Post AiORPD0TtZI84eGpyi by interfluidity@zirk.us
(DIR) More posts by interfluidity@zirk.us
(DIR) Post #AiOOnUcjkP1Zne3J0i by interfluidity@zirk.us
2024-05-29T19:06:08Z
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one requires a universe of infinite dimension so there is always an orthogonal direction to retreat to.
(DIR) Post #AiOREgjx0Uf56ZWQgy by sqrtminusone@emacs.ch
2024-05-29T19:33:26Z
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@interfluidity Wouldn't two suffice? For any given non-zero vector v = (v_x, v_y), there's already one linearly independent vector orthogonal to it: u = (-v_y, v_x)v \dot u = 0
(DIR) Post #AiORPD0TtZI84eGpyi by interfluidity@zirk.us
2024-05-29T19:35:21Z
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@sqrtminusone when i retreat, i don’t want to share the same plane (or hyperplane) with what i am retreating from.
(DIR) Post #AiOSMNzcgzf1ET5SWe by sqrtminusone@emacs.ch
2024-05-29T19:45:58Z
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@interfluidity Then, unless you idea about (hyper-)plane refers to something other than a subspace that has at least one less dimension than the ambient space, three will work.Otherwise your hyperplane is identical to the space, and why wouldn't the same process that made it so keep it so after you've invented a new dimension to retreat?
(DIR) Post #AiOTtu8EK1IIQ4ex7Y by interfluidity@zirk.us
2024-05-29T20:03:19Z
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@sqrtminusone that’s why i need infinity. the whole space gets crowded, polluted. only fleeing somewhere orthogonal to everything will suffice.
(DIR) Post #AiOVSaNjqLEHFw0yTA by scheidegger@mastodon.social
2024-05-29T20:20:45Z
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@interfluidity I’ve always thought it was a Deep Thing about linear algebra that infinite dimensional linear operators don’t always admit eigenvectors. The typical example is the shift operator, and it does precisely this: it “creates a new dimension” a la Hilbert Hotel that is in the orthogonal complement of its range, so you can’t find a “fixed point”
(DIR) Post #AiOZczjeplA0bKUCPI by admitsWrongIfProven@qoto.org
2024-05-29T21:07:28Z
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@interfluidity @sqrtminusone Why infinity? You can have the same thing if you have <thing you are retreating from> + 1 dimensions at your disposal. With that, dimensions are bounded by how often you have to retreat in your lifetime + 1, assuming the next thing does not start out with a higher amount than you.
(DIR) Post #AiOZhUnBJ6kw53HS8O by admitsWrongIfProven@qoto.org
2024-05-29T21:08:18Z
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@interfluidity @sqrtminusone Why infinity? You can have the same thing if you have <thing you are retreating from> + 1 dimensions at your disposal. With that, dimensions are bounded by how often you have to retreat in your lifetime + 1, assuming the next thing does not start out with a higher amount than you. Think with some efficiency in mind! O notation is a privilege!
(DIR) Post #AiPE92UC8fvwZ65WuO by interfluidity@zirk.us
2024-05-30T04:41:27Z
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@the_roamer i just often feel this way …