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Avenhaus, Rudolf
and
Fichtner, John
1984.
Quantitative Assessment in Arms Control.
p.
143.
Article contents
The Richardson theory of ‘arms races’: themes and variations
Published online by Cambridge University Press: 26 October 2009
Extract
The first difficulty facing an enquiry into the Richardson theory, apart from the quirky and unconventional style of Richardson's own presentation of his ideas (and I am emphatically not referring to his use of mathematics), is to decide precisely what the theory refers to. Richardson seems first to formulate his model in terms of the relationship between the rate at which a state acquires additional armaments and the level or stock of armaments at that moment in time in its possession and that of its presumed, probable opponent. He does this, reasonably enough, by connecting the rate at which each state acquires armaments directly and positively to the level of its opponent's stock of armaments and negatively to its own, and to a term independent of the size of stocks.
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References
page 119 note 1. Richardson, Lewis F.Arms and Insecurity (London, 1960)Google Scholar, edited by N. Rashevsky and E. Trucco, p, 14.
page 119 note 2. Ibid. p. 32.
page 120 note 1. dx/dt is a function in differential calculus whose meaning has often caused difficulty to subtle and learned minds as well as to the untutored. Here, it is enough to think of it as a shorthand way of expressing the division of the difference between two values of x, closely adjacent in time, by that small interval of time over which the difference grew up - if x refers to distance, dx/dt is speed, and d(dx/dt)dt or d2x/dt2 is acceleration.
page 121 note 1. Mathematically, this is equivalent to the typically rapid rise over time of a sum invested at compound interest, interest continuously reinvested.
page 121 note 2. Pursuing the analogy, this case is equivalent to the slower rise of a sum invested at simple interest,
page 123 note 1. The constant, k in fact, is related to the others by the identity k = wf + j(I−f).
page 124 note 1. Bellany, Ian, ‘MIRVs and the Strategic Balance’, Nature, ccxxvi (1970), pp. 412–13Google Scholar.
page 124 note 2. Kupperman, Robert H. and Smith, Harvey A., ‘Strategies of Mutual Deterrence’, Science, clxxvi (1972), pp. 18–23CrossRefGoogle Scholar.
page 125 note 1. This may be seen more clearly if we thought of the probability of failing to get heads, say, on any of r tosses of a coin. The probability of a head on a single toss is 1/2, the probability of no head is (1 - 1/2), on r tosses the probability of no heads becomes (1 - 1/2)r. If r were six, say (1 - 1/2)r becomes 1/64.
page 125 note 2. For an extended discussion of the. factors involved here see Bellany, , ‘The Essential Arithmetic of Deterrence’, Journal of the Royal United Services Institute, i (1973), pp. 28Google Scholar, 34,
page 127 note 1. Bellany, , ‘Strategic Arms Competition and the Logistic Curve’, Survival, xvi (1974), pp. 228CrossRefGoogle Scholar, 230.
page 127 note 2. Following the translation by Fink of the vague terms of the United States' ‘assured destruction’ doctrine into actual force levels. See Fink, Daniel J., ‘Strategic Warfare’, Science and Technology (1968), pp. 54Google Scholar, 68.
page 129 note 1. Bellany, ‘Strategic Arms Competition and the Logistic Curve’, op. cit. p. 230.
page 129 note 2. Strategic Survey 1969, (London, 1970), p. 33Google Scholar.
page 130 note 1. Bellany, ‘Strategic Arms Competition and the Logistic Curve’, op. eit. p. 230.
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