Episode list

PBS Infinite Series

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Stochastic Supertasks
Wed, Aug 09, 2017
  • SUnknown
  • Stochastic Supertasks
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A Breakthrough in Higher Dimensional Spheres
Hyperspheres are spheres of more than three dimensions. A natural thing to do with sphere is to find the best way to stack them. Seems easy but it took a couple hundred years before Thomas Hale prove our natural why of stacking oranges is the best. And only recently (2016) was the best way to pack eight and twenty-four dimensional spheres proven. All the other dimensions are still unknown. And that's just the start of the counter-intuitive feature of hyperspheres.
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A Hierarchy of Infinities
Infinities is counter intuitive, even to mathematicians. Rules about infinity tend to resist proof so mathematicians have settles for some conventions. And they have come to the conclusion that infinity comes in different sizes. And the counting number are a smaller number than the real numbers.
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