On six more occasions you can have an ideal experience of dance by visiting the Degas exhibition at the Royal Academy and then going to see Balanchine’s Jewels at the Opera House.

Edit, edit. Inside TeZukA there’s a charming, elliptical, hugely stylish piece begging to be sliced and trimmed into focus - just as the manga master Osamu Tezuka must have daily occupied himself with as he prepared his graphic cartoons. The visuals in Sidi Larbi Cherkaoui’s piece are spectacular video animations of Tezuka’s fastidiously drawn scenes, the kerpows and the Zen landscapes, Black Jack, the transfigured rabbit. If it does nothing else, this show should whet your appetite for manga.

Shen Wei is only 43, but he’s packed an epic amount into his career. A child sent from home aged nine to study opera; an emigrant to New York; a return to China to choreograph the Beijing Olympics. His urge to put this extraordinary tale into dance theatre is understandable. That Re-Triptych, a semi-biographical creation that’s one of the Edinburgh International Festival’s features in its Asian dance programme this year, is only intermittently intriguing to watch, and largely inchoate in choreography, seems also understandable. Some experiences are just too much to render in art.

The bayadere bears on her shoulder a vase of holy water, and the story of the ballet La bayadère is of her refusal to compromise. She could better her life in two political deals: become the high priest’s mistress, or later, when bitten by a poisonous snake, take the antidote and live on while watching her sworn lover marry the princess who he knows tried to murder her. She refuses both. She remains, morally, the vessel of a purity that it would kill her spirit to give up.

The Mariinsky Ballet has just completed a three-week season, with terrific highs (and the odd low). This was the 50th anniversary of the Mariinsky's (then Kirov's) first London visit, in 1961, and it is worth highlighting the role impresarios Victor and Lilian Hochhauser have played in the cultural life of London. They brought the Mariinsky to London in 1961, and, half a century later, they have once more given Londoners a summer of artistic richness, with 10 ballets, six choreographers and numerous casts. We owe a great deal to this extraordinary couple.

So, to work.

This week we've a glittering, shimmering ballet score with an aquatic theme, and a brilliant British pianist shows off his compositional skills. Plus, in a week where we all need cheering up, 20th-century music's scariest genius shows that he had a fully developed sense of humour.

What you see in the picture is the money shot, and yes, it's a miracle that you won't fully believe, even as you watch it. But there are plenty of other belief-defying miracles in the Guangdong Acrobats’ version of Swan Lake - just don’t make the mistake of calling it a ballet, especially not in earshot of the haute-couture Mariinsky Ballet, currently up the road at Covent Garden.

It is claimed that the philosopher GE Moore had a fantasy. After many years’ work, Tolstoy had finally finished War and Peace. Sonya had copied it out for the umpteenth time. The thing goes off to the printer. Peace reigns. And then, in the middle of the night, Tolstoy leaps out of bed, shrieking, “I forgot to put in a yacht race!”

Great Mariinsky ballerinas are a breed apart, even from Bolshoi women. They take the stage with a consciousness of entitlement that’s thrilling to watch, and when this almost sacred sense of mystique and grace instilled in St Petersburg comes with vivid expressive distinction too, then there really is nothing like it. Even if three American 20th-century ballets might not be thought the likeliest territory to make such discoveries, what a night for ballerinas last night was. Viktoria Terëshkina and Alina Somova are on their way to joining the peerless Uliana Lopatkina at the high table.

It is all too easy to be cynical about the ballet version of Don Quixote. With almost no part for the title character, it is a 19th-century Russian take on faux-Spanish dancing, a farce in which the barber Basilio longs for the charming Kitri, while her father wants her to marry a rich fop. As the Radio Times used to say, “Much hilarity ensues.”