There are various disinterments of supposedly iconic dance-makers going on in this year's Dance Umbrella (some live ones more dead than the dead ones), but no one is going to beat for sheer éclat Lucinda Childs’ astonishingly beautiful minimalist 1979 creation Dance, on this week at the Barbican.

Minimalism is now a comfortable old sofa for today’s generations of dance-watchers, often handed very small platefuls of ideas, but this 60-minute piece has an understated poise and rich cleverness that shows American modern dance at the very top of its artistic game.

Art about art is one of my favourite kinds of art. Paintings, drawings, sculptures, films - works of art which talk about what art is, what the image is, what art can represent and what it can't - all appeal. It is not just a picture of some prostitutes and some African masks - it is Les demoiselles d'Avignon by Picasso and it blows apart the boundaries of painting by cramming three dimensions into two. And then there is Frank Stella, in a new survey of his career at Haunch of Venison, the ultimate modern artist-about-art - and I'm left cold.

Exhibitions with titles appended "in Britain" or "and Britain" tend to be the kiss of death: indicating concentration on a brief and insignificant visit, on the subject’s impact on British art or – even worse – the influence of local collectors on his or her reputation. With Mark Rothko, though, it has to be different. The New York abstractionist’s current near-sacred status is such that a show of his dog-ends and nail clippings would probably prove a major draw.

Nine out of 10 attempts to feed an audience's visual responses to abstract music are doomed to failure; a great communicator will always conjure stronger pictures in the listener's mind. And there's no doubt that young violinist Alina Ibragimova communicates at the highest level. But here she simply held her own to work in shadowplay with both the mysterious spaces of London's most atmospheric venue and the even more intangible visions of twins Timothy and Stephan Quay. Their film around Bartók's Solo Violin Sonata, though defying intellectual analysis and easy correspondence with the musical ideas, is pure choreographic poetry.

A town in desperate need of regeneration commissions David Chipperfield, the architect of the moment, to build an art gallery in the hope of attracting visitors with deep pockets. In case you are suffering an attack of déja vu, this is not an action replay of the opening of Turner Contemporary in Margate a month ago, but Wakefield’s turn to use the same tactics.

Max Bill might be the missing link in modern art. He died only in 1994, yet he studied at the Bauhaus in Dessau in the 1920s, taught by Josef Albers, László Moholy-Nagy, Paul Klee and Kandinsky. It is hard to imagine that someone who was working at full strength less than 20 years ago could have a past that is so strongly entwined with these legendary names – hard to imagine, that is, until one looks at the work displayed in this fine retrospective, which even so manages to encompass only five decades of a nearly seven-decade-long career.

John Cage, the focus of an adventurous three-day mini-festival in Bristol, is possibly one of the most influential figures in 20th-century culture. As much a practical philosopher as a composer of note, he made artists, writers and musicians think about the nature of chance, our place in nature and the role of the subject in the creative process.

At its best, and most preposterous, John Cage's work can be a mind-cleanser. The overwhelmingly silly randomised conjunctions and ontological punning of the great Zen master of the 20th-century avant-garde can coax and trick you into letting go of categories and judgments, scale and expectation, and just letting yourself get swept along with the gloriously complex and profoundly nonsensical multidimensional parlour games. Where some artworks might make you feel like you're on drugs, or