I am not sure what you mean by seeing a curvature. Although there is one, I can't see it; it is too slight. The change in elevation over lateral distance (what you could call curvature) is only on the order of 1 part in 10,000. This makes me think that the perception is an illusion.
That is, we can only see to a distance of about 5 km or so. Most of us cannot even see an object of a few meters in elevation at that distance, yet you would have to be able to tell the difference of that change in elevation over some lateral distance of that magnitude to identify the curvature. That is, if you can see 5 km in one direction, the furthest apart any two locations that you can see would be 10 km, but the change in elevation would only be about 4 meters at most from curvature alone. You wouldn't be able to see that difference. The curvature appears in your brain because you have a circular perimeter but not because you can see the actual curve.