"As knowledge proceeds with spiraling movement to penetrate the vast universe of black mystery, one is continually astonished to discover that at the outer limit of awareness where science interfaces with the unknown, there is nothing but a growing edge, where knowledge and ignorance meet. The more one learns, the more one discovers the increasing magnitude of the unknown, as anyone who has tried to do “exhaustive” research knows very well!" (June Singer, "Androgyny: Toward a New Theory of Sexuality", 1976)
"Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does." (Louis J Mordell [quoted by Howard Eves, "Mathematical Circles Adieu", 1977])
"The catalogue of our ignorance has two, not one, gates: there is the obvious exit gate, through which questions answered and settled by experimental and theoretical developments march out and disappear into the textbooks and the applications; but there is also a more important, albeit less perspicuous, entrance gate, through which new riddles come to life in the scientifi c world." (Bruno Bertotti, "The Encyclopaedia of Ignorance: Everything You Ever Wanted to Know About the Unknown", 1977)
"The larger the sphere of our knowledge, the greater its contact with the infi nity of our ignorance." (Arthur Berry, "A Short History of Astronomy", Vol. 83 (1), 1978)
"The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature." (Lewis Thomas, "The Medusa and the Snail: More Notes of a Biology Watcher", 1979)
"One can only conclude that some creationists, recoiling from the fearsome prospect of time’s abyss, have toppled backward into the abyss of ignorance." (Albritton Claude Jr., "The Abyss of Time: Changing Conceptions of the Earth’s Antiquity after the Sixteenth Century ", 1980)
"The difference between myth and science is the difference between divine inspiration of “unaided reason” (as Bertrand Russell put it) on the one hand and theories developed in observational contact with the real world on the other. It is the difference between the belief in prophets and critical thinking, between Credo quia absurdum (I believe because it is absurd–Tertullian) and De omnibus est dubitandum (Everything should be questioned–Descartes). To try to write a grand cosmical drama leads necessarily to myth. To try to let knowledge substitute ignorance in increasingly large regions of space and time is science." (Hannes Alfvén, "Cosmology: Myth or Science?", Journal of Astrophysics and Astronomy, 1984)
"Consider the unlearned, unaware of their ignorance, who think they know everything! As knowledge increases, ignorance decreases, but this kind of ignorance - unlearned ignorance - is no more than the lack of knowledge. With knowledge comes awareness of ignorance - learned ignorance - and the more we know, the more aware we become of what we do not know." (Edward R Harrison, "Masks of the Universe", 1985)
"The attitudes of mathematicians can be found not only in what they wrote, but in what they did not write. It is possible to divide mathematicians into those who gave complex numbers some kind of coverage, and those who sometimes or always ignored them." (Diana Willment, "Complex Numbers from 1600 to 1840" [Masters thesis], 1985)
"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." (James Gleick, "Chaos", 1987)
"It is our responsibility as scientists, knowing the great progress which comes from a satisfactory philosophy of ignorance, the great progress which is the fruit of freedom of thought, to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations." (Richard P (Feynman, "What Do You Care What Other People Think?", 1988)
"Illiteracy and innumeracy are social ills created in part by increased demand for words and numbers. As printing brought words to the masses and made literacy a prerequisite for productive life, so now computing has made numeracy an essential feature of today's society. But it is innumeracy, not numeracy, that dominates the headlines: ignorance of basic quantitative tools is endemic […] and is approaching epidemic levels […]." (Lynn A Steen, "Numeracy", Daedalus Vol. 119 No. 2, 1990)
"Ignorance of science and technology is becoming the ultimate self-indulgent luxury." (Jeremy Bernstein, "Cranks, Quarks, and the Cosmos: Writings on Science", 1993)
"The art of science is knowing which observations to ignore and which are the key to the puzzle." (Edward W Kolb, "Blind Watchers of the Sky", 1996)
"Whether our cosmological view of the universe is right or wrong, or just incomplete, we were brave enough to confront our ignorance and look. We looked with all our might, and with boldness and imagination managed to see a little bit farther than our predecessors. We were not proud of our blindness, but neither were we ashamed of it or intimidated by it, for we chose to look for the light of truth fully cognizant of our blindness. " (Edward W Kolb, "Blind Watchers of the Sky", 1996)
"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?" (Deborah J Bennett, "Randomness", 1998)
"There is no over-arching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something really is complex, it cannot by adequately described by means of a simple theory. Engaging with complexity entails engaging with specific complex systems. Despite this we can, at a very basic level, make general remarks concerning the conditions for complex behaviour and the dynamics of complex systems. Furthermore, I suggest that complex systems can be modelled." (Paul Cilliers, "Complexity and Postmodernism", 1998)
"When the scientist tells you he does not know the answer, he is an ignorant man. When he tells you he has a hunch about how it is going to work, he is uncertain about it. When he is pretty sure of how it is going to work, and he tells you, 'This is the way it is going to work, I’ll bet', he still is in some doubt. And it is of paramount importance, in order to make progress, that we recognize this ignorance and this doubt. Because we have the doubt, we then propose looking in new directions for new ideas. The rate of development in science is not the rate at which you make observations alone but, much more important, the rate at which you create new things to test." (Richard P Feynman, "The Meaning of It All: Thoughts of a Citizen Scientist", 1998)
"Events may appear to us to be random, but this could be attributed to human ignorance about the details of the processes involved." (Brain S Everitt, "Chance Rules", 1999)
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