  In 1960 Edward Lorenz (1917-2008) published a pioneering work on the `maximum
simplification' of the barotropic vorticity equation. He derived a coupled
three-mode system and interpreted it as the minimum core of large-scale fluid
mechanics on a `finite but unbounded' domain. The model was obtained in a
heuristic way, without giving a rigorous justification for the chosen selection
of modes. In this paper, it is shown that one can legitimate Lorenz' choice by
using symmetry transformations of the spectral form of the vorticity equation.
The Lorenz three-mode model arises as the final step in a hierarchy of models
constructed via the component reduction by means of symmetries. In this sense,
the Lorenz model is indeed the `maximum simplification' of the vorticity
equation.
