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“Propongo che si misuri il valore di una nazione in base alla sua creatività, alla produzione di nuove idee scientifiche, artistiche, tecnologiche o sociali, non in termini di denaro."...
"Le nazioni muoiono quando diventano rigide e inflessibili, quando la loro burocrazia domina tutto e ristagnano, quando hanno un'opinione troppo alta di loro stesse."
Gregory Chaitin in Darwin Alla Prova.”
― Proving Darwin: Making Biology Mathematical
"Le nazioni muoiono quando diventano rigide e inflessibili, quando la loro burocrazia domina tutto e ristagnano, quando hanno un'opinione troppo alta di loro stesse."
Gregory Chaitin in Darwin Alla Prova.”
― Proving Darwin: Making Biology Mathematical
“According to Pythagoras everything is number, and God is a mathematician. This point of view has worked pretty well throughout the development of modern science. However now a neo-Pythagorian doctrine is emerging, according to which everything is 0/1 bits, and the world is built entirely out of digital information. In other words, now everything is software, God is a computer programmer, not a mathematician, and the world is a giant information-processing system, a giant computer.”
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“Formal languages avoid the paradoxes by removing the ambiguities of natural languages. The paradoxes are eliminated, but there is a price. Paradoxical natural languages are evolving open systems. Artificial languages are static closed systems subject to limitative meta-theorems. You avoid the paradoxes, but you are left with a corpse!”
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“The halting problem is a theoretical question. It is not a practical question. The world of mathematics is a toy world where we ask fantasy questions, which is why we have nice theories that give nice answers. The real world is messy and complicated. The reason you can use reasoning and prove things in pure mathematics is because it's a toy world, it's much simpler than the real world.”
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“No mechanical process (rules of the game) can be really creative because in a sense anything that comes out was already contained in your starting point. Does this mean that physical randomness, something non mechanical, is the only possible source of creativity?! At least from this (enormously over-simplified!) point of view, it is.”
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