The analogy between networks of nerve cells in the brain, and aggregates of spins in ferromagnetic materials, which was proposed by Cragg & Temperley (1954, 1955), is examined in some detail. A 1:1 correspondence is set up between the systems. It is then found that the Hamiltonian corresponding to a neural network is totally unlike a ferromagnetic Hamiltonian and hence that the original analogy is invalid. In particular, the Hamiltonian normally has the undesirable features of being intractably complicated and also non-Hermitian. This appears to reduce considerably the practical value of any such analogy.