Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
04 July 2020
🅴Maurits C Escher - Collected Quotes
03 July 2020
🅱Jacques Bertin - Collected Quotes
"The aim of the graphic is to make the relationship among previously defined sets appear." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)
"The great difference between the graphic representation of yesterday, which was poorly dissociated from the figurative image, and the graphics of tomorrow, is the disappearance of the congential fixity of the image. […] When one can superimpose, juxtapose, transpose, and permute graphic images in ways that lead to groupings and classings, the graphic image passes from the dead image, the 'illustration,' to the living image, the widely accessible research instrument it is now becoming. The graphic is no longer only the 'representation' of a final simplification, it is a point of departure for the discovery of these simplifications and the means for their justification. The graphic has become, by its manageability, an instrument for information processing." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)
"The plane is the mainstay of all graphic representation. It is so familiar that its properties seem self-evident, but the most familiar things are often the most poorly understood. The plane is homogeneous and has two dimensions. The visual consequences of these properties must be fully explored." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)
"To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)
"As with any graphic, networks are used in order to discover pertinent troups of to inform others of the groups and structures dis(Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)overed. It is a good means of displaying structures, However, it ceases to be a means of discovery when the elements are numerous. The figure rapidly becomes complex, illegible and untransformable." (Jacques Bertin, "Graphics and graphic information processing", 1977)
30 June 2020
🪸On Systems Thinking: On Ecology (2000-2009)
🪸On Systems Thinking: On Ecology (1970-1979)
"For some years now the activity of the artist in our society has been trending more toward the function of the ecologist: one who deals with environmental relationships. Ecology is defined as the totality or pattern of relations between organisms and their environment. Thus the act of creation for the new artist is not so much the invention of new objects as the revelation of previously unrecognized relation- ships between existing phenomena, both physical and metaphysical. So we find that ecology is art in the most fundamental and pragmatic sense, expanding our apprehension of reality." (Gene Youngblood, "Expanded Cinema", 1970)
"Ecology is the scientific study of the interactions that determine the distribution and abundance of organisms." (Charles J Krebs, "Ecology", 1972)
"To do science is to search for repeated patterns, not simply to accumulate facts, and to do the science of geographical ecology is to search for patterns of plants and animal life that can be put on a map." (Robert H. MacArthur, "Geographical Ecology", 1972)
"It is the intertwined and interacting mechanisms of evolution and ecology, each of which is at the same time a product and a process, that are responsible for life as we see it, and as it has been." (James W. Valentine, "Evolutionary Paleoecology of the Marine Biosphere", 1973)
"This paper introduces a concept of organizational ecology. This refers to the organizational field created by a number of organizations, whose interrelations compose a system at the level of the field as a whole. The overall field becomes the object of inquiry, not the single organization as related to its organization-set. The emergence of organizational ecology from earlier organization theory is traced and illustrated from empirical studies. Its relevance to the task of institution-building, in a world in which the environment has become exceedingly complex and more interdependent, is argued." (Eric Trist , "A concept of organizational eecolog", Australian journal of management 2 (2), 1977)
"We argue that in order to deal with the various inertial pressures the adaptation perspective must be supplemented with a selection orientation. We consider first two broad issues that are preliminary to ecological modelling. The first concerns appropriate units of analysis. Typical analyses of the relation of organizations to environments take the point of view of a single organization facing an environment." (Michael T Hannan, "The Population Ecology of Organizations", 1977)
"The social dynamics of human history, even more than that of biological evolution, illustrate the fundamental principle of ecological evolution - that everything depends on everything else. The nine elements that we have described in societal evolution of the three families of phenotypes - the phyla of things, organizations and people, the genetic bases in knowledge operating through energy and materials to produce phenotypes, and the three bonding relations of threat, integration and exchange - all interact on each other." (Kenneth E Boulding, "Ecodynamics: A New Theory Of Societal Evolution", 1978)
29 June 2020
🪸On Systems Thinking: On Ecology (1960-1969)
"The thing the ecologically illiterate don't realize about an ecosystem is that it's a system. A system! A system maintains a certain fluid stability that can be destroyed by a misstep in just one niche. A system has order, a flowing from point to point. If something dams the flow, order collapses. The untrained miss the collapse until too late. That's why the highest function of ecology is the understanding of consequences." (Frank Herbert, "Dune", 1965)
"A system has order, flowing from point to point. If something dams that flow, order collapses. The untrained might miss that collapse until it was too late. That's why the highest function of ecology is the understanding of consequences." (Frank Herbert, "Dune", 1965)
"The thing the ecologically illiterate don't realize about an ecosystem is that it's a system. A system! A system maintains a certain fluid stability that can be destroyed by a misstep in just one niche." (Frank Herbert, "Dune", 1965)
"For population genetics, a population is specified by the frequencies of genotypes without reference to the age distribution, physiological state as a reflection of past history, or population density. A single population or species is treated at a time, and evolution is usually assumed to occur in a constant environment. Population ecology, on the other hand, recognizes multispecies systems, describes populations in terms of their age distributions, physiological states, and densities. The environment is allowed to vary but the species are treated as genetically homogeneous, so that evolution is ignored." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)
"Evolution cannot be understood except in the frame of ecosystems." (Ramón Margalef, "Perspectives in Ecological Theory", 1968)
🪸On Systems Thinking: On Ecology I(1950-1959)
"In calling society an ecological system we are not merely using an analogy; society is an example of the general concept of an 'ecosystem' that is, an ecological system of which biological systems - forests, fields, swamps - are other examples." (Kenneth E Boulding, "A Reconstruction of Economics", 1950)
"Reality, in its quantitative aspect, must be considered as a system of populations. […] The general study of the equilibria and dynamics of populations seems to have no name; but as it has probably reached its highest development in the biological study known as 'ecology,' this name may well be given to it." (Kenneth E Boulding, "A Reconstruction of Economics", 1950)
"The general study of the equilibria and dynamics of populations seems to have no name; but as it has probably reached its highest development in the biological study known as 'ecology,' this name may well be given to it." (Kenneth E Boulding, "A Reconstruction of Economics", 1950)
"Can any of us fix anything? No. None of us can do that. We're specialized. Each one of us has his own line, his own work. I understand my work, you understand yours. The tendency in evolution is toward greater and greater specialization. Man's society is an ecology that forces adaptation to it. Continued complexity makes it impossible for us to know anything outside our own personal field — I can't follow the work of the man sitting at the next desk over from me. Too much knowledge has piled up in each field. And there are too many fields. (Philip K. Dick, "The Variable Man", 1952)
"If we have been slow to develop the general concepts of ecology and conservation, we have been even more tardy in recognizing the facts of the ecology and conservation of man himself. We may hope that this will be the next major phase in the development of biology. Here and there awareness is growing that man, far from being the overlord of all creation, is himself part of nature, subject to the same cosmic forces that control all other life. Man's future welfare and probably even his survival depend upon his learning to live in harmony, rather than in combat, with these forces. (Rachel Carson, "Essay on the Biological Sciences" in Good Reading, 1958)
🪸On Systems Thinking: On Ecology (1900-1949)
"At a time when ecology and genetics are each racing swiftly towards one new concept after another, yet with little contact of thought between the two subjects, there may be some advantage in surveying, if only synoptically and in preliminary fashion, the largely uncharted territory between them." (Charles S Elton, 1938)
"If there are favourable habitats and favorable forms of association for animals and plants, as ecology demonstrates, why not for men? If each particular natural environment has has its own balance; is there not perhaps an equivalent of this in culture?" (Lewis Mumford, "The Culture of Cities", 1938)
"That land is a community is the basic concept of ecology, but that land is to be loved and respected is an extension of ethics." (Aldo Leopold, "A Sand County Almanac", 1949)
31 May 2020
🪷On Mind: Mental Models XLVIII
"From the mental models that people have, they can define the world around them. They can relate and share ideas with others as a way of improving their lives. […] Looking at the bigger picture, mental models not only help people in understanding how the world works, but it also draws people to comprehend their position in it." (Adam Feel, "Mental Models", 2019)
🅵Jay W Forrester - Collected Quotes
"Negative feedback is the form normally encountered in the control of physical systems. Yet, positive feedback dominates in the growth and decline patterns of social systems." (Jay W Forrester, "Modeling the Dynamic Processes of Corporate Growth", 1964)
"Our social systems are highly nonlinear. It seems likely that such nonlinearities, coupled with the unstable tendencies caused by amplifications and time delays, create the characteristic modes of behavior […]" (Jay W Forrester, "Modeling the Dynamic Processes of Corporate Growth", 1964)
"[The engineer] must identify the significant and critical problems, but in his education, problems have been predetermined and assigned. He must develop the judgment to know what solutions to problems are possible, but in school the problems encountered are known to have answers." (Jay W Forrester, "Engineering Education and Engineering Practice in the Year 2000", 1967)
"Formulating a model of a system should start from the question 'Where is the boundary, that encompasses the smallest number of components, within which the dynamic behavior under study is generated?'" (Jay W Forrester, "Principles of Systems", 1968)
"[…] complex systems are counterintuitive. That is, they give indications that suggest corrective action which will often be ineffective or even adverse in its results." (Jay W Forrester, "Urban Dynamics", 1969)
"Nonlinear coupling allows one feedback loop to dominate the system for a time and then cause this dominance to shift to another part of the system where behavior is so different that the two seem unrelated." (Jay W. Forrester, "Urban Dynamics", 1969)
"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 Forrester, "Urban dynamics", 1969)
"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 non‐linear 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." (Jay F Forrester, "Urban Dynamics", 1969)
"To model the dynamic behavior of a system, four hierarchies of structure should be recognized: closed boundary around the system; feedback loops as the basic structural elements within the boundary; level variables representing accumulations within the feedback loops; rate variables representing activity within the feedback loops." (Jay W Forrester, "Urban Dynamics", 1969)
"Each of us uses models constantly. Every person in his private life and in his business life instinctively uses models for decision making. The mental image of the world around you which you carry in your head is a model. […] A mental image is a model. All our decisions are taken on the basis of models." (Jay W Forrester, "Counter-Intuitive Behaviour of Social Systems", Technological Review 73, 1971)
"Mental models are fuzzy, incomplete, and imprecisely stated. Furthermore, within a single individual, mental models change with time, even during the flow of a single conversation. The human mind assembles a few relationships to fit the context of a discussion. As debate shifts, so do the mental models. Even when only a single topic is being discussed, each participant in a conversation employs a different mental model to interpret the subject. Fundamental assumptions differ but are never brought into the open. […] A mental model may be correct in structure and assumptions but, even so, the human mind - either individually or as a group consensus - is apt to draw the wrong implications for the future." (Jay W Forrester, "Counterintuitive Behaviour of Social Systems", Technology Review, 1971)
"A model for simulating dynamic system behavior requires formal policy descriptions to specify how individual decisions are to be made. Flows of information are continuously converted into decisions and actions. No plea about the inadequacy of our understanding of the decision-making processes can excuse us from estimating decision-making criteria. To omit a decision point is to deny its presence - a mistake of far greater magnitude than any errors in our best estimate of the process." (Jay W Forrester, "Policies, decisions and information sources for modeling", 1994)
"First, social systems are inherently insensitive to most policy changes that people choose in an effort to alter the behavior of systems. In fact, social systems draw attention to the very points at which an attempt to intervene will fail. Human intuition develops from exposure to simple systems. In simple systems, the cause of a trouble is close in both time and space to symptoms of the trouble. If one touches a hot stove, the burn occurs here and now; the cause is obvious. However, in complex dynamic systems, causes are often far removed in both time and space from the symptoms. True causes may lie far back in time and arise from an entirely different part of the system from when and where the symptoms occur. However, the complex system can mislead in devious ways by presenting an apparent cause that meets the expectations derived from simple systems."(Jay W Forrester, "Counterintuitive Behavior of Social Systems", 1995)
"Second, social systems seem to have a few sensitive influence points through which behavior can be changed. These high-influence points are not where most people expect. Furthermore, when a high-influence policy is identified, the chances are great that a person guided by intuition and judgment will alter the system in the wrong direction." (Jay W Forrester, "Counterintuitive Behavior of Social Systems", 1995)
"System dynamics models are not derived statistically from time-series data. Instead, they are statements about system structure and the policies that guide decisions. Models contain the assumptions being made about a system. A model is only as good as the expertise which lies behind its formulation. A good computer model is distinguished from a poor one by the degree to which it captures the essence of a system that it represents. Many other kinds of mathematical models are limited because they will not accept the multiple-feedback-loop and nonlinear nature of real systems."
"Third, social systems exhibit a conflict between short-term and long-term consequences of a policy change. A policy that produces improvement in the short run is usually one that degrades a system in the long run. Likewise, policies that produce long-run improvement may initially depress behavior of a system. This is especially treacherous. The short run is more visible and more compelling. Short-run pressures speak loudly for immediate attention. However, sequences of actions all aimed at short-run improvement can eventually burden a system with long-run depressants so severe that even heroic short-run measures no longer suffice. Many problems being faced today are the cumulative result of short-run measures taken in prior decades." (Jay W Forrester, "Counterintuitive Behavior of Social Systems", 1995)
"Complex systems defy intuitive solutions. Even a third-order, linear differential equation is unsolvable by inspection. Yet, important situations in management, economics, medicine, and social behavior usually lose reality if simplified to less than fifth-order nonlinear dynamic systems. Attempts to deal with nonlinear dynamic systems using ordinary processes of description and debate lead to internal inconsistencies. Underlying assumptions may have been left unclear and contradictory, and mental models are often logically incomplete. Resulting behavior is likely to be contrary to that implied by the assumptions being made about' underlying system structure and governing policies." (Jay W. Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
"Models
are present in everything we do. One does not have a family or corporation in
one's head. Instead, one has observations about those systems. Such
observations and assumptions constitute mental models, which are then used as
the basis for action. System dynamics models have little impact unless they
change the way people perceive a situation. They must relate to and improve
mental models if they are to fill an effective role." (Jay W. Forrester,
"Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
"System dynamics models have little impact unless they change the way people perceive a situation. A model must help to organize information in a more understandable way. A model should link the past to the present by showing how present conditions arose, and extend the present into persuasive alternative futures under a variety of scenarios determined by policy alternatives. In other words, a system dynamics model, if it is to be effective, must communicate with and modify the prior mental models. Only people's beliefs - that is, their mental models - will determine action. Computer models must relate to and improve mental models if the computer models are to fill an effective role." (Jay W. Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)
29 May 2020
🆃James R Thompson - Collected Quotes
"Among the advantages of a simulation approach is principally that it enables us to eliminate time-consuming and artificial approximation theoretic activities and to spend our time in more useful pursuits. More importantly, simulation will enable us to deal with problems that are so complex in their 'closed form' manifestation that they are presently attacked only in ad hoc fashion." (James R Thompson, "Empirical Model Building", 1989)
🅼Michel de Montaigne - Collected Quotes
"It is the sharpness of our mind that gives the edge to our pains and pleasures." (Michel de Montaigne, "Essais", 1580 ...