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Thinking outside the 10-dimensional box

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Further reading 1

What does a matrix do, and which outputs can disappear? →Read a column as an arrow, then a matrix as an action on that arrow. Solving an equation becomes a question about reachable targets, giving collapse, eigenvectors and rotations a geometric interpretation.This video helps answer · Which distance survives when the higher-dimensional picture fails?

Caption notes

With centers at coordinates ±1, the corner distance grows as √d while the nearest outer face stays two units away. In ten dimensions the central sphere tangent to the corner spheres can extend past that outer box.

Video or transcript source ↗
Original passages · 2
the radius of the inner circle is square root of 2 minus 1
Thinking outside the 10-dimensional box · ▶ 9:58–10:10
the face of the box is always two units away from the origin
Thinking outside the 10-dimensional box · ▶ 21:50–21:59

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