On Intuition (1980-1989)

“Real progress in understanding nature is rarely incremental. All important advances are sudden intuitions, new principles, new ways of seeing.” (Marilyn Ferguson, “The Aquarian Conspiracy: Personal and Social Transformation in the 1980s”, 1980)

“We are now compelled to accept the fact that there is no such thing as an absolute proof or a universally acceptable proof. We know that, if we question the statements we accept on an intuitive basis, we shall be able to prove them only if we accept others on an intuitive basis.” (Morris Kline, “Mathematics: The loss of certainty”, 1980)

“[…] science must be understood as a social phenomenon, a gutsy, human enterprise, not the work of robots programmed to collect pure information. […] Science, since people must do it, is a socially embedded activity. It progresses by hunch, vision, and intuition.” (Stephen J Gould, “The Mismeasure of Man”, 1980)

“In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort of mathematical intuition to ‘see’ the universe of mathematics and determine by a sort of empirical process what is true. This alone is not enough, of course. Once one has discovered a mathematical truth, one tries to find a proof for it.” (Rudy Rucker, “Infinity and the Mind: The science and philosophy of the infinite”, 1982)

“That is to say, intuition is not a direct perception of something existing externally and eternally. It is the effect in the mind of certain experiences of activity and manipulation of concrete objects (at a later stage, of marks on paper or even mental images).” (Philip J Davis & Reuben Hersh, “The Mathematical Experience”, 1981)

"Analytic thought is based on detailed defined relations between two elements at a time. Intuitive thought is based on an emotional state associated with all the elements in the field of knowledge (overall impression). " (Tony Bastick, “Intuition: How we think and act”, 1982)

"Intuition takes many different forms in science and mathematics, though all forms of it have certain properties in common: the suddenness of their origin, the wholeness of the conception they embody, and the absence of conscious premeditation." (Peter Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

“Intuition can be understood as the mind turning in on itself and apprehending the result of processes that have taken place outside of awareness.” (Philip Goldberg, “The Intuitive Edge”, 1983) 

"It seems that truth is progressive approximation in which the relative fraction of our spontaneously tolerated residual error constantly diminishes." (R Buckminster Fuller, "Humans in Universe", 1983)

 “The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.” (Richard Hamming, “Methods of Mathematics Applied to Calculus, Probability, and Statistics”, 1985)

“The common perception of science as a rational activity, in which one confronts the evidence of fact with an open mind, could not be more false. Facts assume significance only within a pre-existing intellectual structure, which may be based as much on intuition and prejudice as on reason.” (Walter Gratzer, The Guardian, 1989)