Discussion on the first day’s papers

Abstract

I am grateful to have been invited to contribute to the discussion of the fascinating material we have heard today at this unusual joint meeting of the Royal Society and British Academy on ‘Predictability in Science and Society’. I can add little to the many important specific points brought out in the excellent formal presentations by two economists and two physical scientists and in various contributions from the floor, so I offer a few general remarks under the headings ‘language’, ‘experiments’ and ‘time-series analysis’. Mathematics gives us the operational methods used in predictability work and it also provides concepts, terminology and language, which we have to employ correctly in our efforts to promote working links between various disciplines. The term ‘predictability horizon’ has been used by several speakers today and the irreverent thought crossed my mind that there are several undeniable meteorological consequences of some of the basic theorems of algebraic topology, namely that for all predictability horizons (from minus infinity to plus infinity!): ( a ) the wind-speed must vanish somewhere, ( b ) the wind direction takes all possible values relative to the perimeter of any region of the atmosphere within which the wind-speed is everywhere non-zero, and ( c ) on global contour maps of any meteorological variable such as pressure, the number of ‘highs’ plus the number of 'lows’ minus the number of ‘cols’ is always equal to two! The hard-pressed weather forecaster is unlikely to be impressed by such mathematical gems, but from his perusal of the literature of dynamical meteorology he will already be acquainted with terms from topology and other branches of mathematics with which some of the more theoretical papers in his subject are now liberally sprinkled. ‘Poincaré surface’, ‘strange attractor’, ‘central manifold theorem’, ‘intransitivity’, ‘Hausdorff dimension’, ‘fractal’, ‘bifurcation tree’, ‘Feigenbaum numbers’, ‘Hénon map’, ‘deterministic chaos’, ‘phase portrait’, ‘swallowtail catastrophe’, ‘Cantor set’, ‘Cantor dust’, ‘Sierpinski gasket’, ‘Lorenz equations’, ‘multiple equilibria’, ‘multi-dimensional torus’ and many other terms which I cannot immediately recall are now employed in several disciplines and we must use them with confidence and precision.