Walk up Central Park West, past the Dakota building and all those plush-looking podiatrists’ offices with their gold plaques, and just before you get to the Museum of Natural History you’ll find the New-York Historical Society and Museum at 77th Street (it also houses a great research library, open to all). Descending its steps is a life-size replica of Marcel Duchamp’s Nude Descending a Staircase (pictured below), and on the day I visited some school kids were yelling, "That’s a nude woman? What? Where? I don’t see it."

In his 1970 television documentary for Granada, I Was a Soldier, British filmmaker Michael Grigsby was one of the first to look into the experience of US soldiers returning home from Vietnam. “Vietnam syndrome” may have been a few years away from any formal diagnosis, but Grigsby caught the mood of three young Texans – David, Dennis and Lamar – back from the conflict and struggling to re-engage with a society that has become alien to them.

John Cage is funny: this much we know. The deadpan prankster at the heart of 20^th-century artistic experimentalism was always about the inadvertent punchline, the chuckle that comes from unexpected disjunction, the relief that comes from reminders of the absurdity of reality, as much as he was ever about any engagement with progress, technology, the transcendent. It's entirely natural, then, that Stewart Lee (pictured below), who has spent his whole career reaching outwards from the comedy circuit towards the avant-garde, should want to present his work.

Sometimes a record tells you whether you're going to like it before you've even hit play. With electronica this goes double: track titles like "Scanlon's Leaping Gore Pull", "Pneuquonsis on Return" and "Fewton Tension Chords" are either going to intrigue a potential listener, or make you think "stop playing silly buggers". If the former, then this collection is for you; if the latter, then there's not one nanosecond in the collection of grinding, bending, warping electronic sounds that is going to make you think otherwise.

The first and most unusual aspect of Caro at Chatsworth is that it is there: 15 outstanding sculptures by Sir Anthony Caro, placed in an irregular pattern around the formal 950ft early-18th-century Canal Pond, situated facing the southern vista of the great Baroque house. For these sculptures are tough, the antithesis of any sentimental attachment to a rural Arcadia, almost relentlessly urban and even architectural. Caro once used the term "archisculpture" for his ambitious work.

Conversations between artists both verbal and visual are the flavour of the month: the big voice of Picasso is almost but not quite drowning out a septet of British artists over at Tate Britain. Now joining the chorus is a fascinating exploration of the 1930s, in which the Brit Ben Nicholson and his Dutch friend and colleague Piet Mondrian are described by that hotbed of art history, the Courtauld, as "leading forces of abstract art in Europe”. 

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.