Artist and critic Matthew Collings purported to set out the rules of abstraction through taking the viewer on a very bumpy ride through 20^th century painting, with a nod to Cézanne to get us started. He set the scene by telling us that abstraction as a concept in art has been around for 100 years and early on we were presented with a genuine surprise: the large canvases, in relatively soothing colours, of freehand geometric forms that appeared wholly abstract by the almost totally unknown female – yes, female – Swedish artist Hilma Af Klint, from 1907.

It’s 70 years since Mondrian died in New York, leaving unfinished his last painting, Victory Boogie-Woogie, an ebullient title quite at odds with the buttoned-up asceticism we normally associate with this artist. The Courtauld Gallery showed a small survey two years ago, which paired his flat grid compositions with the paintings and white reliefs of Ben Nicholson, focusing only on his two years in London (1938 to 1940).

Bridget Riley’s mural for St Mary’s Hospital in Paddington, which was unveiled in April this year, is something I’ve seen only in photographs. And on seeing it for the first time my reaction, I’m afraid, was, “Oh no". It obviously didn’t help that the photographer had wildly exaggerated the one-point perspective, so that the parallel lines of two facing walls converging sharply made you feel the vertiginous pull of a rabbit hole.

In a near-perfect, outward-looking Swiss city sharing borders with France and Germany, on a series of cloudless April days that felt more like balmy June than capricious April, anything seemed possible. The doors of perception which had slammed, I thought, irrevocably shut for me 45 minutes and four chords into the first act of Philip Glass’s Satyagraha could well open again in two concerts – London is to get three on a UK tour this week - around the musical Minimalist theme from Dennis Russell Davies and the excellent Basel Symphony Orchestra.

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”.