In the late afternoon of Thursday, Oct. 4, 1973, a phone rang in London. On the line was a tense man who wanted to speak to “Alex” about “a lot of chemicals.” Alex’s name wasn’t Alex and there were no chemicals. What the caller was saying, in an agreed-upon code, was that a cataclysmic war was about to break out in the Middle East. By the end of the weekend thousands would be dead.

The man on the phone, Ashraf Marwan, was an official at the pinnacle of the Egyptian regime, an aide to President Anwar Sadat and the son-in-law...