Quotable Mathematics

 "Diagrams are of great utility for illustrating certain questions of vital statistics by conveying ideas on the subject through the ey...

"A diagram is a representamen [representation] which is predominantly an icon of relations and is aided to be so by conventions. Indice...

"[…] deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of ...

"Why do people use mental models? First, they are used as inference tools to predict the behavior of a system under novel conditions. T...

"[...] for merely theoretical purposes the rule of formation would be very simple. It would merely be to begin by drawing any closed fi...

"The materialistic point of view in psychology can claim, at best, only the value of an heuristic hypothesis." (Wilhelm Wundt, ...

"The study of theory must go hand in hand with that of facts: and for dealing with most modern problems it is modern facts that are of ...

"This is the greatest degree of impoverishment; the [mental] image, deprived little by little of its own characteristics, is nothing mo...

"In comparison with Predicate Calculus encoding s of factual knowledge, semantic nets seem more natural and understandable. This is due...

"Judged by the only standards which are admissible in a pure doctrine of numbers i is imaginary in the same sense as the negative, the ...

"Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, co...

"[…] mathematics is not just a symbolism, a set of conventions for the use of special, formal vocabularies, but is intimately connected...

"When a person has learned a symbolic system well enough to use it, she has established a portable self-contained world within the mind...

"Precision is greatly enhanced by the human capacity to symbolize. Symbols can be devised to stand for mathematical ideas, entities, op...

"It hath been an old remark, that Geometry is an excellent Logic. And it must be owned that when the definitions are clear; when the po...

"The preliminary examination of most data is facilitated by the use of diagrams. Diagrams prove nothing, but bring outstanding features...

"Any pattern of activity in a network, regarded as consistent by some observer, is a system, Certain groups of observers, who share a c...

"We form in the imagination some sort of diagrammatic, that is, iconic, representation of the facts, as skeletonized as possible. The i...