowledge of the game and of his opposition; that is, he knows in full detail the rules of the game as well as the payoffs of all other players.
    
   
5. All decision makers are rational; that is, each player, given two alternatives, will select the one that yields him the greater payoff.

1. A structure, configuration, or pattern of physical, biological, sociological, or psychological phenomena so integrated as to constitute a functional unit with properties not derivable from its parts in summation. This German word is considered by many system thinkers (e.g., von Bertalanffy, Angyal) to convey more accurately the concept of organized wholes than the word system. (Steven Rogers)
    
   
2. The organized structure or pattern that makes up all of a person's experience of some system. This integrated view is more than the sum of the individual elements by which the field can be described. (Iberall)

1. End toward which effort is directed. (Webster's)
    
   
2. A statement, expressed in the following form: To (Action Word) (Object) (Qualifying Phrase). (John Warfield)
    
   
3. A preferred outcome in a particular situation that can be obtained within a specified time period. (Ackoff)
    
   
4. An end state consciously selected a priori. (Larry Richards)

1. Characterizing a system in which the internal parameters can be changed when necessary through feedback.
    
   
2. A heuristic idea serves as a guide for discovery. It serves as a valuable aid for empirical research but may be unproved or incapable of proof. (Umpleby)

1. A form of organization resembling a pyramid. Each level is subordinate to the one above it. See HETERARCHY. (Umpleby)
    
   
2. An organization whose components are arranged in levels from a top level down to a bottom level. (Arbib)
    
   
3. A partially-ordered structure of entities in which every entity but one is successor to at least one other entity; and every entity except the basic entities is a predecessor to at least one other entity. (Rogers)
    
   
4. Narrowly, a group arranged in order of rank or class; we interpret it to denote a rank arrangement in which the nature of function at each higher level becomes more broadly embracing than at the lower level. (Iberall)

1. Dynamic self-regulation.
    
   
2. The condition of a system when it is able to maintain its essential variables within limits acceptable to its own structure in the face of unexpected disturbances. The concept was formulated by W.B. Cannon in 1929-32.

1. the representation of ideas by graphic symbols.
    
   
2. the use of ideograms to express ideas.

1. as synonymous with CONSEQUENCE;
    
   
2. to mean any consequence (beneficial or adverse) that reaches beyond the direct purpose of a given COURSE OF ACTION, as in: "the impact of the new steel plant on employment opportunities in the region;"
    
   
3. as in (2), but the meaning restricted to adverse consequences, as in "the impact of industrial growth on the ecological environment." (IIASA)

1. that which reduces UNCERTAINTY. (Claude Shannon);
    
   
2. that which changes us. (Gregory Bateson)

where Yi is the consumption of product i by final consumers. In a model with three sectors, we have, for example, for the output product X2:

X2 = A2l Xl + A22 X3 + Y2

1. The immediate knowing or learning of something without the conscious use of reasoning. (Webster's)
    
   
2. In its cognitive function it is a psychic organ or means to apprehend reality. It is a synthetic function in the sense that it apprehends the totality of a given situation or psychological reality. It does not work from the part to the whole -- as the analytical mind does -- but apprehends a totality directly in its living existence. (Assagioli)
    
   
3. It is by logic that we prove, but by intuition that we discover. (Poincare, CY sq.)

1. A mapping of one entity into another having the same elemental structure, whereby the behaviors of the two entities are identically describable. (John Warfield)
    
   
2. A formal correspondence of general principles or even of special laws. (Bertalanffy)
    
   
3. A set of principles may be transferred from one field to another without need to duplicate the effort. (Weinberg)
    
   
4. a one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.

1. the amount of appropriate selection that can be performed is limited by the amount of information available.
    
   
2. for appropriate regulation the variety in the regulator must be equal to or greater than the variety in the system being regulated. Or, the greater the variety within a system, the greater its ability to reduce variety in its environment through regulation. Only variety (in the regulator) can destroy variety (in the system being regulated). The law was formulated by Ross Ashby. (Umpleby)

1. a state-determined system; any system showing behavior such that the specification of a state determines the subsequent state; a set of states closed under a mapping. (Ashby, Handout, l96l)
    
   
2. a unity in the physical space, defined by its organization, which connotes a non-animistic outlook, and whose dynamisms are apparent. (Maturana and Varela, 1979)

(a) the proper object of the discipline,

(b) the manner in which it develops,

(c) the type of statements or generalizations it involves,

(d) its philosophical foundations or assumptions, and

(e) its relation with other disciplines and eventually its applications. (Dict. of Philosophy)

1. evolutionary development of the structure of an organism or part.
    
   
2. embryological development of the structure of an organism or part.
    
   
3. The process in complex system-environment exchanges that tends to elaborate a system's given form or structure. Examples are the growth of an animal from a fertilized ovum, biological evolution, learning, and societal development. A morphogenic system is capable of maintaining its continuity and integrity by changing essential aspects of its structure or organization. (Von Bertalanffy, GST, pp. 148-9)

1. The environment is assumed to consist of large numbers of subsystems that have many states of equilibrium. The environment is thus assumed to be polystable.
    
   
2. Whether because the primary joins between the subsystems are few, or because equilibria in the subsystem are common, the interaction between subsystems is assumed to be weak.
    
   
3. The organism coupled to this environment will adapt by the basic method of ultrastability, i.e., by providing second-order feedbacks that veto all states of equilibrium except those that leave each essential variable within its proper limits.
    
   
4. The organism's reacting part is itself divided into subsystems between which there is no direct connection. Each subsystem is assumed to have its own essential variables and second order feedback. To trace the behavior of the multistable system, suppose that we are observing two of the subsystems, e.g., A and B and that their main variables are directly linked so that changes of either immediately affect the other, and that for some reason all the other subsystems are inactive. The first point to notice is that, as the other subsystems are inactive, their presence may be ignored; for they become like the 'background'. Even some are active, they can still be ignored if the two observed subsystems are separated from them by a wall of inactive subsystems. The next point to notice is that the two subsystems, regarded as a unit, form a whole which is ultrastable. This whole will therefore proceed, through the usual series of events, to a terminal pattern of behavior. If, however, we regard the same series of events as occurring, not within one ultrastable whole, but as interactions between a minor environment and a minor organism, each of two subsystems, then we shall observe behaviors homologous with those observed when interaction occurs between 'organism' and 'environment'. Trial and error will appear to be used; and, when the process is completed, the activities of the two parts will show co-ordination to the common end of maintaining the essential variables of the double system within their proper limits. Exactly the same principle governs the interactions between three subsystems. If the three are in continuous interaction, they form a single ultrastable system which will have the usual properties. As illustration, we can take the interesting case in which two of them, A and C say, while having no immediate connection with each other, are joined to an intervening system B, intermittently but not simultaneously. Suppose B interacts first with A: by their ultrastability they will arrive at a terminal pattern of behavior. Next B and C interact. If B's step-mechanisms, together with those of C, give a stable pattern of behavior to the main variables of B and C, then that set of B's step-mechanism values will persist indefinitely; for when B rejoins A the original stable pattern of behavior will be re-formed. But if B's set with C's does not give stability, then it will be changed to another set. It follows that B's step-mechanisms will stop changing when, and only when, they have a set of values which forms fields stable with both A and C. (Ashby, l960, pp. 208-2l0)

An objective may be specified in a more or less general Fashion, may be quantified or not quantified, and is usually part of a HIERARCHY OF OBJECTIVES. The term GOAL is sometimes used to denote a very general objective( at the top of the hierarchy) and TARGET is used to mean a very definite objective. Example: "The goal of allocating money to the municipality was to increase the quality of urban life. The immediate objectives were to improve public transportation and fire services. A 10% reduction of average travel time from home to work and a 70% decrease of average alarm-to-action time taken by the fire brigades were set forth as targets."

1. One who watches without participating.
    
   
2. The source of factual evidence; a person who communicates his sense impression of the external environment.
    
   
3. Everything said is said to an observer. (Witz, in Von Foerster, 1974)
    
   
4. Observer dependence - the concept that knowledge of reality is dependent upon the perceptions of the observer.
    
   
5. Observer inseparability - the concept that observation or measurement affects the state of the object being observed, that is, objective measurement or observation from outside a system is not possible, and the act of observing makes the observer part of the system under study. Therefore, the observer or measuring device should be included in the definition of the system. (Weinberg)
    
   
6. A system which, through recursive interactions with its own linguistic states, may always linguistically interact with its own states as if with representations of its interactions. (Maturana and Varela, 1979)

Q = f(Xl,X2,...Xn)

constraint relations, usually of the form

Gi(Xl,X2,.....Xn) greater than or equal to O, i = l,2,.....m.

1. an outstandingly clear or typical example or archetype. (Webster's)
    
   
2. The total pattern of perceiving, conceptualizing, acting, validating, and valuing associated with a particular image of reality that prevails in a science or a branch of science. (Kuhn)
    
   
3. A theoretical model to explain a type of social behavior. (Dict. of Anthropology)

1. Suppose there is a small town that consists only of men. There are two kinds of men in this town--those who shave themselves and those who are shaved by the barber. Who shaves the barber? If he shaves himself, then he is shaved by the barber. But if he is shaved by the barber, then he shaves himself. If the barber is assumed to be in one set, he appears in the other. This situation occurs because the barber both appears in the set and is used to define the set.
    
   
2. A person from the island of Crete asserts, "All Cretans are liars." We can conclude that if he is telling the truth, then he is lying. But if he is lying, then he is telling the truth. Once again an element of the set is referring to the set.
    
   
3. Consider a businessman accused of accepting a bribe. He claims, "I did not take the bribe." There are two possible interpretations of this statement. Either he is a knowledgeable observer making a correct statement, or he is a knowledgeable observer lying to avoid going to jail. The businessman is both the observer and the person being observed. We have no way of knowing which role he is playing.

1. that which determines the structure of a system. Parameters themselves can be changed by inputs, but usually the parameters determine how input will be transformed into outputs. In the linear equation y = ax + b, the slope "a" and the y-intercept "b" are the parameters; "x" is the independent variable and "y" the dependent variable. (Umpleby)
    
   
2. In computer science PARAMETER is an entry in a command or routine that must be replaced with specific data prior to execution. (Arbib)
    
   
3. In a system theory PARAMETERS are used to distinguish between systems that are described by similar sets of equations--the choice of parameters fits the model to a specific situation. (Arbib)

1. the study of all possible appearances in human experience, during which considerations of objective reality and of purely subjective response are temporarily left out of account.
    
   
2. a philosophical movement based on phenomenology, originated by Edmund Husserl about 1905.

1. power resides where information resides (McCulloch, see the PRINCIPLE OF REDUNDANCY OF POTENTIAL COMMAND;
    
   
2. power is the ability to limit choice. (Von Foerster in the mid 1960's), A does not have power over B unless A is able to constrain a necessary transaction of B;
    
   
3. a power relationship requires compliance (Maturana);
    
   
4. power is the consequence, submission is the cause (von Foerster, 1983).
    
   
5. Indirect or secondary exercise of power occurs when A constrains the necessary transactions of C so C will constrain the necessary transactions of B. A secondary boycott is an example.
    
   
6. Power distorts information. Hence, the President, who needs to be well informed, is often poorly informed because his power distorts the information given to him. No adviser wants to be the bearer of bad news or news which the President is thought not to want to hear. Deliberate steps are required to achieve accurate information.
    
   
7. If one accepts the idea that one is powerless, then one feels justified in threatening those one defines as powerful. However, the "powerful" usually feel threatened by the "powerless" who invariably outnumber them. Threats by the powerless against the powerful can make the powerful feel that repression is necessary in order to preserve the safety of themselves and their families.

So in going from any state to one of the equilibria, the system is going from a larger number of states to a smaller. In this way, it is performing a selection, in the purely objective sense that it rejects some states, by leaving them, and retains some other state, by sticking to it. Thus, as every determinate system goes to equilibrium, so does it select. We have heard ad nauseam the dictum that a machine cannot select; the truth is just the opposite; every machine, as it goes to equilibrium, performs the corresponding act of selection." (Ashby in W. Buckley (ed.) MODERN SYSTEMS RESEARCH FOR THE BEHAVIORAL SCIENTIST, P.115)

1. if an environmental variable (such as temperature) or an input or output variable (such as the flow demand on a system) changes and the system can nearly compensate for those changes in some other variable (such as outlet pressure) then the system is said to be regulated or regulated for that variable. If the regulation is obtained by a static compensation in which some linkage or component is introduced that diminishes the sensitivity to change, then this is static regulation (e.g., a spring scale is designed with materials that thermally compensate the spring against temperature change; a dc motor is designed by the choice of its field windings to give a speed regulation against changes in the load put on the motor; a chemical buffer shifts the operating point of chemical equilibrium to hold the pH of a solution constant). In dynamic regulation, two different switch states (an "on" and an "off" state) are arranged so that the system switches from one state to the other when the regulated parameter rises to an upper limit (an on-off thermostat). In feedback regulation (or control as it is technically referred to), an error signal is produced between the existing state of a system and the desired regulated level. This error signal is operationally acted upon, amplified in power, and fed to an actuator to operate a network which can influence the regulated variable so as to reduce the error, e.g., in biology the Na+ angiotension system. The signal is the sodium concentration. When this concentration decreases, aldosterone is liberated from the adrenal cortex. This agent acts on the kidney distal cubules to increase the reabsorption of sodium ions and re-establish the proper concentration of sodium. (Iberall)
    
   
2. a notion valid in the domain of description of heteropoiesis, that reflects the simultaneous observation and description made by the designer (or its equivalent) of interdependent transitions of the system that occur in a specified order and at specified speeds. (Maturana and Varela, 1979)

1. The measure of a system's ability to remain within a domain of stability in response to fluctuations of the system by a disturbance, and the ability of the system to return to that stable domain having once left. (Holling)
    
   
2. The ability of a system to make a smooth transition to a new stable state in response to changes in external conditions. The wider the range of external fluctuations in which the system can obtain a stable state, the greater is the resiliency of the system. (Turoff) See also STABILITY.
    
   
3. a measure of the ability of a system to absorb changes and still persist. (Holling)

1. In DECISION THEORY and in statistics, risk means UNCERTAINTY for which the probability distribution is known. Accordingly, [RISK ANALYSIS] means a study to determine the outcomes of decisions along with their probabilities -- for example, answering the question: "What is the likelihood of achieving a l,000,000 schilling profit in this ALTERNATIVE?" In SYSTEMS ANALYSIS, a DECISION MAKER is often concerned with the probability that a project (the chosen alternative) cannot be carried out with the time and money available. This risk of failure may differ from alternative to alternative and should be estimated as part of the analysis.
    
   
2. In another usage, risk means an uncertain and strongly adverse IMPACT, as in "the risks of nuclear power plants to the population are..." In that case, risk analysis or RISK ASSESSMENT] is a study composed of two parts, the first dealing with the identification of the strongly adverse impacts, and the second with determination of their respective probabilities. (IIASA)

1. a FORECAST based on loose assumptions rather than on a more formal inference from the past or
    
   
2. a synopsis of a proposed COURSE OF ACTION. (IIASA)
    
   
3. a sequence of possible events to be studied in a system of interest. (Arbib)

1. Define a problem,
    
   
2. Gather pertinent data,
    
   
3. Form a working hypothesis or explanation,
    
   
4. Do experiments to test the hypothesis,
    
   
5. Interpret the results,
    
   
6. Draw a conclusion and modify the hypothesis as needed.

1. Clausius (l822-l888) It is impossible that, at the end of a cycle of changes, heat has been transferred from a colder to a hotter body without at the same time converting a certain amount of work into heat.
    
   
2. Lord Kelvin (l824-l907) In a cycle of processes, it is impossible to transfer heat from a heat reservoir and convert it all into work, without at the same time transferring a certain amount of heat from a hotter to a colder body.
    
   
3. Ludwig Boltzmann (l844-l906) For an adiabatically enclosed system, the entropy can never decrease. Therefore, a high level of organization is very improbable.
    
   
4. Max Plank (l858-l947) A perpetual motion machine of the second kind is impossible.
    
   
5. Caratheodory (l885-l955) Arbitrarily near to any given state there exist states which cannot be reached by means of adiabatic processes.

A chain made out of paper clips suggests that someone has taken the trouble to link paper clips together to make a chain. It is not in the nature of paper clips to make themselves up into a chain. But, if you take a number of paper clips, open them up slightly and then shake them all together in a cocktail shaker, you will find at the end that the clips have organized themselves into short or long chains. The chains are not so neat as chains put together by hand but, nevertheless, they are chains. A teacher can organize her class into groups by assigning each child to a specific group and picking the group leaders. She could also tell the children to organize themselves into groups of five and then let them get on with it in a self-organizing fashion. The diagram shows an object that has a magnet out on a prong (bottom of a Y) and two metal plates on the bulb (top of a Y). If we shake up a number of these objects we find that they tend to organize themselves into the arrangement shown. Once the magnet comes into contact with the metal plate it tends to stick there. In other words once something has happened, it does not un-happen so easily. It is this asymmetry that is the basis of self-organization. In the way our mind deals with the outside world in terms of perception we can find a self-organizing system. (De Bono) See also PRINCIPLE OF SELF-ORGANIZATION.

     Y Y
      Y
       Y
        Y Y
         Y
        Y
         Y Y
          Y

1. the operation of a dynamic model in order to obtain a sequence of?utcomes that could occur in a real world system. Simulations of social processes can be accomplished either by human player games or by computer programs or by a combination of the two. Rather than simple computing the solution to a set of equations, a simulation produces a synthetic history oh the process. Beginning with a set of initial conditions, the simulation plays through the various kinds of events which might occur.
    
   
2. Simulation is the term applied to the process of modeling the essential features of a situation and then predicting what is likely to happen by operating with the MODEL cace by case--i.e., by estimating the results of proposed actions from a series of imaginary experiments (imaginary because they are performed on the representation of the situation, the model, rather than on the situation itself). Most frequently, the simulation is a [COMPUTER SIMULATION] in which the representation is carried out numerically on a digital computer. It may also be done on an analogue computer or by means of a physical representation, say by a wooden airfoil in a wind tunnel. [MAN-MACHINE SIMULATION] is a simulation that employs a MAN-MACHINE MODEL.

1. a set of variables selected by an observer. (Ashby, 1960)
    
   
2. Usually three distinctions are made: 1. An observed object. 2. A perception of an observed object. This will be different for different observers. 3. A model or representation of a perceived object. A single observer can construct more than one model or representation of a single object. Some people assume that 1. and 2. are the same. This assumption can lead to difficulties in communication. Usually the term "system" is used to refer to either 1. or 2. "Model" usually refers to 3. Ashby used the terms "machine," "system," and "model" in that order for the three distinctions. (Umpleby)
    
   
3. a set or arrangement of entities so related or connected so as to form a unity or organic whole. (Iberall)
    
   
4. Any definable set of components. (Maturana and Varela, 1979)

1. In economics, utility means the real or fancied ability of a good or service to satisfy a human want. An associated term is WELFARE FUNCTION (synonym: utility function--not to be confused with UTILITY FUNCTION in DECISION THEORY; see below), which relates the utility derived by an individual or group to the goods and services that it consumes. MARGINAL UTILITY is the change in utility due to a one unit change in the quantity of a good or service consumed.
    
   
2. In DECISION THEORY, utility is a measure of the desirability of CONSEQUENCES of courses of action that applies to decision making under RISK--that IS, under UNCERTAINTY with known probabilities.

The concept of utility applies to both SINGLE-ATTRIBUTE and MULTIATTRIBUTE CONSEQUENCES. The fundamental assumption in UTILITY THEORY is that the DECISION MAKER always chooses the ALTERNATIVE for which the expected value of the utility (EXPECTED UTILITY) is maximum. If that assumption is accepted, utility theory can be used to predict or prescribe the choice that the decision maker will make, or should make, among the available alternatives. For that purpose, a utility has to be assigned to each of the possible (and mutually exclusive) consequences of every alternative. A UTILITY FUNCTION is the rule by which this assignment is done and depends on the preferences of the individual decision maker. In utility theory, the utility measures u of the consequences are assumed to reflect a decision maker's preferences in the following sense: (i) the numerical order of utilities for consequences preserves the decision maker's preference order among the consequences; (ii) the numerical order of expected utilities of alternatives (referred to, in utility theory, as gambles or lotteries) preserves the decision maker's preference order among these alternatives (lotteries). For example if alternative A can have three mutually exclusive consequences, x,y,z, and the decision maker prefers z to y and x to z, the utilities Ul, U2, U3 assigned to x,y,z must be such that U3)U2)U1. If the probabilities of the consequences x,y,z are P1,P2,1-p1,-p2, respectively, the expected utility of alternative A is calculated as

E(u/P) = PlUl + P2U2 + (l-Pl-P2)U3

where P means the probability distribution, characteristic for the alternative (i.P1, P2, 1-P1-P2). (IIASA) If the decision maker prefers alternative B, which has probability distribution Q, to alternative A, the utility assignments in both alternatives must be such that

E(u/Q) 1/2 > E(u/P).

Utility theory provides a basis for the assignment of utilities to consequences by formulating necessary and sufficient conditions to satisfy (i) and (ii). A utility function is defined mathematically as a function u(.) from the set of consequences Y into the real numbers that provides for satisfaction of (i) and (ii). There exist various methods for constructing utility functions. The best-known method is based on indifference judgments of the decision maker about specially constructed alternatives(lotteries). Utility theory permits one to distinguish RISK-PRONE, RISK- NEUTRAL and RISK-AVERSE DECISION MAKERS. For example, if the mutually exclusive payoffs xl,x2,x3 of an alternative A are all expressed in the same units (e.g., schillings), the decision maker is risk-prone if he prefers the alternative A (prefers the lottery) to receiving, with no risk, the expected value of the payoffs (calculated directly as

E(x/P) = plxl + p2x2 + (l-pl-p2)x3).

This preference can also be expressed as

E(u/P) > u(E(x/P))

In [VALUE ANALYSIS,] one considers that the value v is related to the physical or other objective measure y of a consequence by a subjectively defined [VALUE FUNCTION,] so that v = f(y). A value function usually departs from proportionality, i.e.,it usually is a nonlinear dependence. A typical example is the subjective value of money to an individual: the first l,000 schillings in his savings account are probably of more value to him that the l,000 schillings that would increase the state oh his account from 100,000 to 101,000 schillings. The value of a multiattribute consequence with VALUE-RE?ANT ATTRIBUTES y1,y2,..yn can be expressed by a MULTIATTRIBUTE VALUE FUNCTION, v(yl,y2,..yn). A multiattribute value function must satisfy the following condition:

v(yl,y2,...yn) is greater than or equal to v(y'l,y'2,...y'n)

if and only if the multiattribute consequence (yl,y2,..yn) is preferred or indifferent to (y'1,y'2,...y'n).

1. in relation to a set of distinguishable elements, either (l) the number of distinct elements, or
    
   
2. the logarithm to the base 2 of that number, the context indicating the sense used. When variety is measured in the logarithmic form, its unit is the "bit," a contraction of "BInary digiT." (Ashby, 1956, P. 126)

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