About Cybernetics

This page last updated 23 February 2003


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The Institute of Cybernetics
Brunel University, UK
Syllabus of taught course for research students

Please note that this course is no longer running



Group I

I Introduction to Cybernetics

1. The Meaning of Cybernetics:

Meaning of the word 'Cybernetics'. History of cybernetic ideas. Origins of the modern science. Scope and influence of the subject. Links with mathematics. Artificial systems. Natural systems. Applied cybernetics.

2. The Content of Cybernetics:

Conceivable, feasible and naturally occurring organisms. Communication and control as interaction between systems. Energy and information. Information theory. Input, output and internal state. Description of automata by means of transition matrices. Transition diagrams.

3. Systems in Action:

State description and trajectory. Stability, ultra-stability and multi-stability. Phase space. The homeostats. Self-organising systems. Initially unorganised systems. Growth, decay and evolution. Goals, purposes and teleology. The motivation of systems.

4. The logic of behaviour:

Finite and non-finite automata. Temporal propositional expressions and logical nets. Representation of events. Fundamentals of Turing Machine theory. Specification and program. Stored program machines. Universal automata. Computability, representability and general behaviour. Self- reproducing automata.

5. Cybernetics in practice:

Relation between concepts of psychology and those of cybernetics. Cybernetics as a framework for psychology. .Man-machine systems and the cybernetic approach to ergonomics. Artificial cybernetic ideas to social and economic systems. Cybernetics in industrial management and in government.

II Basic concepts of cybernetics and general systems theory

1. Introduction:

The history of cybernetics as related to technical development and the growth of scientific philosophy. Main areas of application and the broad concepts of communication. Control and goal directed system.

2. Groundwork:

Basic definitions. Properties, values, states, behaviours, abstract systems, subsystems and stability. Models. State graphs, flow charts and functionally partitioned systems. Adaptation and habituation. Observation, experimentation and control. Metalanguages and object languages. The status of models relative to the physical or normative systems they represent. Explanation and reducibility .The form of knowledge. Real and abstract machines. Various limits. The concept of a hierarchical structure. Different sorts of hierarchy.

3. The abstract representation of systems:

Elementary information theory. .Information from the point of view of an observer and a subsystem. Redundancy and measures of organisation. Uncertainty. Variety and invariance. The self-organising system. Basic ideas of general systems theory. Game theory. Competition, co-operation and communication. Finite and infinite automata. Simplification. Reproduction and self-reproduction.

4. Important processes and simulation models:

Evolution. Development. Various simulated systems. The goal-directed system as a generalised control system. Requisite variety. Game playing. Problem solving. Models of abduction, deduction and conductive inference. Conceptions, strategies, hypotheses and plans. Heuristic rules. Discriminations and abstraction. Models of learning. Multi-level interaction. Metagames. Conversation in contrast to communication. Parallel (in contrast to sequential) operations. Pertinent models and simulations. Revision of ideas of unique causality and" state".

5. Recent developments:

Some techniques. The design of artefacts and models. Possible, practicable and economic organisations. Discussion of various logical structures as vehicles for representing organisations.

III Logic

1. Traditional formal logic:

Propositions and sentences. Symbols and distribution. Immediate and mediate inference. Aristotelian syllogistic. Hypothetical argument. Disjunctive argument. Logical division and definitions.

2. Calculus of classes:

Class, class-membership and universe. Null class. Subtraction, multiplication and addition of classes. Diagrams of Euler and Venn. Boolean algebra.

3. Calculus of propositions:

Variables and constants. Negation, conjunction, disjunction, equivalence and implication. Well formed formulae. Principal normal forms. Predicate calculus. Quantifiers.

4 Truth value:

Truth tables and truth functions. Standard array. Characteristic lines of constants. Proof by truth tables. Tautology and contingency. Decision procedures.

5 Postulational systems:

Definitions, postulates and theorems. Rules of inference. Principia Mathematica axioms. Proof by manipulation of formulae. Foundations of mathematics. Gödel's theorem.

IV Scientific method

1. Nature of scientific enquiry:

Objects of research. Description, prediction, prescription and explanation. Methods of experimental enquiry. .Parameters. Variables. Logical constructs and intervening variables. Scales of measurement.

2. Theory construction:

Observation, generalisation and systems of empirical propositions. Logical propositions and deductive systems. Postulates, hypotheses, and hypothetico-deductive systems. Types of theory.

3. Models:

Systems and relations. Isomorphy and homomorpny. Paper systems. Calculi. Didactic analogies and analogues. Argument by analogy and its dangers. Model-building. Abstractions and concepts.

4. Induction:

Testing of hypotheses. Verification and support. Statistical hypotheses. Logical and empirical theories of probability. Tautology and corrigibility. Justification of induction.

5. Scientific explanation:

Criteria for explanatory propositions. Theories of truth. Value in scientific enquiry. Corpus of knowledge. Laws of Nature. Causality. Causal and teleological explanation. Purpose, teleology and evolution.

V Information theory

1. History of information theory:

Boltzmann, Entropy and thermodynamics. Szilard. Von Neumann. Nyquist. Hartley. Kolmogoroff. Wiener. Fisher. Shannon.

2. Communication systems:

Communication. Technical, semantic and pragmatic levels of discussion. Message, signal, source, transmitter, receiver, destination. Noise.

3 information measures:

Information and meaning. Hartley's law. Derivation of Shannon's function. Examples of the noiseless case. Derivation of Wiener's function. Information and unexpectedness .

4. Information and entropy:

Inter-symbol influence. Entropy. Relative entropy and redundancy. Coding and code capacity. Value of redundancy in combating noise. Shannon's tenth theorem and requisite variety.

5. Measurement of organisation:

Information measures of specification. Redundancy as a measure of structure. Quantification of Gestalt notions. Experiments on transmission of information by human beings. Self-organising systems. Logon content.


Group II

I The history and philosophy of cybernetics and systems theory:

This course is conceived of as a seminar or discussion group. Throughout the course, an attempt will be made to show how cybernetic ideas have contributed to the development of knowledge and technology whether or not these ideas were officially called "cybernetics".

1. Historical overview:

Ideas of mechanism and control as advanced by the classical philosophers since Leibniz and Descartes. Thought, cognition and the like. Automata and their interpretation as models. Relation to technical development. Early ideas of teleology and vitalism. The status of the mind body dichotomy in the early 1900s. Views of normative systems, aesthetics and ethics.

2. Case histories:

The work of McCulloch and Pitts, Rashevsky and von Bertelanffy. Shannon, Gabor, Mackay and the information theorists. Wiener and Bigelow's formulation of cybernetics. The breadth of the idea. Sequences of conferences that reflect the development of the subject. The Macy Symposia. The meetings of the International Association of Cybernetics and the Medical Cybernetics Society. The Society for General Systems Research. The conferences on self-organising systems. The Bionics symposia. The Wenner Gren symposia. IFAC, IFIP and the information theory symposia.

3. Present position:

Location of and activity in the main centres for cybernetic research. Some technical and philosophical problems. Research area.

II Cybernetics of Natural Systems

1. Overview:

Applications of Biological cybernetics. Idea that commercial and social and industrial systems belong to the class of organisms. Bionics as engineering guided by biological principles applied at the organisational level.

2. Functional properties of biological systems:

Functional properties of the basic units in neural and cellular systems. Some of the commonly occurring structures. Gross feedback and feedforward control in simple organisms. Exemplars of neural and humoral control in the higher animals. The part played by sequential and parallel computation in these systems. Brief review of evolution of nervous systems. Different brains and their relative merits. Organisational overview of the mammalian brain. Filtering and perception (with emphasis upon the visual system). Models for these processes. The organisation of motor activity. Drive, motivation and the "pleasure centres". Emotional states and their relevance. Attention directing systems. The orienting reaction. Neural concomitants of expectation and anticipation.

3. Models for the activity of the brain:

Models for cortical function at the level of neural activity and at the level of data processing. Advantages of "mass neurons" models and "specifically structured" models. Memory and information storage. Functionally abstract memory systems. Mechanisms involved in the storage and retrieval of information. Synoptic changes, specific macro-molecular changes, storage and the doctrine of specialised neurons. What is a memory system. The "Cognitive Tile". Other hypotheses and models. Neural networks and other models for adaptation and habituation.

4. Animal learning:

Imprinting. Maturation. Animal conditioning and learning. Experiments in learning and problem solving. Different types of learning.

5. Cellular organisation:

Models for the control systems in the cell. Organisation of enzymes. Part played by cybernetic ideas in development of macromolecular biology .

6. Gross biological processes:

Mechanisms for reproduction. Growth. Differentiation. Evolution.

Development. Co-operative interaction. Evolutionary or developmental models.

7. Linguistic, symbolic and social interaction:

Social systems. Ritual, convention and programmatic control in a normative framework. Animal dispersion. Comments on ethology. Languages and sign systems. Some representative ecosystems. Their relation to and interaction with man-made systems.

8. Biological machines:

Discussion of useful artefacts and computing devices built on biological principles.

III Cybernetic aspects of human psychology:

1. Philosophy:

Overview of man as an information processing and control system. Limits of man. Goal directedness. Philosophical ideas. Explanation. Reduction. Forms of psychological model (statistical, normative or organisational, functional, etc.). Identification. Descriptive, prescriptive and predictive use of psychological models. Levels of interpretation. Adoption of "goal directed system" or "control system" or problem solver as the basic unit of behaviour and mentation.

2. Strategy, information and memory:

Human experiments. The subject as a reactive system. The experiment viewed as a game. Conversation with the subject. Need to externalise mental processes. Cybernetic approach as point of view that unifies experimental and social psychology. Man as a strategist versus man as a responder. The brain as a general purpose computer with a programming language. Resulting views of the individual. Information measures. Apparent "capacity" of man as an information processor in different conditions. Legitimacy of constructs such as "capacity". The rival views of man as a "channel" and a problem solver. Different meanings and measures of redundancy. The information transmitted in performing a task. Signal in "noise" models. Relation between stochastic learning models and self-organising systems (information models for learning). Hierarchy of memory systems. The organisation and control of short term information storage (visual and verbal). Models for intermediate or working memory and interference. Long term and associative memory systems.

3. Goal directedness

Hierarchies of goals. Tote units and simple learning. The organisation of perceptual motor and intellectual skills. Plans. Hypotheses. Adaptation. Accommodation. Habituation. Operant conditioning. Elimination of error factors. Instructions. Concept learning. Learning as means of controlling the environment. Hierarchies of control. Learning as an heterarchically organised process. Internalisation of goals. Learning set. Evolutionary models for learning. Reproductive systems. Man as a reproducer of concepts.

4. Experimental methods and specific models:

The cybernetic experimental methods on line control techniques. The stabilisation of performance. Adaptation. Compensation for unwanted learning. Maintenance of constant subjective difficulty. Externalisation by partially cooperative interaction. Conversational methods. Controlled interrogation. Subjective probability estimates over response alternatives and strategic alternatives in game-like experimental structures. Detailed examination of cybernetic learning model programmed with reference to cybernetic experimental situation. Study of learning and study of direction of attention. Models for attention directing mechanisms and the control of learning. Exploration, curiosity and other aspects of motivation.

5. General topics:

Concepts. Artificial intelligence and cognitive systems. The displacement of concepts. Personal images and heuristics. The organisation of small groups. Simple game situations. Teams. Behaviour in games that require higher level solutions. Interpersonal interaction. On line control of group activities. Some experiments on the development of communication patterns. Ethical systems. Evaluation. Creative activity, insight and intention. Symbolic evolution. Environments that favour typically human pursuits.

IV programmed learning:

1. Programmed learning:

History of the subject. Linear and branching methods, and the development of mixed methods. Skinner, Crowder, et al.

2. Teaching machines:

Branching, linear and other types of teaching machine. The method of simulation machines. Some examples of each type, and a discussion of different machine constraints.

3. Group teaching machines:

The work of Pask and others; problem solving, game playing and cooperative games. The theory of group activities of various kinds.

4. Programming teaching machines:

The specification. Analysing the data, flow-charting. Program writing. Testing and validation of programs. Some examples of programs and how they were compiled.

5. Computer assisted instruction:

The work so far done in CAI. The use of Coursewriter and other special languages. The next stages in the development of CAI.

6. Programmed learning and cybernetics:

The concept of teaching and its relation to learning. Automata theory, and the effective use of feedback through participation and knowledge of result.

7. The new education:

The Clark Project. The Nuffield Foundation work. The new mathematics and the ideas of cybernetic education. A reappraisal of information processing in the educational context.

V cybernetic teaching and training systems:

1. Introduction:

The cybernetic interpretation of teaching and training as the control of a learning process. Need for a model for learning in order to design a controller. Human versus mechanised instruction. Tutorial conversation. Learning models. Models for cognition and skilled performance. Error factors. Conditioning. Instructions. Concepts. Interference. Positive transfer of training. Goals. Motivation. Programmed instruction. Comparative study of simple programming. Branching programming, mathetics, systematics.

2. Adaptive teaching systems:

Justification in terms of error factor theory. Justification on cybernetic grounds. Some practical adaptive teaching systems (with or without use of computing machines).

3. Specific cases:

Detailed account of teleprinter training and the training of other perceptual motor skills. Extension to industrial training as a whole. Teaching intellectual skills such as managerial decision making. Group teaching systems.

4. Advanced topics:

Metasystem. Genuine conversational interaction between the teacher and student. Use of simulated learning models. Account of development method and design of a conversational training using a computer simulated learning model.

5. Research in progress


Group III

I Philosophical issues in cybernetics:

1. Thinking and creativity:

Can a mechanical chess-player outplay its designer? Can artefacts be made to think, build others more complex than themselves, or create works of art?

2. Life and matter:

What are the criteria for life? Can living artefacts be made?

3. Purpose and teleology:

Can an artefact have purposes other than those of its designer, or modify its own goals? What is the relation between causal and teleological explanations of behaviour?

4. Values and morals:

Can an artefact judge works of art, be worth consulting on moral questions, or be held responsible for what it does?

5. Mind and mechanism:

Does cybernetics throw any new light on the mind-body problem? Can a computer mean what it says? Can an artefact feel pain, be happy, or have a sense of humour?

II Management cybernetics:

1. Management cybernetics:

The comparison between human nervous systems and other systems, including those of business and government. Analogies and concepts and their use in explanation. An overview of the course and the purposes of management cybernetics.

2. Operational research:

The basic ideas of operational research (O.R.). The work of O.R. teams. The notion of O.R. in practice, and its relation to cybernetics.

Russell Ackoff, Stafford Beer and others. Some of the standard methods of O.R.: Queuing Theory, Linear programming and the like.

3. Ergonomics and work study:

The relationship between the various techniques used in management sciences is the central feature. A taxonomy is suggested which proposes an appropriate interaction.

4. Heuristic programming:

A description of the use of heuristic methods in systems organisation. The work of Tonge, Burstall, Clarkson, et al. Critical Path Analysis, and other such techniques. Heuristic programs for computers.

5. Decision processing:

Risk analysis. Venture analysis, the models of Wald, Hurwicz, et al. Probabilistic weighting of decisions. Bayes Rule; the work of Suppes, Ward Edwards and Jeffreys.

6. Dynamic programming:

The basic notions of dynamic programming. Bellman, Dreyfus. The relationship to theory of games, linear programming and stochastic processes.

III Theory of automata:

1. Logic:

The basic concept of a logistic system, and the notion of formalisation. The representation of automata. This summarises some of the traditional calculi.

2. Finite automata:

The basic concept of finite automata definitions in different degrees of depth and precision. The importance of Automata Theory for cybernetics.

3. Infinite automata:

Turing Machines, Turing Machine computations, and the underlying ideas. Universal machines. The relation of automata theory to recursive functions.

4. Varieties of automata:

Kleene, Moore et al, and their various representations, and the properties of such representations. McNaughton. Possible automata and the notion of robots. Culbertson.

5. Neural nets:

Notation. McCulloch-Pitts, von Neumann, Lofgren, Cowan and others. Applications. The use of neural nets in both the synthesis and simulation of artificial intelligence. Cognitive faculties modelled by neural nets. Se1f-repair, se1f-correction, replication.

IV Artificial Intelligence:

1. Models of learning

Learning, adaption and perception viewed from various viewpoints. This is the beginning of adaptation and here used as a basis for the synthesis of artificial intelligence. The models of Ashby, Walter, Uttley, etc.

2. Higher cognition:

Thinking, problem solving and heuristic methods. The relation of problem solving to learning and perception. Computer models and partial models leading towards the "complete" artificial system.

3. Logic and computers:

Inference making on the computer, and the relation of logic to language . The calculus of Relations, the propositional and functional calculus in the computer context. Theorem proving.

4. Natural language computing:

Namer, The Oracle, SIR, ALA, PROTOSYNTHEX, Napper Language, DEACON, LIP and all other such natural language systems. Prospects for future development.

5. Heuristic methods:

Algorithms. Heuristics - fixed and adaptive and their application. Heuristic generation. A range of applications for various contexts, with different degrees of urgency and precision .

V Recursive functions:

1. Logical systems:

An outline of logistic systems. The propositional and functiona1 calculi and their principal concepts.

2. Set theory:

The foundations of set theory, in both restricted and axiomatic form. Set theory and mathematics. The importance of set theory for cybernetics.

3. Recursive functions:

The basic notion of a recursive function. The notion of computability. Definitions and examples. Relation to automata theory.

4. Primitive recursive functions:

The extension of general recursive to primitive recursive functions. Definitions and examples.

5. Turing machines:

A simple Turing Machine, an Interrogation Turing Machine and a Universal Turing Machine. The relation of Turing Machines to other automata.

6. Gödel's theorem:

Gödel numbering. The ideas underlying the Gödel notion and its relation to formalism. Hilbert. The incompleteness theorem and its implications.

7. Incompleteness:

A general study of incompleteness. The theorems of Church and Turing. Martin Davis.

8. Undecidability:

The proof that many problems exist which are, by their very nature, undecidable. Martin Davis, Hartley and Minsky.


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