The solution to the Twins Paradox lies in considering the possibility that Curt and Rod were not alone in the womb.
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There’s a rough solution to the “leaky bucket” problem but an exact solution requires some use of fluid dynamics. And the Moon, surprisingly, changes nothing.
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While Gödel’s technique was unheard of in his day, we are very familiar with it today. It is the same technique that computers use to store information.
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These puzzles, associated with the great mathematician Leonard Euler (1707‒1783), have a practical use, for example, in laying water pipes.
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The comparison doesn’t really work but it underlines the *doctrine* that human intelligence is just another type of animal intelligence.
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This classic puzzle in simple graph theory resulted in a commonly used phrase. Can you guess it?
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To solve this Micro Softy, you need to pinpoint the flaw in the logic that hinges on the Law of Conservation of Money.
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Micro Softy 7 is an illustration of Simpson’s Paradox, which says that averaging averages doesn’t always work.
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And here’s the answer to why young Clay’s arithmetic didn’t make sense at first to Claude — but then Claude realized that the boy was right.
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Maybe we need to believe that there is a Mind behind the universe in order to provide guardrails against deeply crazy stuff claiming to be science.
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And here’s the answer to the probability question: What are the chances that Claude and Chloe’s younger child is also a boy?
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A controversy about whether we need language to think pits two MIT scholars against each other: Noam Chomsky (yes) vs. Evelina Fedorenko (no). For a long time, it was only a philosophical issue: Plato saw thinking as a conversation with oneself. If you don’t form concepts into words are you really thinking? Chomsky agreed. But later, neuroscientists like Fedorenko got involved, offering some research findings. Last summer at the New York Times, science writer Carl Zimmer reported, When Dr. Fedorenko began this work in 2009, studies had found that the same brain regions required for language were also active when people reasoned or carried out arithmetic. But Dr. Fedorenko and other researchers discovered that this overlap was a mirage. Part Read More ›
If we want to play around with infinity concepts, we can have fun. But we can’t use them to decide what might or might not happen in our finite universe.
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For example, the baseball player with the highest batting average in any season generally does not do as well the season before or the season after.
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The “strange loop” of life — a loop with no apparent beginning in non-life — was, Robert Rosen concluded, beyond the reach of computing.
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“Evolution” theories about the human mind play a key role in the manufacture of non-knowledge posing as knowledge, and we are urged to treat them as knowledge.
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The limitations created by the nature of computing mean that a mathematician’s true job of discovering novel theorems is quite safe at present.
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Mathematics underlies our entire universe at its most basic level. Correct answers conform to reality. The war on 2 + 2 = 4 is just plain doomed.
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Gödel saw the beauty of numbers and associated them with a transcendent order.
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Chaitin is best known in the math world discovering the remarkable Omega number, which demonstrated the fundamental unknowability of math.
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