Video Infoblog: The Most Important Sequence: The Catalan Numbers

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Video: The Mystery of 137 - Exploring a Most Illuminating Number

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Transcript Intro 0:01 hi everyone michael smith here 0:04 as a numerologist and former engineer 0:06 and stats guy i've always been 0:08 fascinated by number patterns especially 0:10 when the same pattern or number pops up 0:12 in many different places 0:14 one such number is 137 0:17 although it shows up in key places in 0:19 math physics chemistry and other natural 0:21 phenomena y has remained a mystery 0:24 in this video we're going to explore 0:26 this curious number from various angles 0:28 to see if we can shed some light on that 0:30 mystery Curious Appearances of 137 0:33 here are some of the better known 0:34 examples of where 137 shows up to give 0:37 you an idea of why it's considered so 0:39 intriguing 0:40 first and foremost the number 137 0:42 appears in one of the most important 0:44 universal constants of nature 0:46 what's called the fine structure 0:47 constant 0:48 with a value very close to 1 over 137 0:52 this number quantifies the strength of 0:54...
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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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Rudiments of the Cosmic Story

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This question is important only because it reintroduces a different way of thinking about the universe: How can the universe be at least 46 billion light years across but only 14 billion years old? Size is an illusion. The universe only shows the appearance of growing larger faster than it should. In reality, it is the beautiful shape which is maintained. The above picture in principle shows a two dimensional shaped self similar spiral as viewed from the top or plan view and not a manifested three dimensional sphere. Do focus on realm of principles, which is immutable, and not the realm appearances, which is misleading. The universe is about shape maintenance for the sake of beauty. Why? Because it is the conjugate of the Immutable. The universe appears - must appear - fresh and beautiful always. The spiral in question is a logarithmic spiral which also means that it is indelibly and intimately associated with mathematical indices. Briefly, A^0=1 for any A holds true always. This is th...
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