Let's suppose I am an ant who lives in a 2D curved space. Locally the world seems 2d-euclidean to me, but it is not if I consider a large portion of space.
Now let's consider a human being who lives in curved 4d spacetime. Locally the spacetime seems 4d-euclidean --> in fact, the space itself appears 3d-euclidean to us. But if we consider a larger portion of spacetime, then the curvature will inevitably be evident.
However: if I look around me in any moment, the space seems to me 3d euclidean EVERYWHERE, not only locally. I mean, it seems like I can extend my 3d-euclidean-grid forever in space (at least according to my eyes).
How can this be possible if spacetime is curved? Do our eyes give us misleading impressions?