In our mind, space and time are represented as independent dimensions: you cannot mentally rotate between space and time. However, we can probably go to ~4D in general, without nesting.
Position space has interesting mathematical properties, for instance, it can be nested, so each object can have its own subspace, which remains locally invariant under conditions of translation, scaling and rotation.
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There are many other spaces, for instance color space, or the space of all possible chairs, or the space of facial expressions. But these don't have same properties as position space; the operators that combine multiple dimensions may each work differently.
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Spacetime combines a commutative position space with a temporal dimension, but temporal dimensions are causal orderings that mostly describe how objects change, whereas spatial dimensions describe how you can change perspective while they stay the same!
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