Robert M Axelrod - Collected Quotes

"A cognitive map has only two basic types of elements: concepts and causal beliefs. The concepts are treated as variables, and the causal beliefs are treated as relationships between the variables." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A cognitive map is a particular kind of mathematical model of a person's belief system; in actual practice, cognitive maps are derived from assertions of beliefs. [...] Like all mathematical models, a cognitive map can be useful in two quite distinct ways: as a normative model and as an empirical model. Interpreted as a normative model, a cognitive map makes no claims to reflect accurately how a person deduces new beliefs from old ones, how he makes decisions, and so on, but instead claims to show how he should do these things. Interpreted as an empirical model, a cognitive map claims to indicate how a person actually does perform certain cognitive operations, in the sense that the results of the various operations that are possible with the model do, in fact, correspond to the behavior of the per son who is being modeled." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"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)

"A cognitive map is designed to capture the structure of the causal assertions of a person with respect to a particular policy domain, and generate the consequences that follow from this structure." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A decision maker must simplify the manifest complexities of the external world. He must be able to construct a manageable representation of the external world so that he can describe and cope with his environment. The use of this representation for the purposes of making reasoned decisions requires some beliefs that link possible choices with potential outcomes." (Robert M Axelrod, "Decision for Neoimperialism: The Deliberations of the British Eastern Committee in 1918", 1976)

"A mathematical model is a tremendous simplification of what it represents. But it does not simplify everything about its object, or there would be nothing left to model. Instead, it simplifies everything that is not to be examined, and leaves in the model what is to be examined." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"Cognitive mapping is one specific approach to belief systems. It focuses on causal beliefs and values and their structural relationships. Cognitive mapping is, therefore especially suitable to the study of the means-ends arguments people use when they try to evaluate the policy alternatives that they perceive are available to them." (Robert 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)

"What cognitive mapping offers is a systematic way to proceed in our search for understanding how others will act. Its real strength (especially as compared to other formal approaches to decision making) is that it is able to employ the concepts of the decision maker who is being predicted, rather than the concepts of the person who is doing the predicting." (Robert Axelrod, "Structure of Decision: The Cognitive Maps of Political Elites", 1976)

"What difference does it make which cognitive map a person has on a policy issue? Why would we want to know about a person's cognitive map? There are two broad answers to these questions. The first is that we want to know about cognitive maps so that we can better understand the decision-making process. The second is that we want to know about cognitive maps so that we can improve the decision-making process." (Robert Axelrod, "Structure of Decision: The Cognitive Maps of Political Elites", 1976)

On Models: On Mathematical Models (1980-1989)

"Mathematical model making is an art. If the model is too small, a great deal of analysis and numerical solution can be done, but the results, in general, can be meaningless. If the model is too large, neither analysis nor numerical solution can be carried out, the interpretation of the results is in any case very difficult, and there is great difficulty in obtaining the numerical values of the parameters needed for numerical results." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

“Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law.” (Edward O Wilson, “Biophilia”, 1984)

"The large-scale computer models of systems ecology do not fit under the heading of holism at all. Rather they are forms of large-scale reductionism: the objects of study are the naively given 'parts' -abundances or biomasses of populations. No new objects of study arise at the community level. The research is usually conducted on a single system - a lake, forest, or prairie - and the results are measurements of and projections for that lake, forest, or prairie, with no attempts to find the properties of lakes, forests, or prairies in general. Such modeling requires vast amounts of data for its simulations, and much of the scientific effort goes into problems of estimation." (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"Symmetries abound in nature, in technology, and - especially - in the simplified mathematical models we study so assiduously. Symmetries complicate things and simplify them. They complicate them by introducing exceptional types of behavior, increasing the number of variables involved, and making vanish things that usually do not vanish. They simplify them by introducing exceptional types of behavior, increasing the number of variables involved, and making vanish things that usually do not vanish. They violate all the hypotheses of our favorite theorems, yet lead to natural generalizations of those theorems. It is now standard to study the 'generic' behavior of dynamical systems. Symmetry is not generic. The answer is to work within the world of symmetric systems and to examine a suitably restricted idea of genericity." (Ian Stewart, "Bifurcation with symmetry", 1988)

“The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?” (Stephen Hawking, "A Brief History of Time", 1988)