"[...] the task of the theory consists in constructing a picture of the external world that exists purely internally and must be our guiding star in all thought and experiment; that is in completing, as it were, the thinking process and carrying out globally what on a small scale occurs within us whenever we form an idea.” (Ludwig E Boltzmann, “On the Significance of Theories”, 1890)
"If the organism carries a ‘small-scale model’ of external reality and of its possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future simulations before they arise, utilize the knowledge of past events in dealing with the present and the future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it." (Kenneth Craik, "The Nature of Explanation", 1943)
"Thus there are instances of symbolisation in nature; we use such instances as an aid to thinking; there is evidence of similar mechanisms at work in our own sensory and central nervous systems; and the function of such symbolisation is plain. If the organism carries a ’small-scale model’ of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise […]" (Kenneth Craik, "The Nature of Explanation", 1943)
"[…] the intrinsic value of a small-scale model is that it compensates for the renunciation of sensible dimensions by the acquisition of intelligible dimensions." (Claude Levi- Strauss,"The Savage Mind", 1962
"The word model is used as a noun, adjective, and verb, and in each instance it has a slightly different connotation. As a noun 'model' is a representation in the sense in which an architect constructs a small-scale model of a building or a physicist a large-scale model of an atom. As an adjective 'model' implies a degree or perfection or idealization, as in reference to a model home, a model student, or a model husband. As a verb 'to model' means to demonstrate, to reveal, to show what a thing is like." (Russell L Ackoff, "Scientific method: optimizing applied research decisions", 1962)
"In general a small-scale test or experiment will not detect a small effect, or small differences among various products." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)
"The evident power of simple heuristics […] teaches us the important lesson that global behavior patterns, and social organization, can emerge out of local interactions. Organisms do not necessarily need to have an over-riding plan nor do they require awareness of the large-scale. Grand patterns and processes can emerge as the nett effect of small-scale, local behavior."(David G Green, 2000)
"The self-similarity on different scales arises because growth often involves iteration of simple, discrete processes (e.g. branching). These repetitive processes can often be summarized as sets of simple rules." (David G Green, 2000)
"According to mental model theory, human reasoning relies on the construction of integrated mental representations of the information that is given in the reasoning problem's premises. These integrated representations are the mental models. A mental model is a mental representation that captures what is common to all the different ways in which the premises can be interpreted. It represents in 'small scale' how "reality" could be— according to what is stated in the premises of a reasoning problem. Mental models, though, must not be confused with images. A mental model often forms the basis of one or more visual images, but some of them represent situations that cannot be visualized. Instead, mental models are often likened to diagrams since, as with diagrams, their structure is analogous to the structure of the states of affairs they represent." (Carsten Held et al, "Mental Models and the Mind", 2006)
"Physics deals with both the large and the small. Its domain of study includes the interior of the nucleus of an atom as well as the exterior of a galaxy. It is, therefore, natural for the scope of physical theories to switch between global, or large-scale, and local, or small-scale regimes. Such an interplay between the local and the global has existed ever since Newton and others discovered the mathematical translation of this interplay: Derivatives are defined as local objects while integrals encompass global properties." (Sadri Hassani, "Mathematical Methods: For Students of Physics and Related Fields", 2009)
"[…] there’s atomic physics - electrons and protons and neutrons, all the stuff of which atoms are made. At these very, very, very small scales, the laws of physics are much the same, but there is also a force you ignore, which is the gravitational force. Gravity is present everywhere because it comes from the entire mass of the universe. It doesn’t cancel itself out, it doesn’t have positive or negative value, it all adds up." (Michael F Atiyah, [interview] 2013)
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