122
II - Convergence: Discrete variables
great cost, but it was certainly not yet the central computer of the American
Strategic Air Command capable of organising mathematically (?) an attack
leaving 400 millions of corpses 37 on the ground, as well as others uncounted,
including, according to an American admiral, the sailors of the Pacific Fleet
who would be too busy cleaning themselves from radioactive fallout to have
time to chase the Soviet submarines.
After this incursion into the domain of psychopathological additions - a
French humorist remarked in the 1930s that the kepis of the military of high
rank are surrounded by several braids to prevent their skulls from exploding
-, let us return to mathematical additions to show that the commutativity
property established above for series with positive terms no longer applies
when, in a convergent series of real terms, the series of its positive terms (and
so also that of its negative terms) diverges, as is the case for the alternating
37 See in Desmond Ball and Jeffrey Richelson, eds., Strategic Nuclear Targeting
(Cornell University Press, 1986) the articles of David Alan Rosenberg and
Desmond Ball on the (one and only) American plan of war of 1960, particularly pp. 35-36 and 62 for the extent of the attack: at least 1,400 bombs with a
total power of 2,100 megatonnes onto 650 multiple objectives, to a maximum of
3,500 weapons onto 1,050 multiple objectives of which 151 were industrial-urban
centres. The plan estimates that the maximum attack would cause between 360
and 425 million deaths from the Iron Curtain to China inclusive. The operation
would take twenty four hours and, in theory, would be launched in the event that
preparations for a Soviet attack were detected. In Secrets. A Memoir of Vietnam
and the Pentagon Papers (Viking, 2002), pp. 58-59, Daniel EIlsberg, who is in
the best position to know, confirms, with in addition up to 100 million deaths
in neutral countries and as many in allied ones, as told in 1964 to President
Johnson; "A hundred Holocausts", as EIlsberg puts it. The Soviets at that period
had much less means of reaching the USA, but as a former advisor of President
Kennedy, McGeorge Bundy, who had lived through the Cuban Crisis in 1962,
remarked much later, a single bomb on a single large town, let alone ten, would
already be an unimaginable catastrophe.
The Soviet plans, analysed in the first book by a member of the American
intelligence services, put much more emphasis on the destruction of military
forces and of a certain number of industries and of vital means of transport,
avoiding uselessly devastating Europe whose resources would be indispensable
to the reconstruction of the USSR after the "victory"; the prevailing Westerly
winds would anyway demand a certain moderation, also needed so that one might
not exterminate the populations that one desired convert to socialism ... The
objective assigned by General de Gaulle in the 1960s to the French nuclear arms
was the power, in the end, to eliminate about 60 million citizens and 50% of the
Soviet industrial potential. The Soviet reaction to this program is not known.
See also Roger Godement, "Aux sources du modele scientifique americain"
(La Pensee, nO 201, 203 and 204, 1978/79) where one can see, for example, that
in 1958, an IBM 704 "scientific" computer - no matter that a present day PC
is more powerful - had the task of managing about 3,000 planes spread over 70
bases. These uses contributed powerfully to launching the computer industry,
the Internet included, and the role that it now plays in the civil sector has by no
means caused its other face to disappear, quite the contrary since the military
sector now profits greatly from the civil sector. We do not know what Pascal and
Leibniz would have thought of this.
II - Convergence: Discrete variables
great cost, but it was certainly not yet the central computer of the American
Strategic Air Command capable of organising mathematically (?) an attack
leaving 400 millions of corpses 37 on the ground, as well as others uncounted,
including, according to an American admiral, the sailors of the Pacific Fleet
who would be too busy cleaning themselves from radioactive fallout to have
time to chase the Soviet submarines.
After this incursion into the domain of psychopathological additions - a
French humorist remarked in the 1930s that the kepis of the military of high
rank are surrounded by several braids to prevent their skulls from exploding
-, let us return to mathematical additions to show that the commutativity
property established above for series with positive terms no longer applies
when, in a convergent series of real terms, the series of its positive terms (and
so also that of its negative terms) diverges, as is the case for the alternating
37 See in Desmond Ball and Jeffrey Richelson, eds., Strategic Nuclear Targeting
(Cornell University Press, 1986) the articles of David Alan Rosenberg and
Desmond Ball on the (one and only) American plan of war of 1960, particularly pp. 35-36 and 62 for the extent of the attack: at least 1,400 bombs with a
total power of 2,100 megatonnes onto 650 multiple objectives, to a maximum of
3,500 weapons onto 1,050 multiple objectives of which 151 were industrial-urban
centres. The plan estimates that the maximum attack would cause between 360
and 425 million deaths from the Iron Curtain to China inclusive. The operation
would take twenty four hours and, in theory, would be launched in the event that
preparations for a Soviet attack were detected. In Secrets. A Memoir of Vietnam
and the Pentagon Papers (Viking, 2002), pp. 58-59, Daniel EIlsberg, who is in
the best position to know, confirms, with in addition up to 100 million deaths
in neutral countries and as many in allied ones, as told in 1964 to President
Johnson; "A hundred Holocausts", as EIlsberg puts it. The Soviets at that period
had much less means of reaching the USA, but as a former advisor of President
Kennedy, McGeorge Bundy, who had lived through the Cuban Crisis in 1962,
remarked much later, a single bomb on a single large town, let alone ten, would
already be an unimaginable catastrophe.
The Soviet plans, analysed in the first book by a member of the American
intelligence services, put much more emphasis on the destruction of military
forces and of a certain number of industries and of vital means of transport,
avoiding uselessly devastating Europe whose resources would be indispensable
to the reconstruction of the USSR after the "victory"; the prevailing Westerly
winds would anyway demand a certain moderation, also needed so that one might
not exterminate the populations that one desired convert to socialism ... The
objective assigned by General de Gaulle in the 1960s to the French nuclear arms
was the power, in the end, to eliminate about 60 million citizens and 50% of the
Soviet industrial potential. The Soviet reaction to this program is not known.
See also Roger Godement, "Aux sources du modele scientifique americain"
(La Pensee, nO 201, 203 and 204, 1978/79) where one can see, for example, that
in 1958, an IBM 704 "scientific" computer - no matter that a present day PC
is more powerful - had the task of managing about 3,000 planes spread over 70
bases. These uses contributed powerfully to launching the computer industry,
the Internet included, and the role that it now plays in the civil sector has by no
means caused its other face to disappear, quite the contrary since the military
sector now profits greatly from the civil sector. We do not know what Pascal and
Leibniz would have thought of this.