There's something about the way Wallinger composes apparent futilities with such systematic earnestness that is in itself convincing. One classic here, titled 10000000000000000 (above), is of exactly 65,536 (the decimal form of the title's binary number) stones on a chess grid, a reflection of a superperfect number. At the Baltic until 14 October 2012 Photograph: PR
Exploring the lesser-celebrated side of Britain, last year psychogeographer Sinclair and artist-filmmaker Kötting took to Blighty's waterways in a swan-shaped pedalo. Their leg-powered odyssey from Hastings to Hackney is by turns tragicomic and quietly radical, lit up by folk songs and locals' stories. The results can be seen now in an installation of film, photos and artefacts, to be released in movie form next month. At Dilston Grove, SE16, from 27 till 29 July 2012 Photograph: PR
Whether photographing a giant or schoolgirls, Diane Arbus had a genius for revealing her subjects' outre side. The 32 photos here focus on modern tribes, exploring the idea that dressing up or getting into disguise can make you freer to be yourself. There's plenty of strange glamour, from puckish, bare-chested youths in makeup to society dames with matching pillbox hats and elegantly held cigarettes. At Timothy Taylor Gallery, W1, from 26 June to 17 August 2012 Photograph: The Estate of Diane Arbus, LLC
Jenny Saville's monumental paintings of flesh in the raw have made her one of Britain's best-known artists. Her women's engorged bellies, swollen breasts and thighs, shouting of anguished self-image in bloody gobs of pigment, have garnered her a public following to rival the approval heaped on her by critics. This is her first big public gallery show in her home country, tracing her development as a painter over the course of two decades. At Modern Art Oxford and the Ashmolean Museum of Art and Archeology until 16 September 2012 Photograph: PR
A grown man entertains himself in private by stuffing red and blue marker pens up each nostril. He grips two photo-film canisters in his clenched eye sockets and, as a finishing touch, his mouth is gagged by holding a stapler like some kind of robotic beak. If all this weren't loony enough, he takes a photograph of the whole grotesque affair and presents the image as a work of art. The surprising thing with Wurm is that such dada daftness doesn't look just tiresomely wacky, like so many drunken pranks. Delightfully, it's somehow very sophisticated cultural mischief. At Open Eye Gallery until 2 September 2012 Photograph: PR
Madge Gill is one of outsider art's most fascinating figures. A Victorian spiritualist, she began obsessively creating drawings guided by a spirit known as 'Myrninerest', whose signature was often seen in the corner. The repetitive intricacy of her work is tireless: dense squares, cross-hatching and swirling forms, from which spooky, feminine faces peer. At the Nunnery, E3, until 23 August 2012 Photograph: Ollie Harrop
Stanya Kahn's videos are all self-consciously faked, every emotion and thought acted up and played out. But you're reminded of the camera's ubiquitous presence; the costumes are tatty and the props throwaway. In Lookin' Good, Feelin' Good she roams the streets dressed as a giant foam penis. For It's Cool, I'm Good she explores LA wrapped in bandages like an escaped hospital patient. At the Cornerhouse until 16 September 2012 Photograph: PR
