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Exotic spheres, or why 4-dimensional space is a crazy place | plus.maths.org

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The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like? Or might it even be true, as some have suggested, that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square? Just as a 3-dimensional object can be projected onto a 2-dimensional plane, so a 4-dimensional object can be projected onto 3-dimensional space. This image comes from the projection of a 4-dimensional hypersphere. The curves are the projections of the hypersphere's parallels (red), meridians (blue) and so-called hypermeridians (green). Image by Claudio Rocchini, via Wikimedia Commons. According to the early 20th century horror writer H.P. Lovecraf

The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like? Or might it even be true, as some have suggested, that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square? Just as a 3-dimensional object can be projected ont

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