Open the Bayes

By Jerry D. Haight

It was after midnight on a Saturday morning in January of 1966. A cold front moving rapidly northeast just off the Mediterranean coast of Polomares, a small fishing village in Spain, generated a wind velocity of nearly a hundred knots at thirty thousand feet, hurricane strength. As the front steamrolled its way up the coast, it engaged a wall of warm air waging war against it.  Caught up in the battle were two aircraft, massive on the ground, but mere specs in the fathomless sea of air.

The fuel probe of the tanker, a KC135, was fully extended as the B52 bomber of the USAF Strategic Air Command approached. The tanker hit the wall first with a deafening thud that shook the plane fore and aft. It lost speed immediately. The B52 then crashed into the tanker and both planes disintegrated killing the four crew members of the KC and three of the seven of the B52.

The payload of the B52 included four 1.8 megaton Hydrogen Bombs. The crash site of three of the H-bombs was located almost immediately. These bombs would contaminate over 550 acres of farmland. The US government would remove over 2.8 million pounds of earth to a site near Aiken, South Carolina at a cost of more than $80 million. The catastrophe would leave behind an ecological nightmare of useless wilderness on the Spanish landscape.

The whereabouts of the fourth hydrogen bomb remained a mystery for eighty days, then solved only because of the work of an 18th century minister named Thomas Bayes.  

Thomas Bayes lived during the first hexidecade of the 18th century; a perilous time politically and socially. This was a time when political correctness predicated who could hold public office, serve in the military or be awarded a degree from universities like Cambridge or Oxford; a time when anyone deviating from the oppressive laws or sandbagged ideas were termed nonconformists and then criticized, ostracized and persecuted.

Nevertheless, Thomas Bayes was a nonconformist and a life long minister and passionately interested in the field of mathematics developed the Bayes Theorem that would help solve one of the worlds greatest mysteries two centuries later.

At 4:00 a.m. that same Saturday morning, the telephone of Dr. John T. Craven rang. Craven, a colorful character was known throughout the U. S. Navy as an Oceanographer, a spook, mathematician, maverick, eccentric and as a radical extremist among many other adjectives. The man on the other end of the line was U. S. Defense Secretary Robert McNamara. “Dr. Craven, we’ve lost an H-bomb” he declared. “Why are you calling me?”, Craven asked. “The one we lost is presumed in the water and I want you to find it” was the reply. Thus began one of the more bizarre searches in history.   

In 1966, the cold war was raging and the USA and USSR routinely had atomic weapons in the air ready to dissipate large segments of one another’s societies. Both countries’ spies were at work ferreting out one another’s secrets, hoping to gain a technical advantage. At the same time, the rest of the world was trying to stay out of harms way as the massive goliaths rattled their nuclear sabers. Recent events prompted Spain, an integral part in the nuclear wheel of the USA, to close it’s air space to any USA plane carrying nuclear weapons. The USSR would like nothing better than to salvage a US H-bomb and their ships were already heading southward toward the Spanish coast. The generals of the Air Force and the Admirals of the Navy tried to schmooze President Linden B. Johnson, telling him that the fourth bomb is lost and probably neither side would ever recover it. In characteristic fashion, Johnson, blared back to the effect that if they wished to retain their stars and stripes, the bomb damned well better be found, and soon.    

In Craven’s office, his team constructed a grid of the sea bottom around Polomara. Then, like the game of cow plop where a grid is chalked on a field and bets are taken as to where a cow will place the next deposit, Craven’s team created many scenarios each with it’s own array of possible outcomes. Did the bomb disintegrate in the crash? Did one or more of its chutes deploy? Did the bomb hit the wall of warm air? These were just a few of the many variables considered.  Not unlike “cow plop”, Craven invited bets from submarine, salvage and aeronautical engineers on the probability of each of the different scenarios describing where the bomb might be found. Then each possible location was analyzed by a formula based on the odds created by the betting round.  

Craven and his team relied on the Bates’ theorem of subjective probability. Craven figured that even though all the factors relating to the location of the bomb were not known, based the information that was known by his experts the consensus could reasonably extrapolate the unknown within a defined range of probability. When Craven announced, without leaving his office, he had narrowed the search to three locations. The searchers were incredulous. He was ridiculed and criticized but eventually, with no better options, they searched the first location.            

After weeks of work without finding the bomb, President Johnson was furious and demanded an answer as to when the searchers would find it. In answer, Craven’s latest probability charts were sent to the President by the Defense Department. On seeing Craven’s charts, curves and graphs, President Johnson exploded. He yelled, cursed, ranted and raved, becoming repetitive and at times irrational and incoherent. He demanded another team be hired at once since the present one obviously could not give him the results he wanted. His reaction was premature because shortly thereafter, the Alvin, a deep submergence rescue vehicle found the bomb enshrouded in its parachute in 2500 feet of water, the first and primary location suggested by Craven.