Abstract: Edwin Abbott, an English non-mathematician of the Victorian era, wrote a book called "Flatland" about life in a two dimensional world, and its hero's travels to other dimensions.

I will use this dimensional voyage to relate one of my own which will go from one dimension to infinitely many, then settle solidly in two dimensions. The quantum world in two dimensions is even more bizarre than in three dimensions and the algebra we will encounter is being used in an attempt to build a quantum computer based on these very peculiarities.

This talk will be accessible to undergraduates.