February 16, the Soviet foreign minister handed a memorandum to the American ambassador to Moscow, charging the United States with violating the 1963 Limited Test Ban Treaty by dropping bombs on Palomares and contaminating the atmosphere. The following day, the same day that Guest laid out his search plans for the chief of naval operations, the Soviets upped the ante. At a disarmament conference in Geneva, the Soviet delegate, Semyon Tsarapkin, took the floor and read the accusatory memo to the entire assembly. Washington, said Tsarapkin, was endangering foreign lands and people with its B-52 missions. Only “a fortunate stroke of luck” had prevented an atomic catastrophe in Spain; America must end the nuclear flights without delay.

U.S. diplomats dismissed these charges as ridiculous, but they made international news and refocused attention on the missing bomb. And the Soviets weren’t the United States’ only diplomatic headache. A week later, President Charles de Gaulle of France announced that, by 1969, all military bases on French soil would be taken under French control. The United States, at the time, had several large Air Force bases in France, as well as a Navy headquarters and a number of Army supply and communication centers. If de Gaulle kicked the Americans out of France, it would likely heighten the importance of the U.S. bases in Spain. Ambassador Duke received assurances that the Spanish government would not take “Machiavellian advantage” of the situation, but every day the bomb stayed lost, the Spanish government gained more diplomatic clout.

Though not directly involved in any of these incidents, Admiral Guest surely felt pressure from all of them. His daily situation reports were often read by the chief of naval operations and sometimes by the secretary of defense and the president of the United States. Having to report no progress, day after day, was tremendously demoralizing. Red Moody said that he had never — even in combat — seen a flag officer under such pressure as Guest.

The admiral soon faced a problem closer to home: a Soviet spy ship, the Lotsman, cruising near the search areas. Guest, with permission from the Spanish, had established a large restricted zone in the Mediterranean encompassing the Alfa and Bravo search areas. He had then sent a Navy destroyer to patrol the boundaries. On February 17, the destroyer reported the arrival of the Lotsman. The Soviet ship was well known to the Americans — she usually cruised near Rota Naval Air Station — and she didn’t try to hide. For about two weeks Guest sent the Navy destroyer USS Wallace L. Lind to shadow the Soviets, just in case they tried any funny business.

The Lotsman sat low in the water, covered with rust. If anything happened, she was no match for the Lind. The Navy destroyer, about twice the size of the Lotsman, was built for antisubmarine warfare and armed with torpedoes, bombs, and guns. But occasionally the Soviets pushed their luck. On at least one night, the Lotsman steamed toward the Lind, trying to intimidate the American ship and force it to give way. The Lind held its ground. Anthony Colucci, the twenty-five-year-old lieutenant deck officer, recalled the Lotsman coming within twenty-five yards of the Lind. Colucci, who had served on an amphibious ship during the Cuban Missile Crisis, knew a few things about Cold War tension. But this was personal. “There were certainly more important strategic concerns,” he said.

But “when the captain is asleep and the Lotsman is coming in closer and closer to me, what was I thinking? I was thinking ‘Oh crap, there’s gonna be a collision.’” News of the Lotsman’s snooping rippled through the task force, inviting speculation on what the Russians might try next. At the time, the Soviets had two advanced submersibles that could dive to 6,500 feet. Supposed they pulled a Thunderball, dove down, and picked up the bomb themselves?

Or, even worse, suppose a Soviet submarine slipped into the search area and released a timed nuclear device? The bomb would explode, and everyone would point fingers at the Americans.

The Lotsman stayed on scene until early March, usually cruising between five and eleven miles away from Alfa 1. Then she vanished. Nobody knew what she had learned during her stay.

From Washington, Guest’s Technical Advisory Group kept a close eye on the developments in Spain.

Even if the bomb had fallen into the sea, Guest might never find it. If the admiral came up empty-handed, the Navy would have to stand before Congress — and the secretary of defense — and explain why it had spent so much money on an unsuccessful search. Heads would roll.

The TAG understood this clearly. The advisers were not only sending gear to Spain, they were also thinking about the endgame. If the search failed and the Navy brass were hauled before Congress, they would need proof that Guest had done everything possible to find the bomb. Or at least they would need something that seemed like proof-some fancy numbers to wave in front of the politicians. What they needed, they decided, was math.

John Craven of the Technical Advisory Group called Captain Frank Andrews, who had overseen the search for the USS Thresher, and asked for assistance. Andrews had retired from the Navy but was happy to help. He suggested that Craven call Wagner Associates, a small consulting firm outside Philadelphia. Soon Dan Wagner, the owner of the company, was flying to Washington with a member of his staff, a probability expert named Tony Richardson.

In Washington, Craven briefed the two mathematicians on the situation and gave Richardson a rough “probability map” that he had sketched. The map, which showed the area off the coast of Palomares, resembled a contour map. However, the contours on Craven’s map showed not the height of a mountain ridge or the depth of an ocean trench but the probability that the bomb had fallen into certain points in the sea. Craven hadn’t had much information when he had drawn the map, so his initial stab basically outlined what everyone already thought: that the bomb lay either right off the beach or somewhere near the fishermen’s sighting. Craven gave Tony Richardson a copy and sent him and Frank Andrews to Spain.

On the plane to Madrid, Richardson sat next to Andrews and discussed his strategy, sketching out ideas on graph paper. He knew basically how to run a systematic search — mathematicians had been working on search theory since at least World War II. First he had to develop a probability map laying out where the bomb might be hiding. Second — this was the tough part — he had to find a way to evaluate the search as the Navy carried it out. And not just say “good” or “bad” but quantify the search, evaluate it mathematically. Then, as the search continued and new information came in, he would update the probability map, hopefully narrowing down the search area. Richardson could keep the analysis going until the Navy found the bomb or gave up the search.

On the plane, Richardson explained his system to Andrews. He thought he could call it “search failure probability.” In other words, after the Navy had searched a given area, this was the probability that the bomb was there but the Navy had failed to find it. Andrews shook his head.

Tony, he explained, you have it all backwards. You are dealing with the Navy. You can’t talk about failure! You need to talk about success. Richardson objected, showing Andrews a sample probability he had plotted on his graph paper. Andrews looked at it and frowned. The line that Richardson had drawn sloped downward toward the bottom of the page. It looked like a business with a bad quarter or a stock market crash. No, no, no, Andrews explained. In the Navy, graphs need to point up.

Richardson and Andrews reported to Admiral Guest on February 22. Richardson’s reputation had preceded him. The ship had prepared for the arrival of the distinguished mathematician, assigning him a generous stateroom with a private sink and stewards. So Guest was a bit taken aback to discover that Dr. Richardson was a baby-faced twenty-seven-year-old who looked even younger than his age.

Eyeballing this new member of his team, Guest asked Dr. Richardson what he could do for the mission. Richardson launched into a description of his plan — now called search effectiveness probability — and an explanation of Gaussian probability distributions. As Guest’s eyes glazed over, Andrews stepped in and cut Richardson off. After the admiral escaped, Andrews turned to Richardson. Would this kid ever learn? “Tony,” he said, “don’t talk about Gaussian distributions to an admiral!” Later, Guest pulled Frank Andrews aside. “Where the hell did you get this high school kid?”

Soon, however, Guest began to see the value of his new addition. Richardson, working with the grid overlay of the search area, assigned each square a “search effectiveness probability” (or “SEP”) number between 0 and 1. A low number, close to 0, meant that if the bomb lay in that square, searchers probably wouldn’t have found it yet, either because they hadn’t searched there or because they hadn’t used the proper tools. A higher number, such as.95 or.98, meant that if the bomb rested in that area, the searchers probably would have found it by now. The goal was to get each square on the grid from a low number to a higher one.

Some on the task force had doubts about Richardson’s system. After all, the information he used to make

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