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Video with Transcript: Fibonacci Numbers hidden in the Mandelbrot Set - Numberphile

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0:00 So, today I'm gonna tell you about how the Fibonacci sequence appears in the Mandelbrot set. 0:04 Hopefully, your mind will be blown by the end of that sentence. 0:06 So the Fibonacci sequence, the rule is that you take the previous two numbers, 0:10 and you add them together to get the next. Right? So we started with 1 1. Their sum is 2. 0:15 The next number will be the sum of 1 & 2, which is 3. 0:19 The sum of 2 & 3 is 5. The sum of 3 & 5 is 8. I'll do one more. 0:24 And then, you can continue on. 0:26 Brady: "Easy." 0:27 Easy, right? And this occurs everywhere that has interesting connections to things in nature, and all of that, 0:31 but I just want to show you where it appears on the Mandelbrot set. 0:35 So, slightly less easy. So, the Mandelbrot set is a special object inside of the complex plane. So the plane of complex numbers. And 0:43 the way you cook this thing up is by 0:46 considering a certain type of dynamical system. So if you give me ...
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Heisenberg's Uncertainty Principle Explained

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The video demonstrates Heisenberg's Uncertainty Principle through a laser experiment, explaining how narrowing a slit increases position precision but spreads momentum, showcasing light's wave-particle duality. Detailed Summary for [Heisenberg's Uncertainty Principle Explained]( https://www.youtube.com/watch?v=a8FTr2qMutA ) by [Monica]( https://monica.im )   [00:01](https://www.youtube.com/watch?v=a8FTr2qMutA&t=1.56) This video demonstrates Heisenberg's Uncertainty Principle through a laser experiment, illustrating how narrowing a slit affects the behavior of the light spot on the screen.   - Introduction to the experiment showcasing Heisenberg's Uncertainty Principle.} - Observation of the laser spot's behavior as the slit is narrowed.} - Unexpected result: the spot on the wall widens as the slit narrows.} - Introduction to Heisenberg's Uncertainty Principle and its implications on position and momentum.}        [01:26](https://www.youtube.com/watch?v=...
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Islamic Aesthetics - Prof. Nasr

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Islamic Aesthetics -  Seyyed Hossein Nasr  Work:  Islamic art and spirituality - Islamic art and spirituality : Nasr, Seyyed Hossein : Free Download, Borrow, and Streaming : Internet Archive Introduction   Aesthetics, as a branch of philosophy dealing with beauty and art, was not treated as a separate subject by Islamic philosophers (falāsifa or ḥukamā). Unlike Western philosophers such as Hegel or Croce, Islamic thinkers addressed aesthetics indirectly. To understand Islamic aesthetics, one must examine passages from Peripatetic (mashshā’ī) philosophers, the Illuminationist (ishrāqī) school, and Sufi writings, as well as oral traditions transmitted by masters of Islamic arts.   Peripatetic Philosophers and Aesthetics    Islamic Peripatetic philosophers primarily discussed aesthetics in relation to poetry, often commenting on Aristotle’s Poetics. Key figures include:   - Al-Fārābī: Viewed poetry as "imaginative syllogistic proof by ...
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