What the sphereman learned from the Master, is that the inner world could become external.
At first, he assumed that it is merely a metaphor, but the results of the differential topology were quite clear.
Smale’s paradox was only the beginning, because furtheron, with Morin’s adequacy, it was even more impressive.
Without corrugations, but with intersections, the incredible was feasible.
That’s how Klein’s bottle aided, with its variant form of surface, as per Boy.
And later on, he learned about the works of Thurston. Therefore, with the smooth homotopy he realized that, there was also Aitchison’s construction, due to the combination of topology and geometry, which was created specifically for the sphere.
The sphereman, with his liberty and his abilities, could now observe more profound worlds, around him, beside him, inside him.
Then he remembered how things were, when he was told that, a line segment can not do anything.
Yet, nothing reached everything thereon.