The unthinkable - even in the contained world of classical music - sometimes can be explained only over time.

Such is the saga of a particular lost-and-found Paul Hindemith piano concerto. Its history's many enigmas are being clarified in the new book The House of Wittgenstein (Doubleday, $28.95), and its world-premiere recording, by the Curtis Symphony Orchestra for the Ondine label, will be out in May.

Yet the whole truth sometimes seems as far away as ever, opening incredulity-inspiring vistas and raising even more questions. Why was Hindemith's effervescent Klaviermusik mit Orchester dismissed soon after it was written in 1923, and not found until 2002, in a long-barricaded room in rural Pennsylvania?

The central character here is Paul Wittgenstein (1887-1961), a pianist whose monumental sense of entitlement - one that prompted him, after he lost his right arm in combat in World War I, to commission the great composers of the day to write left-hand piano concertos for him - is explored with bemused clarity by Alexander Waugh in House of Wittgenstein.

This entertaining book allows one to imagine the unimaginable lifestyle of the fabulously wealthy Wittgensteins when Vienna's cultural supremacy crumbled in World War I. With so much money, education, intelligence, and cultivation, the family seemed groomed for greatness.

But what about taste? Before the war, two-armed Paul made his official debut performing a concerto by John Field, an early-19th-century Irish composer who wrote vast amounts of tissue-thin music. A debut? In ultra-sophisticated Vienna? What world was he living in?

His own. Consorting with genius was a near-daily activity for the Wittgensteins. Brahms and Mahler visited. The family owned handwritten autographs by Beethoven. But they seemed to take it casually. Wittgenstein's sister Gretl had her portrait painted by none other than Gustav Klimt; she didn't like the way the mouth turned out, and brought in another artist to fix it.

This was not a happy world; three of eight children committed suicide. But they were so disconnected from reality that decades later, when the Nazis marched into Austria, they were surprised to discover they were Jewish. Raised Catholic, rich, patriotic, they couldn't imagine Hitler wouldn't see things their way.

After all, at the start of World War I, the family had lost much of its fortune by investing in Austrian war bonds (no worries, there was plenty of money left), and several sons had served heroically on the battlefield. Paul survived experiences that would have destroyed heartier souls. Not only did he lose his arm, the amputation was performed in battle, and his so-called recovery took place in some of Siberia's worst prison camps. Waugh is full of grisly details and medical facts: After a limb is gone, the brain still tells you it's there, sometimes with pain. How to kill pain in a limb that no longer exists?

While no amount of money could buy Paul a new right arm, he could buy an entire repertoire of left-hand-only piano works. Today, we hear in Hindemith's Klaviermusik mit Orchester logically molded musical ideas, plus a gorgeous slow movement with one of the most beautiful wind solos this side of the still-to-come Ravel Piano Concerto in G. As the Curtis recording shows, the world was deprived of significant loveliness during the piece's 79-year eclipse. Paul worked long and hard, Waugh reports, before declaring it incomprehensible. And that's not the worst.

Bringing those pieces into being guarantees Paul an honored place in music history, but everything else is suspect. It seems he never quite forgave these 20th-century giants for not being John Field. In addition to the Hindemith, he never played Prokofiev's Piano Concerto No. 4 either. His lack of patience for the pieces was no reason to forbid anyone else to play them, but he had lifetime performance rights and exercised them. "You don't build a house just so that someone else can live in it," he wrote a pianist trying to pry Prokofiev from his grasp.

The analogy is unconscionable: Do you build a grand, unique house and leave it empty when others in the neighborhood badly need it? Maybe - if you're a Wittgenstein. His most famous sibling, philosopher Ludwig, formulated a sophisticated world of ideas but addressed the non-philosophy world in such impenetrable prose that he's far better known than read. These were creatures of great sensitivity. At one point, Paul claimed he couldn't practice with Ludwig in the house because he felt his brother's disapproval seeping through the walls.

Our admittedly retrospective age sees art as something created for the ages. Paul saw these pieces as being created just for him - Waugh quotes him saying so - which is the only possible explanation for his tampering with the greatest piece he commissioned, Ravel's Piano Concerto for the Left Hand. A fascinating integration of French impressionism, jazz, and sinister qualities reflecting a society that survived a world war, it's considered a masterpiece.

Waugh described Paul's treatment of the piece as "demolition." He added his own flourishes, reappropriating lines from the orchestration to the piano solo. Many of those changes were retracted, but in his 1937 live recording, some remain.

One could demonize Paul as a power-mad dilettante. During his negotiations with Benjamin Britten, the composer's partner, Peter Pears, characterized him as "stupid." And Paul's best-known recordings aren't impressive. Yet Waugh presents evidence that he was able to mesmerize audiences - something discernible, in spots, from a close hearing of that 1937 performance, in Amsterdam. His nervous disposition meant his artistry was unusually subject to the ups and downs of his personal life.

He also deserves credit for the survival of the Hindemith, as he emigrated from Austria to New York. But how it ended up in rural Pennsylvania, in a somewhat ineptly made copy, remains mysterious. Even by Wittgenstein standards, Paul's departure from Vienna was complicated: The two eldest sisters, who were getting up in years by the late 1930s, wanted to stay. The bulk of the family fortune was in a huge Swiss bank trust fund, and after painful negotiations much of it was handed over to the Nazis in a humiliating exchange for half-breed status (and thus more rights) regarding their Jewish ancestry.

The sisters remained safe. But for Paul, getting the Hindemith manuscript out of Austria had to be problematic. Musical manuscripts were considered national treasures, and though Hindemith was out of favor with the Nazis, he was German and his manuscripts might have fallen under that provision. But a quickly made copy of his Klaviermusik would not be stopped at the border.

Another theory is that the original manuscript, having somehow been smuggled out, was discreetly sold to a private collector, but quickly copied to make sure the piece didn't disappear. The Wittgensteins were never impoverished - even during the Nazi negotiations, Paul walked away with the equivalent of $10 million - but might there be cash-flow problems? Considering that the widow Wittgenstein was legally blind, selling the manuscript might have been one of several financial lifeboats.

A key Waugh revelation is that the widow's domicile wasn't in gracious Bucks County with its vibrant arts community, but rather in more distant Newfoundland, toward Scranton, on a gated estate where she lived in even greater self-imposed obscurity than previously thought. Was she hiding? From what? Waugh says the widow turned away from everybody. The elderly often do. But you know the old saying: Just because you're paranoid doesn't mean people aren't after you.

Contact music critic David Patrick Stearns at dstearns@phillynews.com.