"To us […] the only acceptable point of view appears to be the one that recognizes both sides of reality - the quantitative and the qualitative, the physical and the psychical - as compatible with each other, and can embrace them simultaneously […] It would be most satisfactory of all if physis and psyche (i.e., matter and mind) could be seen as complementary aspects of the same reality." (Wolfgang Pauli', "The Influence of Archetypal Ideas on the Scientific Theories of Kepler", [Lecture at the Psychological Club of Zurich], 1948)
"A model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. A model may be pictorial, descriptive, qualitative, or generally approximate in nature; or it may be mathematical and quantitative in nature and reasonably precise. It is important that effective means for modeling be understood such as analog, stochastic, procedural, scheduling, flow chart, schematic, and block diagrams." (Harold Chestnut, "Systems Engineering Tools", 1965)
"As is used in connection with systems engineering, a model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. Modeling is the process of making a model. Although the model may not represent the actual phenomenon in all respects, it does describe the essential inputs, outputs, and internal characteristics, as well as provide an indication of environmental conditions similar to those of actual equipment." (Harold Chestnut, "Systems Engineering Tools", 1965)
"In the long run, qualitative changes always outweigh quantitative ones. Quantitative predictions of economic and social trends are made obsolete by qualitative changes in the rules of the game. Quantitative predictions of technological progress are made obsolete by unpredictable new inventions. I am interested in the long run, the remote future, where quantitative predictions are meaningless. The only certainty in that remote future is that radically new things will be happening." (Freeman J Dyson, "Disturbing the Universe", 1979)
"[…] the meaning of the word 'solve' has undergone a series of major changes. First that word meant 'find a formula'. Then its meaning changed to 'find approximate numbers'. Finally, it has in effect become 'tell me what the solutions look like'. In place of quantitative answers, we seek qualitative ones."
"Quantify. If whatever it is you’re explaining has some measure, some numerical quantity attached to it, you’ll be much better able to discriminate among competing hypotheses. What is vague and qualitative is open to many explanations." (Carl Sagan, "The Demon-Haunted World: Science as a Candle in the Dark", 1995)
"Quantitative knowing is dependent on qualitative knowledge [...] In quantitative data analysis, numbers map onto aspects of reality. Numbers themselves are meaningless unless the data analyst understands the mapping process and the nexus of theory and categorization in which objects under study are conceptualized." John T Behrens, "Principles and Procedures of Exploratory Data Analysis", 1997)
"Modeling, in a general sense, refers to the establishment of a description of a system (a plant, a process, etc.) in mathematical terms, which characterizes the input-output behavior of the underlying system. To describe a physical system […] we have to use a mathematical formula or equation that can represent the system both qualitatively and quantitatively. Such a formulation is a mathematical representation, called a mathematical model, of the physical system." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)
"Reductionism argues that from scientific theories which explain phenomena on one level, explanations for a higher level can be deduced. Reality and our experience can be reduced to a number of indivisible basic elements. Also qualitative properties are possible to reduce to quantitative ones." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"As every bookie knows instinctively, a number such as reliability - a qualitative rather than a quantitative measure - is needed to make the valuation of information practically useful.
"In order to understand how mathematics is applied to understanding of the real world it is convenient to subdivide it into the following three modes of functioning: model, theory, metaphor. A mathematical model describes a certain range of phenomena qualitatively or quantitatively. […] A (mathematical) metaphor, when it aspires to be a cognitive tool, postulates that some complex range of phenomena might be compared to a mathematical construction." (Yuri I Manin," Mathematics as Metaphor: Selected Essays of Yuri I. Manin", 2007)
"Our culture, obsessed with numbers, has given us the idea that what we can measure is more important than what we can't measure. Think about that for a minute. It means that we make quantity more important than quality." (Donella Meadows, "Thinking in Systems: A Primer", 2008)
"A commonly accepted principle of systems dynamics is that a quantitative change, beyond a critical point, results in a qualitative change. Accordingly, a difference in degree may become a difference in kind. This doesn't mean that an increased quantity of a given variable will bring a qualitative change in the variable itself. However, when the state of a system depends on a set of variables, a quantitative change in one variable beyond the inflection point will result in a change of phase in the state of the system. This change is a qualitative one, representing a whole new set of relationships among the variables involved."
"Whether information comes in a quantitative or qualitative flavor is not as important as how you use it. [...] The key to making a good forecast […] is not in limiting yourself to quantitative information. Rather, it’s having a good process for weighing the information appropriately. […] collect as much information as possible, but then be as rigorous and disciplined as possible when analyzing it. [...] Many times, in fact, it is possible to translate qualitative information into quantitative information." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)
"For although it is certainly true that quantitative measurements are of great importance, it is a grave error to suppose that the whole of experimental physics can be brought under this heading. We can start measuring only when we know what to measure: qualitative observation has to precede quantitative measurement, and by making experimental arrangements for quantitative measurements we may even eliminate the possibility of new phenomena appearing." (Heinrich B G Casimir)
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