The first is the childhood accident that nearly curtailed his cello-playing career before it had even begun. At the time, the 12-year-old Slava - to use his Russian diminutive, which also means "glory" - loved the piano (his mother's instrument) even more than the cello (his father's), but what he loved most of all was beetroot salad. And it was one day in 1939 while dancing wildly round the room, desperate to dig into the big bowl of the stuff that his mother had just made, that Slava leapt on to a stool, slipped and fell backwards onto his right arm. At first, his mother failed to answer his cries: "We lived in a big communal flat," he recalls, "36 people, one loo, one bath. She thought it was just the neighbours arguing again." Eventually, of course, he was found and rushed to hospital, where he was operated on and his arm encased in plaster.
So far, so good - except that, when the cast was finally removed, it appeared that the broken bone had been wrongly set. Slava could no longer even turn his wrist. Worse, he could no longer play his cello. "I just couldn't put the bow to the strings." The doctors who had botched the job offered to cut him open and try again, but he refused. It was a catastrophe, indeed.
But then Slava noticed that, after a hot bath, he could move his wrist a tiny bit more. Day after day, he managed to edge his bow a degree closer to the strings. "That's maybe half year I work," he says, bypassing his interpreter in his eagerness to tell the tale in his own inimitably inflected English. "I dying for that day - that give me such strength inside. And when, after six month, I touch with bow my strings, that already was God open for me the life of the future." He doesn't know what he would have become otherwise: a pianist, perhaps; maybe a composer. "But, after that, I know it's as cellist I come."
A year later, he played so brilliantly in his end-of-term recital that one of his teachers joked: "Maybe I should break all my other students' arms as well!"
In 1945, he won the gold medal in the first All-Soviet Music Competition and was on course to become not only the greatest cellist of the past half-century but the player who has single-handedly more than doubled the cello's repertoire through his passion for performing premieres (over 100 so far - solos, sonatas, chamber pieces and concertos). It really is a miracle, especially when you consider that his arm is still broken - and, putting his left hand to his right wrist, he wobbles the bone an inch or so out of its socket to prove it.
The second example is his expulsion from Russia in 1974. "Before that," he reveals, "I was thinking of suicide. I thought everything was lost." And so indeed it seemed. Overnight, Slava and his wife, the Bolshoi prima donna, Galina Vishnevskaya, found themselves downgraded from golden couple to "non-persons". While she was repeatedly passed over for leading roles at the opera, he was no longer invited to give recitals or to conduct the major orchestras; the only dates they were offered were in obscure provincial towns - and, even then, they would usually arrive to find the concert cancelled or the hall deserted. Their phones were tapped, their homes bugged. Their crime? That in 1970 Slava had written an open letter in support of Alexander Solzhenitsyn, the dissident writer whom he was sheltering at his dacha outside Moscow.
After such persecution, gaining official permission to work abroad seemed like a victory. But when, in 1978, Slava and Galya were suddenly stripped of their Soviet citizenship by President Brezhnev, their extended "foreign tour" was unilaterally transformed into permanent exile, and the bottom seemed to have fallen out of their lives once again. "But, of course, while I have been living in the West," he cheerfully explains through his interpreter, "I have achieved enormous growth as a musician. Because," he himself cuts in, "I had enormous possibility for work with the best orchestras. That's why I so appreciate for the West, that's why I still not take Russian passport." Not even after he made his long-awaited return to Russia in 1990, with his Washington-based National Symphony Orchestra in tow.
A year later, Slava was back in Russia again, this time alone and unheralded, when he famously flew into Moscow at the very height of the August coup, to stand shoulder-to-shoulder with Boris Yeltsin in defence of Russia's fledgling democracy. This is the third example he offers to justify his optimistic outlook on life.
"I was convinced they would shoot me," he insists. "I went there, knowing I would be killed. And again God saved me. It was so unexpected, our victory - it was a miracle."
But what drove him to undertake so apparently suicidal a mission? The music of Shostakovich, it seems.
Sitting in his Paris flat on the day of the coup, Rostropovich scanned Russian TV for hints of what was happening back home. "But all they showed was a young pianist playing Chopin, then Swan Lake, then Swan Lake again."
Finally, there was a press conference. One look at the "ugly, mask-like faces" of the plotters, he says, and he knew the worst. And then, as the conference ended, he heard music in his head. "It was a phrase from the Eighth Symphony of Shostakovich," he recalls. "There was such sadness in it that I started to cry. And immediately I began writing a letter to Galya: `Please forgive me,' I wrote. `I'm going to Russia, I'm going to be killed.' The next day, I said I was going to the bank, but I went to the airport instead." The rest, as they say, is history. Democracy was saved, or so it seemed, and Slava was rewarded with the new State Prize of Russia (to go with his Stalin and Lenin Prizes of old).
The Eighth Symphony - supposedly a response to the Nazi invasion but arguably also a covert portrayal of the terrors of Stalin's genocidal regime - was, as it happens, the first of Shostakovich's works that Rostropovich ever heard, shortly after joining the Moscow Conservatoire (aged 16) in 1943. It is also the first work in an eight-part chronological survey of the composer's late symphonies which Rostropovich is conducting with the LSO at the Barbican this month.
No one knows the composer's works better. Having talked his way into Shostakovich's orchestration class in 1944, Rostropovich graduated from pupil into friend during the dark days of February 1948, when - as a result of Zhdanov's notorious Anti-Formalist Resolution - Shostakovich was instantly dismissed from the Conservatoire ("On the grounds that he lacked the right qualifications!" Slava scoffs) and, along with Prokofiev and other supposed "modernists", had his music banned. "It was very easy to become Shostakovich's friend at the time," Slava now wryly recalls, "because so many others deserted him." Easy or not, it remains to his eternal credit that he risked his own young career by continuing to associate with the banned composer and to champion his music.
His reward came later, in the two concertos that Shostakovich wrote for him. Ask him about the first (for which he will briefly swap conductor's baton for cellist's bow during the fourth of his LSO concerts) and this walking compendium of musical anecdotes will most likely tell you the one about the vodka - of which they both drank so much after their first run-through of the work together, and even more after their second, that the third time round Slava has no idea what he played, while Shostakovich was too sozzled to notice.
"Yet, if he appeared here today," Slava insists, "and asked me to sit down and have a drink, I tell you I wouldn't dare. I would have to say no. Because, during the time that he has been away, he has become a great, great man."
And it remains the one real regret of his exile years that he wasn't able to see him again before he died.
Mstislav Rostropovich conducts Shostakovich with the LSO: Sat, Tue, Wed, 17, 20, 22, 25, 28 Oct, Barbican, London EC2, 0171-638 8891