❄️Systems Thinking: On Causal Maps (Quotes)

"Causal maps are representations of individuals (or groups) beliefs about causal relations. They include elements, with only two kinds of properties. The first property is 'relevance'. The second  is the possibility of being in one (of two) 'influence relationships' (positive or negative) with one (of three) strengths (weak. moderate, or strong)." (Kivia Markoczy & Jeff Goldberg, "A method for eliciting and comparing causal maps", 1995)

"Short-term memory can hold 7 ± 2 chunks of information at once. This puts a rather sharp limit on the effective size and complexity of a causal map. Presenting a complex causal map all at once makes it hard to see the loops, understand which are important, or understand how they generate the dynamics. Resist the temptation to put all the loops you and your clients have identified into a single comprehensive diagram." (John D Sterman, "Business Dynamics Systems Thinking and Modeling for a Complex World", 2000)

"The robustness of the misperceptions of feedback and the poor performance they cause are due to two basic and related deficiencies in our mental model. First, our cognitive maps of the causal structure of systems are vastly simplified compared to the complexity of the systems themselves. Second, we are unable to infer correctly the dynamics of all but the simplest causal maps. Both are direct consequences of bounded rationality, that is, the many limitations of attention, memory, recall, information processing capability, and time that constrain human decision making." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"A causal map is an abstract representation of the causal relationships among kinds of objects and events in the world. Such relationships are not, for the most part, directly observable, but they can often be accurately inferred from observations. This includes both observations of patterns of contingency and correlation among events as well as observations of the effects of experimental interventions. We can think of everyday theories and theory-formation processes as cognitive systems that allow us to recover an accurate causal map of the world." (Alison Gopnik & Clark Glymour, "Causal maps and Bayes nets: a cognitive and computational account of theory-formation" [in "The cognitive basis of science"], 2002)

"Causal mapping is a simple and useful technique for addressing situations where thinking - as an individual or as a group - matters. A causal map is a word-and-arrow diagram in which ideas and actions are causally linked with one another through the use of arrows. The arrows indicate how one idea or action leads to another. Causal mapping makes it possible to articulate a large number of ideas and their interconnections in such a way that people can know what to do in an area of concern, how to do it and why, because the arrows indicate the causes and consequences of an idea or action." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping is [...]  a technique for linking strategic thinking and acting, helping make sense of complex problems, and communicating to oneself and others what might be done about them. With practice, the use of causal mapping can assist you in moving from 'winging it' when thinking matters to a more concrete and rigorous approach that helps you and others achieve success in an easy and far more reliable way" (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal mapping makes it possible to articulate a large number of ideas and their interconnections in such a way that we can better understand an area of concern. Causal mapping also helps us know what to do about the issue, what it would take to do those things, and what we would like to get out of having done so. Causal mapping is therefore a particularly powerful technique for making sense of complex problems, linking strategic thinking and acting, and helping to communicate to others what might or should be done. " (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"When an individual uses causal mapping to help clarify their own thinking, we call this technique cognitive mapping, because it is related to personal thinking or cognition. When a group maps their own ideas, we call it oval mapping, because we often use oval-shaped cards to record individuals’ ideas so that they can be arranged into a group’s map. Cognitive maps and oval maps can be used to create a strategic plan, because the maps include goals, strategies and actions, just like strategic plans." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

"Causal maps include elements called nodes, which are allowed to have causal relationships of different strengths of positive or negative loading depicted with a number, usually in the range of from 1 (weak) to 3 (strong). The relationships of the nodes are depicted with arcs or links labeled with the assumed polarity and loading factor or strength of causality, Links with positive polarity refer to dependency (when A increases B increases proportionally to the loading factor) and negative to inverse dependency (when A increases, B decreases)." (Hannu Kivijärvi et al, "A Support System for the Strategic Scenario Process", Encyclopedia of Decision Making and Decision Support Technologies, 2008)

"Fifth principle: (a) in finding solutions for systemic problems do not be content with symptomatic solutions but look for systemic-structural levers that can produce the more incisive effect; (b) if there are several systemic levers, choose the most efficient, that which produces the maximum effects with the minimum effort; (c) to activate the chosen structural lever identify the most effective decisional lever (action variable) taking into account the time necessary to produce the desired effect; (d) the choice of structural and decisional levers, as well as the intensity of the actions to modify their values, must follow from a careful construction, interpretation and assessment of the system’s causal map." (Piero Mella, "Systems Thinking: Intelligence in Action", 2012)

"(1) The causal maps are only models of a world of variables and processes; (2) They are models suitable for depicting that world only if they represent a logical image; (3) A logical image is made up of a network of arrows that depict the cause and effect connections among the variables and processes in the world; this network cannot be in contradiction to the world; (4) This depiction of the world relates to the boundaries between the represented and the external systems; the causal maps always depict a portion of a vaster world;" (Piero Mella, "Systems Thinking: Intelligence in Action", 2012)

"In constructing causal maps, whatever technique is adopted, there is always the problem of identifying or defining the system’s boundaries, either if we zoom in or broaden our perspective by zooming out." (Piero Mella, "Systems Thinking: Intelligence in Action", 2012)

"A Causal Map is hierarchical in structure (linking means to ends) and built with a focus on achieving goals. The process of creating the maps is ideally a group process and this in itself will add lots of value to a collective understanding of goals around EDI, what is required to achieve these and some of the potential challenges around this." (Nicola Morrill, "Supporting Your Efforts on Diversity", 2021)

🏷️Knowledge Representation: On Causal Maps (Quotes)

 "[…] learning consists not in stimulus-response connections but in the building up in the nervous system of sets which function like cognitive maps […] such cognitive maps may be usefully characterized as varying from a narrow strip variety to a broader comprehensive variety." (Edward C Tolman, "Cognitive maps in rats and men", 1948)

"A person is changed by the contingencies of reinforcement under which he behaves; he does not store the contingencies. In particular, he does not store copies of the stimuli which have played a part in the contingencies. There are no 'iconic representations' in his mind; there are no 'data structures stored in his memory'; he has no 'cognitive map' of the world in which he has lived. He has simply been changed in such a way that stimuli now control particular kinds of perceptual behavior." (Burrhus F Skinner, "About behaviorism", 1974)

"A cognitive map is a specific way of representing a person's assertions about some limited domain, such as a policy problem. It is designed to capture the structure of the person's causal assertions and to generate the consequences that follow front this structure. […]  a person might use his cognitive map to derive explanations of the past, make predictions for the future, and choose policies in the present." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"The concepts a person uses are represented as points, and the causal links between these concepts are represented as arrows between these points. This gives a pictorial representation of the causal assertions of a person as a graph of points and arrows. This kind of representation of assertions as a graph will be called a cognitive map. The policy alternatives, all of the various causes and effects, the goals, and the ultimate utility of the decision maker can all be thought of as concept variables, and represented as points in the cognitive map. The real power of this approach ap pears when a cognitive map is pictured in graph form; it is then relatively easy to see how each of the concepts and causal relation ships relate to each other, and to see the overall structure of the whole set of portrayed assertions." (Robert Axelrod, "The Cognitive Mapping Approach to Decision Making" [in "Structure of Decision: The Cognitive Maps of Political Elites"], 1976)

"The cognitive map is not a picture or image which 'looks like' what it represents; rather, it is an information structure from which map-like images can be reconstructed and from which behaviour dependent upon place information can be generated." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"A fuzzy cognitive map or FCM draws a causal picture. It ties facts and things and processes to values and policies and objectives. And it lets you predict how complex events interact and play out. [...] Neural nets give a shortcut to tuning an FCM. The trick is to let the fuzzy causal edges change as if they were synapses in a neural net. They cannot change with the same math laws because FCM edges stand for causal effect not signal flow. We bombard the FCM nodes with real data. The data state which nodes are on or off and to which degree at each moment in time. Then the edges grow among the nodes."  (Bart Kosko, "Fuzzy Thinking: The new science of fuzzy logic", 1993)

"Under the label 'cognitive maps', mental models have been conceived of as the mental representation of spatial aspects of the environment. A mental model, in this sense, comprises the topology of an area, including relevant districts, landmarks, and paths." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)

"Bounded rationality simultaneously constrains the complexity of our cognitive maps and our ability to use them to anticipate the system dynamics. Mental models in which the world is seen as a sequence of events and in which feedback, nonlinearity, time delays, and multiple consequences are lacking lead to poor performance when these elements of dynamic complexity are present. Dysfunction in complex systems can arise from the misperception of the feedback structure of the environment. But rich mental models that capture these sources of complexity cannot be used reliably to understand the dynamics. Dysfunction in complex systems can arise from faulty mental simulation-the misperception of feedback dynamics. These two different bounds on rationality must both be overcome for effective learning to occur. Perfect mental models without a simulation capability yield little insight; a calculus for reliable inferences about dynamics yields systematically erroneous results when applied to simplistic models." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. To use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems."  (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The robustness of the misperceptions of feedback and the poor performance they cause are due to two basic and related deficiencies in our mental model. First, our cognitive maps of the causal structure of systems are vastly simplified compared to the complexity of the systems themselves. Second, we are unable to infer correctly the dynamics of all but the simplest causal maps. Both are direct consequences of bounded rationality, that is, the many limitations of attention, memory, recall, information processing capability, and time that constrain human decision making." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"A causal map is an abstract representation of the causal relationships among kinds of objects and events in the world. Such relationships are not, for the most part, directly observable, but they can often be accurately inferred from observations. This includes both observations of patterns of contingency and correlation among events as well as observations of the effects of experimental interventions. We can think of everyday theories and theory-formation processes as cognitive systems that allow us to recover an accurate causal map of the world." (Alison Gopnik & Clark Glymour, "Causal maps and Bayes nets: a cognitive and computational account of theory-formation" [in "The cognitive basis of science"], 2002)

"Causal mapping is a technique that is used to elicit and represent domain knowledge of experts in the form of a graphical network called a causal map. A causal map (also called an influence diagram or a cause map) is a directed graph in which causal concepts (or nodes) represent the important variables that make up a domain. Causal connections are the directed arrows that connect these concepts to represent causal relationships between the variables." (S Nadkarni, Aggregated causal maps: An approach to elicit and aggregate the knowledge of multiple experts, 2003) 

"Eliciting and mapping the participant's mental models, while necessary, is far from sufficient [...] the result of the elicitation and mapping process is never more than a set of causal attributions, initial hypotheses about the structure of a system, which must then be tested. Simulation is the only practical way to test these models. The complexity of the cognitive maps produced in an elicitation workshop vastly exceeds our capacity to understand their implications. Qualitative maps are simply too ambiguous and too difficult to simulate mentally to provide much useful information on the adequacy of the model structure or guidance about the future development of the system or the effects of policies." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

"When an individual uses causal mapping to help clarify their own thinking, we call this technique cognitive mapping, because it is related to personal thinking or cognition. When a group maps their own ideas, we call it oval mapping, because we often use oval-shaped cards to record individuals’ ideas so that they can be arranged into a group’s map. Cognitive maps and oval maps can be used to create a strategic plan, because the maps include goals, strategies and actions, just like strategic plans." (John M Bryson et al, "Visible Thinking: Unlocking Causal Mapping For Practical Business Results", 2004)

🪂Mind: On Maps (Quotes)

"[…] learning consists not in stimulus-response connections but in the building up in the nervous system of sets which function like cognitive maps […] such cognitive maps may be usefully characterized as varying from a narrow strip variety to a broader comprehensive variety." (Edward C Tolman, "Cognitive maps in rats and men", 1948)

"A person is changed by the contingencies of reinforcement under which he behaves; he does not store the contingencies. In particular, he does not store copies of the stimuli which have played a part in the contingencies. There are no 'iconic representations' in his mind; there are no 'data structures stored in his memory'; he has no 'cognitive map' of the world in which he has lived. He has simply been changed in such a way that stimuli now control particular kinds of perceptual behavior." (Burrhus F Skinner, "About behaviorism", 1974)

"[…] there is an irreducible difference between the world and our experience of it. We as human beings do not operate directly on the world. Each of us creates a representation of the world in which we live - that is, we create a map or model which we use to generate our behavior. Our representation of the world determines to a large degree what our experience of the world will be, how we will perceive the world, what choices we will see available to us as we live in the world." (Richard Bandler & John Grinder, "The Structure of Magic", 1975)

"[...] it seems (to many) that we cannot account for perception unless we suppose it provides us with an internal image (or model or map) of the external world, and yet what good would that image do us unless we have an inner eye to perceive it, and how are we to explain its capacity for perception? It also seems (to many) that understanding a heard sentence must be somehow translating it into some internal message, but how will this message be understood: by translating it into something else? The problem is an old one, and let’s call it Hume’s Problem, for while he did not state it explicitly, he appreciated its force and strove mightily to escape its clutches. (Daniel Dennett, "Brainstorms: Philosophical essays on mind and psychology", 1978)

"The mapping from linguistic inputs to mental models is not a one-one mapping. So semantic properties of sentences may not be recoverable from a mental model. Reading or listening is typically for content not for form. People want to know what is being said to them, not how it is being said. [...] A mental model is a representation of the content of a text that need bear no resemblance to any of the text's linguistic representations. Its structure is similar to the situation described by the text." (Alan Granham, "Mental Models as Representations of Discourse and Text", 1987)

"[…] a mental model is a mapping from a domain into a mental representation which contains the main characteristics of the domain; a model can be ‘run’ to generate explanations and expectations with respect to potential states. Mental models have been proposed in particular as the kind of knowledge structures that people use to understand a specific domain […]" (Helmut Jungermann, Holger Schütz & Manfred Thuering, "Mental models in risk assessment: Informing people about drugs", Risk Analysis 8 (1), 1988)

"Each of us has many, many maps in our head, which can be divided into two main categories: maps of the way things are, or realities, and maps of the way things should be, or values. We interpret everything we experience through these mental maps. We seldom question their accuracy; we're usually even unaware that we have them. We simply assume that the way we see things is the way they really are or the way they should be."  (Stephen Covey, "The 7 Habits of Highly Effective People", 1989) 

"The more aware we are of our basic paradigms, maps, or assumptions, and the extent to which we have been influenced by our experience, the more we can take responsibility for those paradigms, examine them, test them against reality, listen to others and be open to their perceptions, thereby getting a larger picture and a far more objective view." (Stephen Covey, "The 7 Habits of Highly Effective People", 1989)

"Behavior modeling involves observing and mapping the successful processes which underlie an exceptional performance of some type. It is the process of taking a complex event or series of events and breaking it into small enough chunks so that it can be recapitulated in some way. The purpose of behavior modeling is to create a pragmatic map or 'model' of that behavior which can be used to reproduce or simulate some aspect of that performance by anyone who is motivated to do so. The goal of the behavior modeling process is to identify the essential elements of thought and action required to produce the desired response or outcome. As opposed to providing purely correlative or statistical data, a 'model' of a particular behavior must provide a description of what is necessary to actually achieve a similar result." (Robert B Dilts, "Modeling with NLP", 1998)

"From the NLP perspective, there are inductive transformations, through which we perceive patterns in, and build maps of, the world around us; and there are deductive transformations, through which we describe and act on our perceptions and models of the world. Inductive transformations involve the process of "chunking up" to find the deeper structure patterns ('concepts', 'ideas', 'universals', etc.) in the collections of experiences we receive through our senses. Deductive transformations operate to 'chunk down' our experiential deep structures into surface structures; rendering general ideas and concepts into specific words, actions and other forms of behavioral output." (Robert B Dilts, "Modeling with NLP", 1998)

"Having a choice is better than not having a choice. Always try to have a map for yourself that gives you the widest and richest number of choices. Act always to increase choice. The more choices you have, the freer you are and the more influence you have." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"In NLP terms, then, a master is not someone who already knows the answers and has the solutions but someone who is able to ask worthwhile questions and direct the process of learning, problem solving and creativity to form new maps of the world that lead to useful new answers and possibilities." (Robert B Dilts, "Modeling with NLP", 1998)

"In the NLP view, then, 'reality' is the relationship and interaction between deep structures and surface structures. Thus, there are many possible 'realities'. It is not as if there is 'a map' and 'a territory', there are many possible territories and maps, and the territory is continually changing, partially as a function of the way in which people's maps lead them to interact with that territory." (Robert B Dilts, "Modeling with NLP", 1998)

"NLP operates from the assumption that the map is not the territory. As human beings, we can never know reality, in the sense that we have to experience reality through our senses and our senses are limited. [...] We can only make maps of the reality around us through the information that we receive through our senses and the connection of that information to our own personal memories and other experiences. Therefore, we don't tend to respond to reality itself, but rather to our own maps of reality." (Robert B Dilts, "Modeling with NLP", 1998)

"Our brain is mapping the world. Often that map is distorted, but it's a map with constant immediate sensory input." (Edward O Wilson, [interview] 1998)

"People respond to their experience, not to reality itself. We do not know what reality is. Our senses, beliefs, and past experience give us a map of the world from which to operate." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"The NLP modeling process consists of applying various strategies for examining the mental and physical processes which underlie a particular performance or the achievement of a particular result, and then creating some type of explicit map or description of those processes which can be applied for some practical purpose. Various modeling strategies delineate different sequences of steps and types of distinctions through which relevant patterns may discovered and formed into descriptions."  (Robert B Dilts, "Modeling with NLP", 1998)

"The objective of the NLP modeling process is not to end up with the one 'right' or 'true' description of a particular person's thinking process, but rather to make an instrumental map that allows us to apply the strategies that we have modeled in some useful way. An 'instrumental map' is one that allows us to act more effectively - the 'accuracy' or 'reality' of the map is less important than its 'usefulness'." (Robert B Dilts, "Modeling with NLP", 1998)

"A collective mental map functions first of all as a shared memory. Various discoveries by members of the collective are registered and stored in this memory, so that the information will remain available for as long as necessary. The storage capacity of this memory is in general much larger than the capacities of the memories of the individual participants. This is because the shared memory can potentially be inscribed over the whole of the physical surroundings, instead of being limited to a single, spatially localized nervous system. Thus, a collective mental map differs from cultural knowledge, such as the knowledge of a language or a religion, which is shared among different individuals in a cultural group but is limited by the amount of knowledge a single individual can bear in mind." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

"Our view of reality is like a map with which to negotiate the terrain of life. If the map is true and accurate, we will generally know how to get there. If the map is false and inaccurate, we generally will be lost." (M Scott Peck, "Wisdom from the Road Less Traveled", 2001)

"Eliciting and mapping the participant's mental models, while necessary, is far from sufficient [...] the result of the elicitation and mapping process is never more than a set of causal attributions, initial hypotheses about the structure of a system, which must then be tested. Simulation is the only practical way to test these models. The complexity of the cognitive maps produced in an elicitation workshop vastly exceeds our capacity to understand their implications. Qualitative maps are simply too ambiguous and too difficult to simulate mentally to provide much useful information on the adequacy of the model structure or guidance about the future development of the system or the effects of policies." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

"Maps are models, and every model represents some aspect of reality or an idea that is of interest. A model is a simplification. It is an interpretation of reality that abstracts the aspects relevant to solving the problem at hand and ignores extraneous detail." (Eric Evans, "Domain-Driven Design: Tackling complexity in the heart of software", 2003)

"The value of mapping is that it allows us to understand, plan, and communicate about some experience or phenomenon without having to actually 'be there'." (Robert B. Dilts, "From Coach to Awakener", 2003)

"A map does not just chart, it unlocks and formulates meaning; it forms bridges between here and there, between disparate ideas that we did not know were previously connected." (Reif Larsen, "The Selected Works of T S Spivet", 2009)

See also: Maps as Graphical Representation, Maps as Knowledge Representation

🏷️Knowledge Representation: On Cognitive Maps (Quotes)

"[...] we believe that in the course of learning something like a field map of the environment gets established in the rat's brain [...] and it is this tentative map, indicating routes and paths and environmental relationships, which finally determines what responses, if any, the animal will finally release." (Edward C Tolman, "Cognitive maps in rats and men", Psychological Review 55(4), 1948)

"[…] learning consists not in stimulus-response connections but in the building up in the nervous system of sets which function like cognitive maps […] such cognitive maps may be usefully characterized as varying from a narrow strip variety to a broader comprehensive variety." (Edward C Tolman, "Cognitive maps in rats and men", Psychological Review 55(4), 1948)

"The cognitive map is a construct that has been proposed to explain how individuals know their environment. It assumes that people store information about their environment in a simplified form and in relation to other information they already have. It further assumes that this information is coded in a structure which people carry around in their heads, and that this structure corresponds, at least to a reasonable degree, to the environment it represents. It is as if an individual carried a map or model of the environment in his head." (Stephen Kaplan, "Cognitive maps, human needs and the designed environment", Environmental design research vol. 1, 1973)

"A person is changed by the contingencies of reinforcement under which he behaves; he does not store the contingencies. In particular, he does not store copies of the stimuli which have played a part in the contingencies. There are no 'iconic representations' in his mind; there are no 'data structures stored in his memory'; he has no 'cognitive map' of the world in which he has lived. He has simply been changed in such a way that stimuli now control particular kinds of perceptual behavior." (Burrhus F Skinner, "About behaviorism", 1974)

"A cognitive map is a specific way of representing a person's assertions about some limited domain, such as a policy problem. It is designed to capture the structure of the person's causal assertions and to generate the consequences that follow front this structure. […]  a person might use his cognitive map to derive explanations of the past, make predictions for the future, and choose policies in the present." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"The cognitive mapping approach promises to be more helpful to the decision maker for two reasons. First, since the advice can be expressed in terms of the person's own cognitive map, it can be solidly based in his own experience, using his own concepts, his own causal beliefs. and his own values. Equally important, when the cognitive map approach offers advice, it takes explicit account of the finite capacities of people and the way in which they simplify their images when dealing with a complex policy issue. Thus, with the cognitive mapping approach, a better understanding of how decisions are made can lead to the making of better decisions." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"Briefly, a cognitive map would consist of two major systems, a place system and a misplace system. The first is a memory system which contains information about places in the organism's environment, their spatial relations, and the existence of specific objects in specific places. The second, misplace, system signals changes in a particular place, involving either the presence of a new object or the absence of an old one. The place system permits an animal to locate itself in a familiar environment without reference to any specific sensory input, to go from one place to another independent of particular inputs (cues) or outputs (responses), and to link together conceptually parts of an environment which have never been experienced at the same time. The misplace system is primarily responsible for exploration, a species-typical behaviour which functions to build maps of new environments and to incorporate new information into existing maps." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"The cognitive map is not a picture or image which 'looks like' what it represents; rather, it is an information structure from which map-like images can be reconstructed and from which behaviour dependent upon place information can be generated." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"We would agree that organisms do not 'see' absolute space; cognitive maps are not pictures of the universe, they are schemata from which any portion of space can be constructed. The fact that we cannot perceive unified space does not mean we cannot conceive it; the latter potentiality derives from the possession of a structure which can be used to construct spaces that stretch endlessly in all dimensions." (John O'Keefe & Lynn Nadel, "The Hippocampus as a Cognitive Map", 1978)

"[...] cognitive maps can be seen as a picture or visual aid in comprehending the mappers' understanding of particular, and selective, elements of the thoughts (rather than thinking) of an individual, group or organization. They may also be seen as a representation that is amenable to analysis by both the mapper and others." (Colin Eden, "One the nature of cognitive maps", Journal of Management Studies 29 (3), 1992)

"Bounded rationality simultaneously constrains the complexity of our cognitive maps and our ability to use them to anticipate the system dynamics. Mental models in which the world is seen as a sequence of events and in which feedback, nonlinearity, time delays, and multiple consequences are lacking lead to poor performance when these elements of dynamic complexity are present. Dysfunction in complex systems can arise from the misperception of the feedback structure of the environment. But rich mental models that capture these sources of complexity cannot be used reliably to understand the dynamics. Dysfunction in complex systems can arise from faulty mental simulation - the misperception of feedback dynamics. These two different bounds on rationality must both be overcome for effective learning to occur. Perfect mental models without a simulation capability yield little insight; a calculus for reliable inferences about dynamics yields systematically erroneous results when applied to simplistic models." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. To use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems."  (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The robustness of the misperceptions of feedback and the poor performance they cause are due to two basic and related deficiencies in our mental model. First, our cognitive maps of the causal structure of systems are vastly simplified compared to the complexity of the systems themselves. Second, we are unable to infer correctly the dynamics of all but the simplest causal maps. Both are direct consequences of bounded rationality, that is, the many limitations of attention, memory, recall, information processing capability, and time that constrain human decision making." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Eliciting and mapping the participant's mental models, while necessary, is far from sufficient [...] the result of the elicitation and mapping process is never more than a set of causal attributions, initial hypotheses about the structure of a system, which must then be tested. Simulation is the only practical way to test these models. The complexity of the cognitive maps produced in an elicitation workshop vastly exceeds our capacity to understand their implications. Qualitative maps are simply too ambiguous and too difficult to simulate mentally to provide much useful information on the adequacy of the model structure or guidance about the future development of the system or the effects of policies." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

[cognitive map:] "A mental representation of a portion of the physical environment and the relative locations of points within it." (Andrew M Colman, "A Dictionary of Psychology" 3rd Ed, 2008)

[cognitive map:] "A mental model (or map) of the external environment which may be constructed following exploratory behaviour." (Michael Allaby, "A Dictionary of Zoology" 3rd Ed., 2009)

"There is no reason to believe that cognitive maps are like iconic maps except, rather than being inscribed in the dirt, or on a rock, or imprinted on paper, they are somehow inscribed in neural tissue. They seem to be more like lists of significant places intertwined with bearings and headings between one place and another. The vital significance of these places is part and parcel of the map; the “map” is not a neutral spatial substrate to which vital significance is later attached. The space of cognitive maps is not merely about physical position; it is about needs and satisfiers, vantage points and opportunities for action." (William Benzon, "Maps, Iconic and Abstract", 2011)

[Cognitive Map:] "A representation of the conceptualization that the subject constructs of the system in which he evolves. The set of cognitive representations that emerge make it possible to understand his actions, the links between the factors structuring the cognitive patterns dictating his behaviors." (Henda E Karray & Souhaila Kammoun, "Strategic Orientation of the Managers of a Tunisian Family Group Before and After the Revolution", 2020)

🏷️Knowledge Representation: On Maps (Quotes)

"The world can doubtless never be well known by theory: practice is absolutely necessary; but surely it is of great use to a young man, before he sets out for that country, full of mazes, windings, and turnings, to have at least a general map of it, made by some experienced traveler." (Philip Stanhope, "Letters Written by the Earl of Chesterfield to His Son", 1827)

"The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance." (James J Sylvester, [Presidential Address to British Association] 1869)

"What are the sciences but maps of universal laws, and universal laws but the channels of universal power; and universal power but the outgoings of a universal mind?" (Edward Thomson, "Evidences of Revealed Religion", 1872)

"Just as, in the map of a half-explored country, we see detached bits of rivers, isolated mountains, and undefined plains, not connected into any complete plan, so a new branch of knowledge consists of groups of facts, each group standing apart, so as not to allow us to reason from one to another." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"The first of the principles governing symbols is this: The symbol is NOT the thing symbolized; the word is NOT the thing; the map is NOT the territory it stands for." (Samuel I Hayakawa, "Language in Thought and Action", 1949)

"We all inherit a great deal of useless knowledge, and a great deal of misinformation and error (maps that were formerly thought to be accurate), so that there is always a portion of what we have been told that must be discarded. But the cultural heritage of our civilization that is transmitted to us - our socially pooled knowledge, both scientific and humane - has been valued principally because we have believed that it gives us accurate maps of experience. The analogy of verbal words to maps is an important one [...]. It should be noticed at this point, however, that there are two ways of getting false maps of the world into our heads: first, by having them given to us; second, by creating them ourselves when we misread the true maps given to us." (Samuel I Hayakawa, "Language in Thought and Action", 1949)

"A fundamental value in the scientific outlook is concern with the best available map of reality. The scientist will always seek a description of events which enables him to predict most by assuming least. He thus already prefers a particular form of behavior. If moralities are systems of preferences, here is at least one point at which science cannot be said to be completely without preferences. Science prefers good maps." (Anatol Rapoport, "Science and the goals of man: a study in semantic orientation", 1950)

"No map contains all the information about the territory it represents. The road map we get at the gasoline station may show all the roads in the state, but it will not as a rule show latitude and longitude. A physical map goes into details about the topography of a country but is indifferent to political boundaries. Furthermore, the scale of the map makes a big difference. The smaller the scale the less features will be shown." (Anatol Rapoport, "Science and the goals of man: a study in semantic orientation", 1950) 

"Good design looks right. It is simple (clear and uncomplicated). Good design is also elegant, and does not look contrived. A map should be aesthetically pleasing, thought provoking, and communicative."  (Arthur H Robinson, "Elements of Cartography", 1953)

"The design process involves a series of operations. In map design, it is convenient to break this sequence into three stages. In the first stage, you draw heavily on imagination and creativity. You think of various graphic possibilities, consider alternative ways." (Arthur H Robinson, "Elements of Cartography", 1953)

"Scientific research was much like prospecting: you went out and you hunted, armed with your maps and your instruments, but in the end your preparations did not matter, or even your intuition. You needed your luck, and whatever benefits accrued to the diligent, through sheer, grinding hard work." (Michael Crichton, "The Andromeda Strain", 1969)

"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)

"The orchard of science is a vast globe-encircling monster, without a map, and known to no one man; indeed, to no group of men fewer than the whole international mass of creative scientists. Within it, each observer clings to his own well-known and well-loved clump of trees. If he looks beyond, it is usually with a guilty sigh." (Isaac Asimov, "View from a Height", 1975)

"As we experience space, and construct representations of it, we know that it will be continuous, everything is somewhere, and no matter what other characteristics objects do not share, they always share relative location, that is, spatiality; hence the desirability of equating knowledge with space, an intellectual space. This assures an organization and basis for predictability, which are shared by absolutely everyone. This proposition appears to be so fundamental that apparently it is simply adopted a priori." (Arthur H Robinson & Barbara B Petchenik, "The Nature of Maps: Essays toward Understanding Maps and Mapping", 1976)

"Mapping is based on systems of assumptions, on logic, on human needs, and on human cognitive characteristics, very little of which has been recognized or discussed in cartography." (Arthur H Robinson & Barbara B Petchenik, "The Nature of Maps: Essays toward Understanding Maps and Mapping", 1976)

"A map seems the type of conceptual object, yet the interesting thing is the grotesquely token foot it keeps in the world of the physical, having the unreality without the far-fetched appropriateness of the edibles in Communion, being a picture to the degree that the sacrament is a meal. For a feeling of thorough transcendence such unobvious relations between the model and the representation seem essential, and the flimsy connection between acres of soil and their image on the map makes reading one an erudite act." (Robert Harbison, "Eccentric Spaces", 1977)

"The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient." (Benoit Mandelbrot, "The Fractal Geometry of Nature", 1977)

"Mathematical equations and literary phrases are useful but they are no substitute for the spatial eloquence of the map." (Arthur H Robinson, "Uniqueness of the Map", American Cartographer Vol. 5 (1), 1978)

"Maps containing marks that indicate a variety of features at specific locations are easy to produce and often revealing for the reader. You can use dots, numbers, and shapes, with or without keys. The basic map must always be simple and devoid of unnecessary detail. There should be no ambiguity about what happens where." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"Maps used as charts do not need fine cartographic detail. Their purpose is to express ideas, explain relationships, or store data for consultation. Keep your maps simple. Edit out irrelevant detail. Without distortion, try to present the facts as the main feature of your map, which should serve only as a springboard for the idea you're trying to put across." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"Physicists' models are like maps: never final, never complete until they grow as large and complex as the reality they represent." (James Gleick, "Genius: The Life and Science of Richard Feynman, Epilogue", 1992)

"The prevailing style of management must undergo transformation. A system cannot understand itself. The transformation requires a view from outside. The aim [...] is to provide an outside view - a lens - that I call a system of profound knowledge. It provides a map of theory by which to understand the organizations that we work in." (Dr. W. Edwards Deming, "The New Economics for Industry, Government, Education", 1994)

"The representational nature of maps, however, is often ignored - what we see when looking at a map is not the word, but an abstract representation that we find convenient to use in place of the world. When we build these abstract representations we are not revealing knowledge as much as are creating it." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"A good map tells a multitude of little white lies; it suppresses truth to help the user see what needs to be seen. Reality is three-dimensional, rich in detail, and far too factual to allow a complete yet uncluttered two-dimensional graphic scale model. Indeed, a map that did not generalize would be useless. But the value of a map depends on how well its generalized geometry and generalized content reflect a chosen aspect of reality." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"Not only is it easy to lie with maps, it's essential. To portray meaningful relationships for a complex, three-dimensional world on a flat sheet of paper or a video screen, a map must distort reality. As a scale model, the map must use symbols that almost always are proportionally much bigger or thicker than the features they represent. To avoid hiding critical information in a fog of detail, the map must offer a selective, incomplete view of reality. There's no escape from the cartographic paradox: to present a useful and truthful picture, an accurate map must tell white lies." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"The nature of maps and of their use in science and society is in the midst of remarkable change - change that is stimulated by a combination of new scientific and societal needs for geo-referenced information and rapidly evolving technologies that can provide that information in innovative ways. A key issue at the heart of this change is the concept of ‘visualization’." (Alan MacEachren, "Exploratory cartographic visualization: advancing the agenda", 1997)

"The pursuit of science is more than the pursuit of understanding. It is driven by the creative urge, the urge to construct a vision, a map, a picture of the world that gives the world a little more beauty and coherence than it had before." (John A Wheeler, "Geons, Black Holes, and Quantum Foam: A Life in Physics", 1998)

"Eliciting and mapping the participant's mental models, while necessary, is far from sufficient [...] the result of the elicitation and mapping process is never more than a set of causal attributions, initial hypotheses about the structure of a system, which must then be tested. Simulation is the only practical way to test these models. The complexity of the cognitive maps produced in an elicitation workshop vastly exceeds our capacity to understand their implications. Qualitative maps are simply too ambiguous and too difficult to simulate mentally to provide much useful information on the adequacy of the model structure or guidance about the future development of the system or the effects of policies." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

"[Maps] are a way of cataloguing the 'important' (and ignoring the 'unimportant') features of the earth’s surface and the social world; a way of accounting for the resources, objects and public infrastructure of the earth’s surface; and a tool for the representation and territorialization of space (emphasis in original)." (John Pickles, "A History of Spaces: Cartographic Reason, Mapping and the Geo-Coded World", 2004)

"On the maps provided by science, we find everything except ourselves." (Bryan Appleyard, "Understanding the Present: An Alternative History of Science", 2004)

"There is no end to the information we can use. A 'good' map provides the information we need for a particular purpose - or the information the mapmaker wants us to have. To guide us, a map’s designers must consider more than content and projection; any single map involves hundreds of decisions about presentation." (Peter Turchi, "Maps of the Imagination: The writer as cartographer", 2004)

"A road plan can show the exact location, elevation, and dimensions of any part of the structure. The map corresponds to the structure, but it's not the same as the structure. Software, on the other hand, is just a codification of the behaviors that the programmers and users want to take place. The map is the same as the structure. […] This means that software can only be described accurately at the level of individual instructions. […] A map or a blueprint for a piece of software must greatly simplify the representation in order to be comprehensible. But by doing so, it becomes inaccurate and ultimately incorrect. This is an important realization: any architecture, design, or diagram we create for software is essentially inadequate. If we represent every detail, then we're merely duplicating the software in another form, and we're wasting our time and effort." (George Stepanek, "Software Project Secrets: Why Software Projects Fail", 2005) 

"The way you describe the tale is by telling the story. It is a balancing act and a dream. The more accurate the map, the more it resembles the territory. The most accurate map [...] would be the territory and thus would be perfectly accurate and perfectly useless. The tale is the map that is the territory." (Neil Gaiman, "Fragile Things: Short Fictions and Wonders", 2006)

"Science is the art of the appropriate approximation. While the flat earth model is usually spoken of with derision it is still widely used. Flat maps, either in atlases or road maps, use the flat earth model as an approximation to the more complicated shape." (Byron K Jennings, "On the Nature of Science", Physics in Canada Vol. 63 (1), 2007)

"A map does not just chart, it unlocks and formulates meaning; it forms bridges between here and there, between disparate ideas that we did not know were previously connected." (Reif Larsen, "The Selected Works of T S Spivet", 2009)

"If maps are essentially subjective, interpretative, and fictional constructs of facts, constructs that influence decisions, actions, and cultural values generally, then why not embrace the profound efficacy of mapping in exploring and shaping new realities? Why not embrace the fact that the potentially infinite capacity of mapping to find and found new conditions might enable more socially engaging modes of exchange within larger milieux?" (James Corner, "The Agency of Mapping: Speculation, Critique and Invention", 2011)

"It is ironic but true: the one reality science cannot reduce is the only reality we will ever know. This is why we need art. By expressing our actual experience, the artist reminds us that our science is incomplete, that no map of matter will ever explain the immateriality of our consciousness." (Jonah Lehrer, "Proust Was a Neuroscientist", 2011)

"[...] mapping is not the indiscriminate, blinkered accumulation and endless array of data, but rather an extremely shrewd and tactical enterprise, a practice of relational reasoning that intelligently unfolds new realities out of existing constraints, quantities, facts and conditions." (James Corner, "The Agency of Mapping: Speculation, Critique and Invention", 2011)

"Making a map is the physical production including conceptualization and design. Mapping is the mental interpretation of the world and although it must precede the map, it does not necessarily result in a map artifact. Mapping defined in mathematics is the correspondence between each element of a given set with each element of another. Similarly in linguistics emphasis is on the correspondence between associated elements of different types. For designers all drawings are maps - they represent relationships between objects, places and ideas." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Maps are parenthetical - maps frame what you want to hold apart from the real in the world. Maps do this by creating conceptual representations of the milieu using symbols and relations between symbols. [...] Maps, any map and every map, begin with a frame. This is the literal and conceptual demarcation between what is in the map and what is not. Making a map begins with an observation which is both a thought about thinking and the object of thought itself. The undifferentiated world cannot be apprehended, therefore; all maps have a frame whether a concept or a cosmography." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"The utility of mapping as a form of data visualization isn’t in accuracy or precision, but rather the map’s capacity to help us make and organize hypothesis about the world of ideas and things. hypothesis-making through the map isn’t strictly inductive or deductive, although it can use the thought process of either, but it is often based on general observations." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Using maps as communication tools masks their complexity as a mode of thinking. Maps act like language: we attribute the signs or marks in the map to a natural extension of thought. But post-structuralism exposed maps (like language) as artificial signs whose meaning is tethered to time, place, culture, gesture, smell - in short, a plethora of cognitive and phenomenal attributes of our communication ecology." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"Maps also have the disadvantage that they consume the most powerful encoding channels in the visualization toolbox - position and size - on an aspect that is held constant. This leaves less effective encoding channels like color for showing the dimension of interest." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"We cannot draw a complete map, a complete geometry, of everything that happens in the world, because such happenings - including among them the passage of time - are always triggered only by an interaction with, and with respect to, a physical system involved in the interaction. The world is like a collection of interrelated points of view. To speak of the world 'seen from outside' makes no sense, because there is no “outside” to the world." (Carlo Rovelli, "The Order of Time", 2018)

"Maps can be a metaphor for discovery and for dominion. They embody the same principles of logic, order, and discipline that codify empirical scientific processes." (Murray Dick, "The Infographic: A History of Data Graphics in News and Communications", 2020)

"Maps are a type of chart that can convey relationships about space and relationships between objects that we relate to in the real world. Their effectiveness as a communication medium is strongly influenced by a host of factors: the nature of spatial data, the form and structure of representation, their intended purpose, the experience of the audience, and the context in the time and space in which the map is viewed. In other words, maps are a ubiquitous representation of spatial information that we can understand and relate to." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

See also: Maps as Graphical Representation, Maps and Mind

🏷️Knowledge Representation: On Map vs. Territory (Quotes)

"'That’s another thing we’ve learned from your Nation,' said Mein Herr, 'map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?' [...] 'We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!'" (Lewis Carroll, "Sylvie and Bruno Concluded, 1893)

"Let us imagine that a portion of the soil of England has been levelled off perfectly and that on it a cartographer traces a map of England. The job is perfect; there is no detail of the soil of England, no matter how minute, that is not registered on the map; everything has there its correspondence. This map, in such a case, should contain a map of the map, which should contain a map of the map of the map, and so on to infinity." (Josiah Royce, "The World and the Individual", 1899)

"The map appears to us more real than the land." (David W Lawrence, "Study of Thomas Hardy", cca. 1914)

"If we consider an actual territory (a) say, Paris, Dresden, Warsaw, and build up a map (b) in which the order of these cities would be represented as Dresden, Paris, Warsaw; to travel by such a map would be misguiding, wasteful of effort. In case of emergencies, it might be seriously harmful. We could say that such a map was ‘not true’, or that the map had a structure not similar to the territory, structure to be defined in terms of relations and multidimensional order. We should notice that: A) A map may have a structure similar or dissimilar to the structure of the territory. B) Two similar structures have similar ‘logical’ characteristics. Thus, if in a correct map, Dresden is given as between Paris and Warsaw, a similar relation is found in the actual territory. C) A map is not the territory. D) An ideal map would contain the map of the map, the map of the map of the map, endlessly." (Alfred Korzybski, "Science and Sanity: A Non-Aristotelian System and Its Necessity for Rigour in Mathematics and Physics", 1931)

"A language is like a map; it is not the territory represented, but it may be a good map or a bad map. If the map shows a different structure from the territory represented-for instance, shows the cities in a wrong order, or some places east of others while in the actual territory they are west - then the map is worse than useless, as it misinforms and leads astray. One who made use of it could never be certain of reaching his destination. The use of ellanguage to represent events which operate as-a-whole is, at least, equally misguiding and semantically dangerous." (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1933)

"If words are not things, or maps are not the actual territory, then, obviously, the only possible link between the objective world and the linguistic world is found in structure, and structure alone. The only usefulness of a map or a language depends on the similarity of structure between the empiricalworld and the map-languages. If the structure is not similar, then the traveller or speaker is led astray, which, in serious human life-problems, must become always eminently harmful. If the structures are similar, then the empirical world becomes 'rational' to a potentially rational being, which means no more than that verbal, or map-predicted characteristics, which follow up the linguistic or mapstructure, are applicable to the empirical world." (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1933)

"The map is not the thing mapped. When the map is identified with the thing mapped we have one of the vast melting pots of numerology. Notice also that the relation considered in the map does not (in this instance at least) make sense if it is supposed to hold for the things mapped." (Eric T Bell, Numerology, 1933)

"Two important characteristics of maps should be noticed. A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. If the map could be ideally correct, it would include, in a reduced scale, the map of the map; the map of the map, of the map [...]" (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1933)

"The first of the principles governing symbols is this: The symbol is NOT the thing symbolized; the word is NOT the thing; the map is NOT the territory it stands for." (Samuel I Hayakawa, "Language in Thought and Action", 1949)

"No map contains all the information about the territory it represents. The road map we get at the gasoline station may show all the roads in the state, but it will not as a rule show latitude and longitude. A physical map goes into details about the topography of a country but is indifferent to political boundaries. Furthermore, the scale of the map makes a big difference. The smaller the scale the less features will be shown." (Anatol Rapoport, "Science and the goals of man: a study in semantic orientation", 1950)

"We say the map is different from the territory. But what is the territory? Operationally, somebody went out with a retina or a measuring stick and made representations which were then put on paper. What is on the paper map is a representation of what was in the retinal representation of the man who made the map; and as you push the question back, what you find is an infinite regress, an infinite series of maps. The territory never gets in at all. […] Always, the process of representation will filter it out so that the mental world is only maps of maps, ad infinitum." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"The map is not the territory, and the name is not the thing named." (Gregory Bateson, "Mind and Nature: A Necessary Unity", 1979)

"The ultimate metaphysical secret, if we dare state it so simply, is that there are no boundaries in the universe. Boundaries are illusions, products not of reality but of the way we map and edit reality. And while it is fine to map out the territory, it is fatal to confuse the two." (Ken Wilber, "No Boundary: Eastern and Western Approaches to Personal Growth", 1979)

"Today abstraction is no longer that of the map, the double, the mirror, or the concept. Simulation is no longer that of a territory, a referential being or substance. It is the generation by models of a real without origin or reality: A hyperreal. The territory no longer precedes the map, nor does it survive it. It is nevertheless the map that precedes the territory - precession of simulacra - that engenders the territory." (Baudrillard Jean, "Simulacra and Simulation", 1981)

"The most promising words ever written on the maps of human knowledge are terra incognita, unknown territory." (Daniel J Boorstin, "The Discoverers: A History of Man's Search to Know His World and Himself", 1983)

"For our purposes, a simple way to understand paradigms is to see them as maps. We all know that ‘the map is not the territory’. A map is simply an explanation of certain aspects of the territory. That’s exactly what a paradigm is. It is a theory, an explanation, or model of something else." (Stephen R Covey, "The 7 Habits of Highly Effective People", 1989)

"Principles are the territory. Values are maps. When we value correct principles, we have truth - a knowledge of things as they are." (Stephen R Covey, "The 7 Habits of Highly Effective People", 1989)

"None of us see the world as it is but as we are, as our frames of reference, or maps, define the territory." (Stephen Covey, "Principle Centered Leadership", 1992)

"Today abstraction is no longer that of the map, the double, the mirror, or the concept. Simulation is no longer that of a territory, a referential being or substance. It is the generation by models of a real without origin or reality: A hyperreal. The territory no longer precedes the map, nor does it survive it. It is nevertheless the map that precedes the territory - precession of simulacra - that engenders the territory." (Jean Baudrillard, "Simulacra and Simulation", 1994)

"Our view of reality is like a map with which to negotiate the terrain of life. If the map is true and accurate, we will generally know how to get there. If the map is false and inaccurate, we generally will be lost." (M Scott Peck, "Wisdom from the Road Less Traveled", 2001)

"One describes a tale best by telling the tale. You see? The way one describes a story, to oneself or the world, is by telling the story. It is a balancing act and it is a dream. The more accurate the map, the more it resembles the territory. The most accurate map possible would be the territory, and thus would be perfectly accurate and perfectly useless. The tale is the map that is the territory." (Neil Gaiman, "Fragile Things", 2006)

"But ignorance exists in the map, not in the territory. If I am ignorant about a phenomenon, that is a fact about my own state of mind, not a fact about the phenomenon itself. A phenomenon can seem mysterious to some particular person. There are no phenomena which are mysterious of themselves. To worship a phenomenon because it seems so wonderfully mysterious, is to worship your own ignorance." (Eliezer Yudkowsky, "Mysterious Answers To Mysterious Questions" 2007)

"It is hard to navigate across one’s environment without having some ideas, however coarse, about it. Indeed, to face any situation we must know whether it is real or imaginary, profane or sacred, sensitive or insensitive to our actions, and so on. This is why even lowly organisms develop, if not worldviews, at least rough sensory maps of their immediate environment – as noted by ethologists from the start. But it is generally assumed that only humans can build conceptual models of their environments. And, except for some philosophers, humans distinguish maps from the territories they represent." (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)

"A map does not just replicate the shape of a territory; rather, it actively inflects and works over that territory." (Steven Shaviro, "Post Cinematic Affect", 2010)

“An all-inclusive model would be like the map in the famous story by Borges - perfect and inclusive because it was identical to the territory it was mapping." (Reuben Hersh, ”Mathematics as an Empirical Phenomenon, Subject to Modeling”, 2017)