Manifold, units and differential geometry (actually topology)
We are going to see how the definition of tangent vector as derivation does not work in physics and what is that we actually need instead. Intro (0:00) Tangent spaces and units (0:23) Objection! (2:08) Apply the definition (2:46) Unitless derivations are not physically useful (5:13) Units/coordinates are vector spaces (7:28) Manifolds allow for different units/coordinates (12:48) Differentiability and infinitesimal variations (16:27) "Basis" are actually maps (19:13) Tensors are maps between variations (22:29) Closing remarks (23:34)
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The equivalence between geometrical structures and entropy
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The need for Physical Mathematics
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Mastering Differential Geometry with the Covariant Derivative
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What are quantum superpositions, really?
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Geometric interpretation for all potentials (any dimensions!)
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We can't prepare/measure infinity
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Differential Geometry is Impossible Without These 7 Things
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Understanding Parallel Transport & Connections in Differential Geometry
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Why space is three dimensional
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The push forward of vectors on manifolds
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Hamiltonian mechanics in 12 equivalent characterizations
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Why care about differential forms? | Differential forms #1
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Weird Things Happen When Energy Goes Negative
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Manifolds, Tangent Spaces, and Coordinate Basis | Tensor Intuition
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Reinventing Entropy | Compression is Intelligence Part 1
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When Math Isn’t Based in Reality
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The Core of Differential Geometry
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Why does quantum allow superpositions?
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