Could an Arms-Race End Without Fighting?

Abstract

THERE have been only three great arms-races. The first two of them ended in wars in 1914 and 1939; the third is still going on. From so few events we cannot hope to draw any reliable conclusions by statistics. Let us instead see whether an analysis of motives throws any light on the problem. Arms, in peace-time, are intended to overawe possible enemies; therefore the motive of submission must come into the picture. Arms, in peace-time, in fact provoke possible enemies to prepare to defend themselves; so defensiveness must be taken into account. There is also considerable grumbling about the cost of rearmament. The behaviour of large groups of people is more regular and less capricious than the behaviour of individuals. It is instructive to regard large groups as deterministic, and to represent their behaviour by differential equations, provided that we remember that such a treatment is a caricature. The following simultaneous pair of equations were published¹ for that purpose in 1939. Here t is time, x and y are the war-like preparations of the opposing sides, and the other letters are constants. Of these, k and l are positive ‘defence coefficients’, σ and ρ are positive measures of ‘sub-missiveness’, α and β are positive measures of the objection to the cost of rearmament; but g and h, which represent feelings, not about arms but about the treaty-situation, may have either sign. The names of the opposing nations do not appear, because the motives are supposed to be common to mankind; but the numerical values of the constants may differ from nation to nation.