The example here is a simple mathematical illustration of the problem. The space of possible brain configurations is vast, well beyond what one can take a representative sample of. One may naively assume that if they study 100 people with schizophrenia, then the 101st person with the same diagnosis who comes along will have the same problem, treatable in the same way.
Now this illustration will only make sense to those who know a little linear algebra. Consider a vector space \(V\) of very high dimension, say one million. Suppose we have a set \(X\) of 100 vectors in \(V\). These span a subspace of dimension at most 100. Call this subspace \(U\). If we now pick a vector at random \(v\) from \(V\), what is the probability that \(v\in U\)? Almost zero.
When you collect together people with a common diagnosis, it is a little like this. There are so many ways in which they differ, and many of those details will be significant. It is not, as I often say, a fair assumption that if Alice is experiencing mania, and Bob is experiencing mania, then they are experiencing the same thing. To assume as such, is akin to assuming that, using our vector space example above, that a randomly chosen vector in \(V\) will be contained in \(U\).
(The main difference with the space of possible configurations of neurons is that it doesn't have the nice mathematical symmetries of something like a vector space. But that only makes the theoretical task of understanding problems harder, and makes the naive assumptions that 'same diagnosis implies same problem' more appealing.)