"Every part of the system is so related to every other part that a change in a particular part causes a changes in all other parts and in the total system." (Arthur D Hall, "A methodology for systems engineering", 1962)
"Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole." (Herbert A Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society, Vol. 106 (6), 1962)
"To say a system is 'self-organizing' leaves open two quite different meanings. There is a first meaning that is simple and unobjectionable. This refers to the system that starts with its parts separate (so that the behavior of each is independent of the others' states) and whose parts then act so that they change towards forming connections of some type. Such a system is 'self-organizing' in the sense that it changes from 'parts separated' to 'parts joined'. […] In general such systems can be more simply characterized as 'self-connecting', for the change from independence between the parts to conditionality can always be seen as some form of 'connection', even if it is as purely functional […] 'Organizing' […] may also mean 'changing from a bad organization to a good one' […] The system would be 'self-organizing' if a change were automatically made to the feedback, changing it from positive to negative; then the whole would have changed from a bad organization to a good." (W Ross Ashby, "Principles of the self-organizing system", 1962)
"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected.” (Richard Feynman, "The Feynman Lectures on Physics" Vol. 1, 1963)
"In a general way it may be said that to think in terms of systems seems the most appropriate conceptual response so far available when the phenomena under study - at any level and in any domain--display the character of being organized, and when understanding the nature of the interdependencies constitutes the research task. In the behavioral sciences, the first steps in building a systems theory were taken in connection with the analysis of internal processes in organisms, or organizations, when the parts had to be related to the whole." (Fred Emery, "The Causal Texture of Organizational Environments", 1963)
"Formulating and structuring a system provide methods for relating (1) what the system consists of in the mind of the persons or group desiring it; (2)what it means in terms of the persons or group designing and building it; and (3) in terms of the persons or groups operating, using and servicing it. They provide a set of 'reasonable"'parts and methods of relating them so that the many persons working on the system can understand the whole in sufficient detail for their purposes, and their particular parts in explicit detail so that they may contribute their best efforts to the extent required. A further purpose of system formulation is to recognize the magnitude of the job, including the possible pitfalls." (Harold Chestnut, "Systems Engineering Tools", 1965)
"Formulating consists of determining the system inputs, outputs, requirements, objectives, constraints. Structuring the system provides one or more methods of organizing the solution, the method of operation, the selection of parts, and the nature of their performance requirements. It is evident that the processes of formulating a system and structuring it are strongly related." (Harold Chestnut, "Systems Engineering Tools", 1965)
"The process of formulating and structuring a system are important and creative, since they provide and organize the information, which each system. "establishes the number of objectives and the balance between them which will be optimized". Furthermore, they help identify and define the system parts. Furthermore, they help identify and define the system parts which make up its 'diverse, specialized structures and subfunctions'." (Harold Chestnut, "Systems Engineering Tools", 1965)
"The Systems engineering method recognizes each system is an integrated whole even though composed of diverse, specialized structures and sub-functions. It further recognizes that any system has a number of objectives and that the balance between them may differ widely from system to system. The methods seek to optimize the overall system functions according to the weighted objectives and to achieve maximum compatibility of its parts." (Harold Chestnut, "Systems Engineering Tools", 1965)
"Just as no thing or organism exists on its own, it does not act on its own. Furthermore, every organism is a process: thus the organism is not other than its actions. To put it clumsily: it is what it does. More precisely, the organism, including its behavior, is a process which is to be understood only in relation to the larger and longer process of its environment. For what we mean by 'understanding' or 'comprehension' is seeing how parts fit into a whole, and then realizing that they don't compose the whole, as one assembles a jigsaw puzzle, but that the whole is a pattern, a complex wiggliness, which has no separate parts. Parts are fictions of language, of the calculus of looking at the world through a net which seems to chop it up into bits. Parts exist only for purposes of figuring and describing, and as we figure the world out we become confused if we do not remember this all the time." (Alan Watts, "The Book on the Taboo Against Knowing Who You Are", 1966)
"Nor does complexity deny the valid simplification which is part of the process of analysis, and even a method of achieving complex architecture itself." (Robert Venturi, "Complexity and Contradiction in Architecture Complexity and Contradiction in Architecture", 1966)
"A synthetic approach where piecemeal analysis is not possible due to the intricate interrelationships of parts that cannot be treated out of context of the whole;" (Walter F Buckley, "Sociology and modern systems theory", 1967)
"Now we are looking for another basic outlook on the world - the world as organization. Such a conception - if it can be substantiated - would indeed change the basic categories upon which scientific thought rests, and profoundly influence practical attitudes. This trend is marked by the emergence of a bundle of new disciplines such as cybernetics, information theory, general system theory, theories of games, of decisions, of queuing and others; in practical applications, systems analysis, systems engineering, operations research, etc. They are different in basic assumptions, mathematical techniques and aims, and they are often unsatisfactory and sometimes contradictory. They agree, however, in being concerned, in one way or another, with ‘systems’, ‘wholes’ or ‘organizations’; and in their totality, they herald a new approach." (Ludwig von Bertalanffy, "General System Theory", 1968)
"System' is the concept that refers both to a complex of interdependencies between parts, components, and processes, that involves discernible regularities of relationships, and to a similar type of interdependency between such a complex and its surrounding environment." (Talcott Parsons, "Systems Analysis: Social Systems", 1968)
"The system problem is essentially the problem of the limitation of analytical procedures in science. This used to be expressed by half-metaphysical statements, such as emergent evolution or ‘the whole is more than the sum of its parts,’ but has a clear operational meaning." (Ludwig von Bertalanffy, "General System Theory", 1968)
"You cannot sum up the behavior of the whole from the isolated parts, and you have to take into account the relations between the various subordinate systems which are super-ordinated to them in order to understand the behavior of the parts." (Ludwig von Bertalanffy, "General System Theory", 1968)
"In complex systems cause and effect are often not closely related in either time or space. The structure of a complex system is not a simple feedback loop where one system state dominates the behavior. The complex system has a multiplicity of interacting feedback loops. Its internal rates of flow are controlled by nonlinear relationships. The complex system is of high order, meaning that there are many system states (or levels). It usually contains positive-feedback loops describing growth processes as well as negative, goal-seeking loops. In the complex system the cause of a difficulty may lie far back in time from the symptoms, or in a completely different and remote part of the system. In fact, causes are usually found, not in prior events, but in the structure and policies of the system." (Jay Wright Forrester, "Urban dynamics", 1969)
"Synergy is the only word in our language that means behavior of whole systems unpredicted by the separately observed behaviors of any of the system's separate parts or any subassembly of the system's parts." (Buckminster Fuller, "Operating Manual for Spaceship Earth", 1969)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
16 February 2020
From Parts to Wholes (1960-1969)
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