But one should not imagine non-Euclidean geometry only as a simulation within Euclidean geometry, for this would miss out on the view of non-Euclidean geometry as its own robust independent geometric concept; it has its own essential geometric nature, with its own geometric character that is fundamentally different from classical Euclidean geometry in important respects. One should imagine inhabiting hyperbolic space as it is, not merely as it is simulated inside Euclidean space. Conversely, one may also find simulations of Euclidean geometry inside non-Euclidean geometry. Imagine an alien
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