Marching as to War
Dying in a Markov chain
As they have before
What is a Markov chain. Very few people involved with practical prolems of human technology and behavior have the slightest notion or the slightest understanding of the role of the Markov chain in the decline and fall of Rome, in the disaster of the Crusades, in Napoleans retreat from Moscow` in the the Iraqi retreat on the Road to Bagdad and in the probable outcome of the pending United States attack on Iraq. Indeed the scientific community first came upon the Markovian process (without knowing what it was) through the experience and work of Ralph Bagnold an Officer in the Britsh Army.
in Trans-Jordan, in the Sinai, and in that part of the northeast Sahara known as the Libyan Desert.
They discovered that the greates impediment to transport over these desert were the giant sand dunes
that were created by the wind. Bagnold studied the " and striking geometry and symetry of the sand dunes".
Without ever identifying the process he had identified the first "Markov chain" of significance to mankind.
These chains occur when particles of any type are randomly introduced into a "pipe". As they are transported
by a physical phenomenon the slowly moving particles trap the rapidly moving particles until a dune or clump
is formed in which the rate at which particles are trapped equals the rate at which prticles escape. The whole
clump or dune now moves majestically forward until it is dissapated when it leaves the constraining geometry
of the physical or geophysical pipe.
Craven, that's me, examined and identified this phenomenon in his PhD. study of the movement of sand in pipe
lines. He identified the phsyical parameters associated with each type of dune formation without realizing
hta he could have predicted this movement if were acquainted with the mathematical function known as the "Markov chain"
Know all of us in an automotive society know what a Markov chain is. We know that as automobiles enter
a highway at different velocities it is only a short traverse that results in "dunes of cars" separated by
relatively empty stretches of highways.
But other physicists identified tghis process in the remarkable development of the electric Klystron.
Here electrons are intorduced univormly and quasi randomly in the entrance to a Klystron pipe and emerge
in highly energetic pulses of electrical power at the outlet. The frequencey of the pulses depends upon
the configuration of the pipe. I do not know if Markovian mathematics was used in the design of the
Klystron and the literature sheds little light on this discovery or non discovery.
I next encounter Markovian process in my participation in the search for the H-Bomb which was lost by the
United States at Palomares Spain. I commissioned a company Wagner Associates to develop a thoery of
opimum search. They exceeded my expectation with a book entitled the "theory of optimal search"
published in 1975. It was used later by the Coast Guard in developing their search doctrines and I now
discover that the book was updated in 1996. Chapter nine of the fist book deals with Markovian Target motion.
It is suddenly clear that the disaster of the Crusades, Napoleans retreat from Moscow,
Marlboroughs invasion of the Rhine ending in the disaster at Blenheim, that the Civil War Battles
of Antietam, Gettysburg, Shiloh were all the result of the aggregate dunes of men and machines and guns
and logistic supply systems associated with the Markovian movement of two armies, their retinues
their camp followers and others in an adaptive sets of Markov chains. Silarly the retreat in the Gulf War by the Iraqi's
on the road to Bagdad was delayed by the clumps of men and machines entangled in the
traffic jam of destruction. This of course resulted in General McCaffery's famous "turkey shoot" that ended
Iraqi resistance.
Now we can start to analyze other wars and other battles and not that the pipe lines which generate
Markov chains begin with roads until they are destroyed by battle. They then shift to Rivers as in the case of Marlborough
and the Rhine and the Balkans and the Danube and Peter the Great and his victory on the river at Poltava.
And now our troops will entger the pipeline of the Tigris without an understanding that the very existence of
Bagdad is the result of an ancinet oxbow in that River. Let us hope that I am wrong in this analyses for we have 300,000 men poised for this adventure.
Will we sing once again "Where have all the young men gone" I hope not and if I see any silver linings in
the clouds that now envelope us, I will report it in the daily modification of this page on the web.