The Alexander horned sphere
No. 4, 1967 (Topology, theory of embeddings of manifolds)
India ink on paper, 22 x32.5 cm.
This ribbed, stonelike convolution of space is an object known as the Alexander sphere, or horned sphere, familiar in the area of mathematics called the topology of manifolds. Here, a surface is contorted in such a way that, once topologically embedded in space, it partitions that space into two domains, which are non-simply-connected. As a result, an object forms with fingered hands that link without touching, a process that continues to infinity. At each step the number of fingers, or horns, that grow out of the shape doubles. The embedding of horns in space becomes more and more complex.
In this image, consider a human figure, whose arms lead to hands that divide into fingers, endlessly dividing and intertwining with each other.
