Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself… - Freeman Dyson

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Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry? ...It cannot be answered by a definition.

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About Freeman Dyson

Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-born American physicist, mathematician, and futurist, famous for his work in quantum mechanics, nuclear weapons design and policy, and the search for extraterrestrial intelligence. He was the winner of the Templeton Prize in the year 2000.

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Birth Name: Freeman John Dyson
Alternative Names: Freeman J. Dyson
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After sketching his program for the scientific revolution that he foresaw, Bacon ends his account with a prayer: "Humbly we pray that this mind may be steadfast in us, and that through these our hands, and the hands of others to whom thou shalt give the same spirit, thou wilt vouchsafe to endow the human family with new mercies". That is still a good prayer for all of us as we begin the twenty-first century.

I have felt it myself. The glitter of nuclear weapons. It is irresistible if you come to them as a scientist. To feel it's there in your hands, to release this energy that fuels the stars, to let it do your bidding. To perform these miracles, to lift a million tons of rock into the sky. It is something that gives people an illusion of illimitable power, and it is, in some ways, responsible for all our troubles — this, what you might call technical arrogance, that overcomes people when they see what they can do with their minds.

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The information flood has also brought enormous benefits to science. The public has a distorted view of science because children are taught in school that science is a collection of firmly established truths. In fact, science is not a collection of truths. It is a continuing exploration of mysteries. Wherever we go exploring in the world around us, we find mysteries. Our planet is covered by continents and oceans whose origin we cannot explain. Our atmosphere is constantly stirred by poorly understood disturbances that we call weather and climate. The visible matter in the universe is outweighed by a much larger quantity of dark invisible matter that we do not understand at all. The origin of life is a total mystery, and so is the existence of human consciousness. We have no clear idea how the electrical discharges occurring in nerve cells in our brains are connected with our feelings and desires and actions. Even physics, the most exact and most firmly established branch of science, is still full of mysteries. We do not know how much of Shannon’s theory of information will remain valid when quantum devices replace classical electric circuits as the carriers of information. Quantum devices may be made of single atoms or microscopic magnetic circuits. All that we know for sure is that they can theoretically do certain jobs that are beyond the reach of classical devices. Quantum computing is still an unexplored mystery on the frontier of information theory. Science is the sum total of a great multitude of mysteries. It is an unending argument between a great multitude of voices. Science resembles Wikipedia much more than it resembles the Encyclopaedia Britannica.

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