"[…] as a model of a complex system becomes more complete, it becomes less understandable. Alternatively, as a model grows more realistic, it also becomes just as difficult to understand as the real world processes it represents." (Jay M Dutton & William H Starbuck," Computer simulation models of human behavior: A history of an intellectual technology", IEEE Transactions on Systems, 1971)
"Models are to be used, but not to be believed." (Henri Theil, "Principles of Econometrics", 1971)
"Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework." (Melvin Schwartz, "Principles of Electrodynamics", 1972)
"Nature is a network of happenings that do not unroll like a red carpet into time, but are intertwined between every part of the world; and we are among those parts. In this nexus, we cannot reach certainty because it is not there to be reached; it goes with the wrong model, and the certain answers ironically are the wrong answers. Certainty is a demand that is made by philosophers who contemplate the world from outside; and scientific knowledge is knowledge for action, not contemplation. There is no God’s eye view of nature, in relativity, or in any science: only a man’s eye view." (Jacob Bronowski, "The Identity of Man", 1972)
"A theory has only the alternative of being right or wrong. A model has a third possibility: it may be right, but irrelevant." (Manfred Eigen, 1973)
"Models are models of something, namely, [they are] reflections, representations of natural and artificial originals, that can themselves be models again. […] Models, in general, do not cover all the attributes of the originals they are representing, but only those [attributes] that seem relevant to the actual model creators and/or model users." (Herbert Stachowiak, "Allgemeine Modelltheorie", 1973)
"Models are not assigned per se uniquely to their originals. They perform their replacement function: a) for definite – cognitive and/or handling, model-using – subjects, b) within definite time intervals, c) under restrictions of definite operations of thought or fact. […] Models are not only models of something. They are also models for somebody, a human or an artificial model user. They perform thereby their functions in time, within a time interval. And finally, they are models for a definite purpose." (Herbert Stachowiak, "Allgemeine Modelltheorie", 1973)
"One aim of the physical sciences has been to give an exact picture of the material world. One achievement of physics in the twentieth century has been to prove that that aim is unattainable." (Jacob Bronowski, "The Ascent of Man", 1973)
"The pre-eminence of astronomy rests on the peculiarity that it can be treated mathematically; and the progress of physics, and most recently biology, has hinged equally on finding formulations of their laws that can be displayed as mathematical models." (Jacob Bronowski, "The Ascent of Man", 1973)
"The model of an object, process or phenomenon is some other object, process or phenomenon having certain features in common with the original. It is ordinarily assumed that the model is a simplified version of the object of study. However, it is not always easy to give precise meaning to the concept 'simpler than the original', for the simple reason that in reality all entities or phenomena are infinitely complicated and their study can be carried out with differing and constantly increasing degrees of accuracy."
"A model is an abstract description of the real world. It is a simple representation of more complex forms, processes and functions of physical phenomena and ideas." (Moshe F Rubinstein & Iris R Firstenberg, "Patterns of Problem Solving", 1975)
"A model is an attempt to represent some segment of reality and explain, in a simplified manner, the way the segment operates." (E Frank Harrison, "The managerial decision-making process" , 1975)
"A model is an abstract description of the real world. It is a simple representation of more complex forms, processes and functions of physical phenomena and ideas." (Moshe F Rubinstein & Iris R Firstenberg, "Patterns of Problem Solving", 1975)
"A model is an attempt to represent some segment of reality and explain, in a simplified manner, the way the segment operates." (E Frank Harrison, "The managerial decision-making process" , 1975)
"The hard thing in a model realization is to receive and often to construct necessary data which in many cases have considerable errors and sometimes are completely absent, since none needed them previously. Difficulties of principle lie in the future prediction data and in the estimation of industry development variants." (Leonid V Kantorovich, "Mathematics in Economics: Achievements, Difficulties, Perspectives", [Nobel lecture] 1975)
"The value of a model lies in its substitutability for the real system for achieving an intended purpose." (David I Cleland & William R King, "Systems analysis and project management" , 1975)
"The value of a model lies in its substitutability for the real system for achieving an intended purpose." (David I Cleland & William R King, "Systems analysis and project management" , 1975)
"Real-life phenomena are generally so complicated in relation to the mathematical methods at our disposal that we cannot hope to represent and account for their every characteristic. Consequently, some simplifying hypotheses must be made. The moment that we do this, we are leaving the real world and beginning to make a (mathematical) model." (Peter Lancaster, "Mathematics: Models of the Real World", 1976)
"Since all models are wrong the scientist cannot obtain a ‘correct’ one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity." (George Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"The aim of the model is of course not to reproduce reality in all its complexity. It is rather to capture in a vivid, often formal, way what is essential to understanding some aspect of its structure or behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)
"A model of the universe does not require faith, but a telescope. If it is wrong, it is wrong." (Paul C W Davies, "Space and Time in the Modern Universe", 1977)
"The model of the natural world we build in our minds by such a process will forever be inadequate, just a little cathedral in the mountains. Still it is better than no model at all." (Timothy Ferris, "The Red Limit", 1977)
"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model." (Rutherford Aris, "Mathematical Modelling", 1978)
"A model […] is a story with a specified structure: to explain this catch phrase is to explain what a model is. The structure is given by the logical and mathematical form of a set of postulates, the assumptions of the model. The structure forms an uninterpreted system, in much the way the postulates of a pure geometry are now commonly regarded as doing. The theorems that follow from the postulates tell us things about the structure that may not be apparent from an examination of the postulates alone." (Allan Gibbard & Hal R. Varian, "Economic Models", The Journal of Philosophy, Vol. 75, No. 11, 1978)
"Here is one way to look at physics: the physicists are men looking for new interpretations of the Book of Nature. After each pedestrian period of normal science, they dream up a new model, a new picture, a new vocabulary, and then they announce that the true meaning of the Book has been discovered." (Richard Rorty, "Philosophy as a Kind of Writing", 1978)
"Ideas that require people to reorganize their picture of the world provoke hostility." (James Gleick, "Chaos: Making a New Science" , 1987)
"One of the most insidious and nefarious properties of scientific models is their tendency to take over, and sometimes supplant, reality." (Erwin Chargaff, "Heraclitean Fire: Sketches from a Life Before Nature", 1978)
"Since all models are wrong the scientist cannot obtain a ‘correct’ one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity." (George Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)
"The aim of the model is of course not to reproduce reality in all its complexity. It is rather to capture in a vivid, often formal, way what is essential to understanding some aspect of its structure or behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)
"A model of the universe does not require faith, but a telescope. If it is wrong, it is wrong." (Paul C W Davies, "Space and Time in the Modern Universe", 1977)
"The model of the natural world we build in our minds by such a process will forever be inadequate, just a little cathedral in the mountains. Still it is better than no model at all." (Timothy Ferris, "The Red Limit", 1977)
"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model." (Rutherford Aris, "Mathematical Modelling", 1978)
"A model […] is a story with a specified structure: to explain this catch phrase is to explain what a model is. The structure is given by the logical and mathematical form of a set of postulates, the assumptions of the model. The structure forms an uninterpreted system, in much the way the postulates of a pure geometry are now commonly regarded as doing. The theorems that follow from the postulates tell us things about the structure that may not be apparent from an examination of the postulates alone." (Allan Gibbard & Hal R. Varian, "Economic Models", The Journal of Philosophy, Vol. 75, No. 11, 1978)
"Here is one way to look at physics: the physicists are men looking for new interpretations of the Book of Nature. After each pedestrian period of normal science, they dream up a new model, a new picture, a new vocabulary, and then they announce that the true meaning of the Book has been discovered." (Richard Rorty, "Philosophy as a Kind of Writing", 1978)
"Ideas that require people to reorganize their picture of the world provoke hostility." (James Gleick, "Chaos: Making a New Science" , 1987)
"One of the most insidious and nefarious properties of scientific models is their tendency to take over, and sometimes supplant, reality." (Erwin Chargaff, "Heraclitean Fire: Sketches from a Life Before Nature", 1978)
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