In one of his popular and philosophical writings, Science and Hypothesis 1901, he wrote of his model as an imaginary universe occupying the interior of a disc in the Euclidean plane. The inhabitants (and we shall meet one of these later in the form of Poincaré's bug) are seen by us, as observers of their world, to 'shrink' as they approach the infinitely distant horizon, the boundary of the disc. They do not register the effect as their 'ruler' shrinks with them. They think that they live in a normal non-Euclidean space, we see them in a Euclidean space with their dimensions behaving strangely.
Poincaré said 'one geometry cannot be more true than another; it can only be more convenient'
2 dimensional geometry
A
line in the Poincaré disc
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