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Quote by Euclid

“A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.”

Quote by Euclid

Book:Euclid's Elements
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Euclid's Elements

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Euclid
Euclid

Euclid (435 BC - 365 BC), one of the most famous Greek mathematicians, is known as the 'Father of Geometry'. His work, 'Elements', is one of the most influential mathematical treatises in history, profoundly affecting the development of mathematics. more

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ScienceWorkTravelMathematicsMathGeometryEuclidEuclidean GeometryFuchsian FunctionsGeological
Author:Henri Poincaré
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“There have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely the whole of existence, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidean earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions.”

GodEuclidean GeometryThe Limitedness Of Human Mind
Book:The Brothers Karamazov
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“INTROSPECTION AND INSANITY: A GODELIAN PROBLEM I think it can have suggestive value to translate Godel's Theorem into other domains, provided one specifies in advance that the translations are metaphorical and are not intended to be taken literally. That having been said, I see two major ways of using analogies to connect Godel's Theorem and human thoughts. One involves the problem of wondering about one's sanity. How can you figure out if you are sane? This is a Strange Loop indeed. Once you begin to question your own sanity, you can get trapped in an ever-tighter vortex of self-fulfilling prophecies, though the process is by no means inevitable. Everyone knows that the insane interpret the world via their own peculiarly consistent logic; how can you tell if your own logic is 'peculiar' or not, given that you have only your own logic to judge itself? I don't see any answer. I am just reminded of Godel's second Theorem, which implies that the only versions of formal number theory which assert their own consistency are inconsistent...”

ConsciousnessMental HealthMathAiSanityTheorems
Author:Douglas Hofstadter
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