It has been nearly a century since modernism decreed that “art” is whatever is produced by an artist, and “an artist” is whoever claims to be one. Mostly I agree with this, and my eyeballs tend to roll back in my head when the conversation moves on to the “my three-year-old could do this” refrain. But I’ve got to say, with David Shrigley, a lot of me spent a lot of time in the Hayward thinking, “Um, is this art?”

Turner and the Elements is a visual joy and an intellectual pleasure. The backbone of the selection is Turner’s genuine engagement with the scientists of the day. The argument is that he amalgamated the traditional segregation of the elements – earth, air, fire and water – into a fusion of all four; that technically, instead of schematic compositions divided into discernable sections and monocular viewpoints, he painted, so to speak, from the centre out.

In one small room of the Freud Museum, which was once the home of Sigmund in the last year of his life, are the works Jane McAdam Freud made in the final months of her father’s life. Below an imposing photograph of Freud the elder, the progenitor of the clan, are two detailed, tender sketches of Lucian in profile. In the right sketch the dying artist stares resolutely ahead, his gaze, coupled with the firm set of his jaw, capturing a sense of absolute stillness. The left sketch shows the artist now more gaunt, eyes closed, in death, we imagine, or possibly just asleep.  

These are, we are told, David Hockney's landscape works, and in that they depict the outdoors - early Grand Canyons and LA scenes, Yorkshire from the Nineties to now - that is correct. As a description, however, it comes nowhere near encapsulating the mystical, profound, plain beautiful pictures presented at the Royal Academy.

It’s safe to say that the diary of Tryggve Gran does not capture the mood of this centenary exhibition. “This life is of little interest," he wrote; "one day is just as monotonous as the next.” Gran was the Norwegian hired by Captain Scott to teach his men to ski and was in the party which discovered the frozen bodies of Scott, Edward Wilson and "Birdie" Bowers. On the sledge which Scott and his exhausted men had hauled through nearly 1,000 miles, they found 30 pounds of geological specimens. Gran hazarded a sceptical note: “I think they might have saved themselves the weight.”

2011 was a year when now was difficult to find. The YBA/heroic monetarist era was definitively over – though Tracey Emin was accorded a far better retrospective than she deserved at the Hayward (see image below right). Yet whatever will be replacing the dominant art trend of the last three decades, The British Art Show – a vast five yearly survey of cutting edge contemporary art – felt very much not the place to be looking for it.

My Top 10 movies of 2011, in order, are: Mysteries of Lisbon, Melancholia, Meek’s Cutoff, A Dangerous Method, Aurora, Hugo, The Princess of Montpensier, City of Life and Death, The Descendants, Midnight in Paris.

It took a relatively little-noticed television documentary, Vlad’s Army, broadcast in Channel 4’s Unreported World strand to confirm that theartsdesk has a readership in Russia. Peter Oborne’s film (the presenter pictured below) caught the pro-Kremlin youth movement, the Nashi, with its defences down, and the result depicted, no holds barred, how politics works there today.

In a year when eyes turned to London for the riots, the budget cuts and the hacked phones, there seemed to be a fair amount of middle England portrayed by British creatives. Alecky Blythe and Adam Cork’s London Road at the National retold 2006’s Ipswich murders as a darkly comical contemporary musical, with middle-aged gardening competitions and dull community-centre realism success. Tracey Emin’s retrospective, Love is What You Want brought Margate’s grey, salty waters to the South Bank through giant blankets and explosive short films.

While I'm still learning to disentangle my mezzo from my Meistersinger, I enjoyed a lot of the opera on offer in London this year, especially at English National Opera. Parsifal was perfect and Rameau's Castor and Pollux, while probably a little too Germanic in direction with its dancing amputated legs and unerotic nudity, was wonderfully sung. I especially enjoyed the premiere of Nico Muhly's Two Boys, whose internet-era set design suited its perverse modern "love" story.