After World War II, Berlin was an island" surrounded by
the Soviet -dominated East Germany, and Berlin was also partitioned into
West and East Berlin. In 1948, the Soviets tried to force American, British
and French forces out of Berlin by blockading land routes to the sectors
each of these powers occupied. This Berlin Blockade was thwarted
(until its abandonment in Sept., 1949) by a massive airlift of food, fuel,
and other supplies needed by Berliners. The success of this airlift, with
a limited number of aircraft, was primarily due to careful planning using
a mathematical tool, linear programming, finding solutions to its
problems by means of a simplex algorithm developed by an American
mathematician, George Dantzig.
After the success of Dantzig's work became known to the mathematical
world and some of the general public, it became known that a Soviet mathematician,
Alexi Kantorevich, has earlier obtained these results. But Kantorevich's math was
ignored, after being criticized, because it seemed in conflict with Marxist dogma.
After North Korea invaded South Korean, President Truman ordered
Air Force and Navy forces into Korea on June 27, 1945 -- thereby instituting
Aerica's first UNDECLARED WAR. (America has not been in a declared
war since Aug. 15, 1945.) U. S. Forces, under General Douglas MacArthur
landed at Inchon and inflicted great losses on N. Korean forces. UN forces
(U. S. and Allies) pursued N. Korean forces to the border of China on Nov.
20. To the great surprise of MacArthur, Chinese forces crossed the border
into Korea on Nov. 26, routing UN forces and putting them in jeopardy.
After a regathering of forces, Gen. MacArthur advocated attacking Chinese
bases in Manchuria, blockading the Chinese coast, and reinforcing the UN
command with Nationalist Chinese troops from Taiwan. When denied permission
by President Truman to risk war with China, Gen. MacArthur tried to bypass
the President by writing Rep. Joseph X, Speaker of the House of Representatives,
thinking he could obtain Congressional support for his mission. On Apr.
11, Pres. Truman removed Gen. MacArthur from his command for unauthorized
policy statements.
Truman's decision was influenced by an input-output analysis
by Wassily Leontief (a kind of "National Spreadsheet"), which had been
commissioned to determine U. S. readiness to fight another war.
Leontief's analysis predicted that the U. S. would require two years to
provide the equipment and supplies to effectively support our forces. But,
meanwhile, they would be fighting against Chinese forces who might sometimes
be engaged on their own soil and who could live off the land, wherever
engaged. When word of this analysis spread among Truman's advisers, those
previously supporting MacArthur switched their opinions.
(I knew personally the problem involved, since I had lived
under "unprepared" conditions in the period before "Pearl Harbor" had propelled
America into World War II. I enlisted in the Army Air Corps on Jan. 27,
1941, and went to Texas. I had no uniform for four months after enlisting.
We lived in tents, shaved at outdoor watering troughs with cold water before
dawn, and lacked basic equipment. We went on guard duty with only wooden
clubs as defense. In that first disheartening year of the War, we often
saw smoke rising from the Gulf -- from American merchant ships sunk by
German submarines. In general, it took America two years to get on war
footing. And now, not yet recovered from the costs of World War II,
we would be faced with a war with the most populous country in the world!)
The mathematical
purpose of linear programming is to find a subset of numbers
from a prescribed set of numbers which MAXIMIZES or MINIMIZES a given polynomial
(algebraic) form. A representative case is known as "The Diet Problem":
how to prescribe a diet which will MAXIMIZE NOURISHMENT while MINIMIZING
COST. In the Berlin Blockade case, a giant flight plan should MAXIMIZE
THE SUPPLY LOAD FLOWN while MINIMIZING the aircraft and personnel involved.
Typically, constraints on the problem are formulated as a set of polynomial
inequalities, which graph as a sector in an n-dimensional region, where
n is the number of constraints. Dantzig's simplex algorithm iteratively
"whittles" the relationship down to a solution.
In the instances, as in MANY OTHERS, MATHEMATICS (often in the form of ALGEBRA)
helped CHANGE THE WORLD! (A personal
note on linear programming).