Using the statistical technique of fuzzy clustering, regimes of inflation and unemployment are explored for the United States, the United Kingdom and Germany between 1871 and 2009. We identify for each country three distinct regimes in inflation/unemployment space. There is considerable similarity across the countries in both the regimes themselves and in the timings of the transitions between regimes. However, the typical rates of inflation and unemployment experienced in the regimes are substantially different. Further, even within a given regime, the results of the clustering show persistent fluctuations in the degree of attachment to that regime of inflation/unemployment observations over time. The economic implications of the results are that, first, the inflation/unemployment relationship experiences from time to time major shifts. Second, that it is also inherently unstable even in the short run. It is likely that the factors which govern the inflation/unemployment trade off are so multi-dimensional that it is hard to see that there is a way of identifying periods of short run Phillips curves which can be assigned to particular historical periods with any degree of accuracy or predictability. The short run may be so short as to be meaningless. The analysis shows that reliance on any kind of trade off between inflation and unemployment for policy purposes is entirely misplaced.