Information Theory

• With perfect coding, the encoded message must be indistinguishable from random.

Links and knots are 1-dimensional manifolds, but we need 4 dimensions to be able to untangle all of them. Similarly, one can need yet higher dimensional space to be able to unknot n-dimensional manifolds. All n-dimensional manifolds can be untangled in 2n+2 dimensions. [http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/]