On Similarity (1975-1999)

 "Symbol and myth do bring into awareness infantile, archaic dreads and similar primitive psychic content. This is their regressive aspect. But they also bring out new meaning, new forms, and disclose a reality that was literally not present before, a reality that is not merely subjective but has a second pole which is outside ourselves. This is the progressive side of symbol and myth." (Rollo May, "The Courage to Create", 1975)

"In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics." (Stanislaw M Ulam, "Adventures of a Mathematician", 1976)

"All nature is a continuum. The endless complexity of life is organized into patterns which repeat themselves - theme and variations - at each level of system. These similarities and differences are proper concerns for science. From the ceaseless streaming of protoplasm to the many-vectored activities of supranational systems, there are continuous flows through living systems as they maintain their highly organized steady states." (James G Miller, "Living Systems", 1978)

"One should employ a metaphor in science only when there is good evidence that an important similarity or analogy exists between its primary and secondary subjects. One should seek to discover more about the relevant similarities or analogies, always considering the possibility that there are no important similarities or analogies, or alternatively, that there are quite distinct similarities for which distinct terminology should be introduced. One should try to discover what the "essential" features of the similarities or analogies are, and one should try to assimilate one’s account of them to other theoretical work in the same subject area – that is, one should attempt to explicate the metaphor." (Richard Boyd, "Metaphor and Theory Change: What Is ‘Metaphor’ a Metaphor For?", 1979)

"If explaining minds seems harder than explaining songs, we should remember that sometimes enlarging problems makes them simpler! The theory of the roots of equations seemed hard for centuries within its little world of real numbers, but it suddenly seemed simple once Gauss exposed the larger world of so-called complex numbers. Similarly, music should make more sense once seen through listeners' minds." (Marvin Minsky, "Music, Mind, and Meaning", 1981)

"Myths and science fulfill a similar function: they both provide human beings with a representation of the world and of the forces that are supposed to govern it. They both fix the limits of what is considered as possible." (François Jacob, "The Possible and the Actual", 1982)

"Whenever I have talked about mental models, audiences have readily grasped that a layout of concrete objects can be represented by an internal spatial array, that a syllogism can be represented by a model of individuals and identities between them, and that a physical process can be represented by a three-dimensional dynamic model. Many people, however, have been puzzled by the representation of abstract discourse; they cannot understand how terms denoting abstract entities, properties or relations can be similarly encoded, and therefore they argue that these terms can have only 'verbal' or propositional representations." (Philip Johnson-Laird,"Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness", 1983)

"A scientific problem can be illuminated by the discovery of a profound analogy, and a mundane problem can be solved in a similar way." (Philip Johnson-Laird, "The Computer and the Mind", 1988)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"Finite Nature is a hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities. [...] We take the position that Finite Nature implies that the basic substrate of physics operates in a manner similar to the workings of certain specialized computers called cellular automata." (Edward Fredkin, "A New Cosmogony", PhysComp ’92: Proceedings of the Workshop on Physics and Computation, 1993)

"Metaphor plays an essential role in establishing a link between scientific language and the world. Those links are not, however, given once and for all. Theory change, in particular, is accompanied by a change in some of the relevant metaphors and in the corresponding parts of the network of similarities through which terms attach to nature." (Thomas S Kuhn, "Metaphor in science", 1993)

"A fuzzy set can be defined mathematically by assigning to each possible individual in the universe of discourse a value representing its grade of membership in the fuzzy set. This grade corresponds to the degree to which that individual is similar or compatible with the concept represented by the fuzzy set. Thus, individuals may belong in the fuzzy act to a greater or lesser degree as indicated by a larger or smaller membership grade. As already mentioned, these membership grades are very often represented by real-number values ranging in the closed interval between 0 and 1." (George J Klir & Bo Yuan, "Fuzzy Sets and Fuzzy Logic: Theory and Applications", 1995)

"Particular landforms or surface morphologies may be generated, in some cases, by several different processes, sets of environmental controls, or developmental histories. This convergence to similar forms despite variations in processes and controls is called equifinality." (Jonathan Phillips, "Simplexity and the Reinvention of Equifinality", Geographical Analysis Vol. 29 (1), 1997)

"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder."  (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"We do not learn much from looking at a model - we learn more from building the model and manipulating it. Just as one needs to use or observe the use of a hammer in order to really understand its function, similarly, models have to be used before they will give up their secrets. In this sense, they have the quality of a technology - the power of the model only becomes apparent in the context of its use." (Margaret Morrison & Mary S Morgan, "Models as mediating instruments", 1999)