  One important feature of the mammalian immune system is the highly specific
binding of antigens to antibodies. Antibodies generated in response to one
infection may also provide some level of cross immunity to other infections.
One model to describe this cross immunity is the notion of antigenic space,
which assigns each antibody and each virus a point in $\mathbb{R}^n$. Past
studies have suggested the dimensionality of antigenic space, $n$, may be
small. In this study we show that data from hemagglutination assays suggest a
high dimensional random walk (or self avoiding random random walk). The
discrepancy between our result and prior studies is due to the fact that random
walks can appear low dimensional according to a variety of analyses. including
principal component analysis (PCA) and multidimensional scaling (MDS).
