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Despite the admirals' reluctance, Craven wasn't about to give up, not now that he was convinced he had enough information to find Scorpion and prove what killed her. He began to mathematically construct a map of the ocean bottom, using Bayes' theorem of subjective probability, the same algebraic formula he had employed during the search for the H-bomb.

Few of the officers involved in the search for Scorpion had taken much note of Palornares. And by the time Craven was finished explaining that he was going to use a system of Las Vegas-style bets to factor the value of a hunch into his data, some of the operational commanders were convinced that he had gone completely over the edge. To them, it sounded like he was talking about ESP. Craven once again tried to explain that Bayes seemed to draw on the knowledge that even experts are not always consciously aware they have. The commanders remained highly skeptical.

Still, Craven pushed on, asking a group of submarine and salvage experts to bet on the probability of each of the different scenarios being considered to explain Scorpion's loss. To keep the process interesting, and in line with previous wagers, the men bet bottles of Chivas Regal.

Scorpion could have glided down to the ocean bottom at speeds between 30 and 60 knots. His submarine experts bet that Scorpion had glided downward at between 40 and 45 knots.

Next, the experts were asked to bet on whether they believed Scorpion was trying to shut down a hot-running torpedo and was therefore traveling east. About 60 percent of the bets favored the torpedo theory. Craven, it seems, was winning some converts.

In a third round of betting, the experts picked a glide path. At the most, Scorpion could have moved 7 feet forward for every foot she descended; at the least, she could have nosedived straight down. The bets favored a glide path of about 3 or 4 feet forward for every foot down. That meant Scorpion would have traveled 6 to 8 miles after the first explosion.

By the time the bets were finished and Craven sat down to draw a probability map, the calculations had become so complicated that he had to rehire the group of mathematicians who had helped him with the H-bomb. They concluded that Scorpion was east of Point Oscar, 400 miles from the Azores, on the edge of the Sargasso Sea.

Years later, the mathematicians would write a book based on their work with Craven, entitled Theory of Optimal Search. The U.S. Coast Guard would adopt the method for search and rescue, and the Navy would use Craven's interpretation of Bayes to help Egypt clear sunken ordnance from the Suez Canal. But in the Scorpion search, naval officers just shook their heads at Craven's acoustic evidence and his probability map. The scientist may have been convinced that Scorpion lay further east, but the Mizar had found the three scraps of debris to the west, and that's where the Navy wanted to keep searching.

Weeks passed. Craven waited, trading messages nearly every night with Buchanan. By late August, nothing new had been found and the jubilation within the Navy that had accompanied the Mizar's find of the supposed umbrella and the monkey's fist knot diminished. By September, all of the likely spots between Point Oscar and Norfolk were almost ruled out. By October, the weather was getting so bad that the Navy decided it would end the search by the end of the month.

But Mizar still hadn't really searched east. And it had never searched the site Craven had pinpointed. By now, Buchanan was sporting a fully grown Vandyke beard and was willing to point Mizar east one last time.

Almost as soon as Mizar passed east of Point Oscar, its long-range sonar registered iron, and lots of it. Mizar steamed ahead full speed, right past Craven's point of highest probability, and then lowered its cameras for another look. All it found was iron ore-filled rock.

That was it. The end. Schade and Clarey had had about all the disappointment they could take. The decision was made. It was time to give up. Time to call Buck Buchanan and Mizar home.

Buchanan, pugnacious and stubborn as ever, refused to accept their decision. He flashed a message to Craven.

"Can't you get the Navy to let us stay out another month, or a week or two weeks? Tell them I need to calibrate the area for future operations."

Craven knew that there was nothing left to "calibrate." But Craven also knew that if Buck Buchanan wanted to stay out, it could mean only one thing. The oceanographer was going to take Mizar to the spot Craven and his team had pinpointed. Craven went to the admirals and began mixing his rapid-fire logic with pleas. By the time he was finished, he had won two more weeks.

Exactly one week later, Craven received a one-line missive from the survey ship: "Buchanan shaved his beard."

Craven didn't need any translation. Scorpion had been found. It was October 29, almost five months to the day that she had been declared missing.

Mizar found Scorpion within 220 yards, one-eighth of a mile, of where Craven, his mathematicians, and a group of experts betting for bottles of scotch had said she would be. The sub was 11,000 feet underwater.

Dangling cameras, Mizar took photographs showing Scorpion halfburied in silt and sand and separated into two pieces that were barely held together by a small hinge of metal. The forward part of the engine room had imploded and, in a fraction of a second, collapsed like a telescope into the auxiliary machine space.

The propeller and the propeller shaft were separated from the hull altogether. So was the submarine's sail. Lying near the submarine was Scorpion's sextant-an age-old symbol of navigation. No navigator, officer, or crewman was anywhere in sight. It was impossible to see inside the submarine or even the outside in much detail. Although Mizar's cameras dangled only between 10 and 50 feet over Scorpion, the overhead pictures looked as though they'd been photographed through a deep fog.

A court of inquiry looking into the disaster was made up of seven naval officers and chaired by retired Vice Admiral Bernard L. "Count" Austin, who had also led the inquiry into Thresher's sinking. In a January 1969 press release, the Navy told the public that the court of inquiry, after a six-month investigation, had concluded that the Scorpion disaster remained a mystery, that the cause could not be "ascertained from any evidence now available," and that "no incontrovertible proof of the exact cause" could be found.

Indeed, the Navy publicly appeared to rule out a torpedo disaster of any sort, saying, "Procedures used in handling ordnance on board were consistent with established safety precautions." Then it went on to boast that testimony "also established a long history of safety in submarine torpedoes."

Technically, the Navy told the truth, but in such a limited form that the result was a massive evasion that bordered on an outright lie. In fact, when the court's more detailed findings were finally released in 1993, they showed that it had concluded that the top three probable causes of Scorpion's loss all involved torpedo accidents.

Leading the list was Craven's theory that there was a hot-running torpedo on board Scorpion, perhaps caused when crewmen tested torpedoes in preparation for their arrival home. But then the court veered from Craven's theory that the torpedo exploded on hoard Scorpion. Instead, it speculated, "Acting on impulse, and perhaps influenced by successful ejection of a Mark 37 exercise shot which was running hot in the tube in December 1967, the torpedo was released from the tube, became fully armed, and sought its nearest target, SCORPION."

The court acknowledged there was no evidence of an external torpedo hit but reasoned that there was also a lack of any visible torpedo-room debris near Scorpion, which would prove that the explosion occurred inside the sub.