Can you imagine a 7D hypercube? Me neitherhttps://twitter.com/jezzamonn/status/1149842845735350272 …
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I can imagine a 7D hypercube better than many “ordinary” things in 3D! Can you imagine a tree with 6,342 leaves? I can picture something vaguely like that, but if you ask me for details I’ll contradict myself eventually. But I can tell you anything about a 7D hypercube.
Yes but can you imagine 6,342 7-dimensional leaves? I’m not quite sold that imagining an approximate number of leaves is a relevant analogy for visualizing extra dimensions
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“Visualising extra dimensions” is meaningless if taken literally; we don’t have the visual cortex of 7D beings. But I can still tell you anything about a 7D cube, with a similar mixture of mental imagery and reasoning as I’d apply to a 3D cube.
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Shouldn't we distinguish here between "imagine" as "have a model of" and "imagine" as "visualize". There's no real barrier to understanding >3D objects, but can anyone visualize them without resorting to lower D analogies?
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We should distinguish those things—and what I’m also arguing is that most people need a mixture of model and imagery to deal with all but the simplest, most familiar 3D cases. If you describe a 3D cube with 7 holes drilled in it in 7 places, I’ll struggle more than with a 7-cube.
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