EYES WIDE OPEN

You have to observe quite a few rules to see the mind-boggling and then heartbreaking David Hockney retrospective at Tate Britain in London, where the life's work of the now 79-year-old Hockney – possibly "the best-known and best-loved artist of our time," according to Chris Stephens, the museum's lead curator – is on display until the end of May, at a price of £19.50 (or about $32) a strictly timed entry. This is especially true if, like your hapless correspondent, you found yourself in Britain suddenly, to attend a funeral, and didn't have a chance to reserve an earlier, expandable entry time in advance and so ended up with no choice but to see the show in the last available 90-minute time slot on a Saturday evening, while gallery employees followed close behind like a cleansing dose of EZ-prep, moving everyone along to the exit.

Then again: It's Hockney. Despite his high-minded and thinky concerns – he is at least as interested in how pictures are made, and in the aesthetics of how we see them, as he is in the pictures themselves – he's still one of the most popular painters in the history of art. He pulled that rare trick off by painting what he liked, when he liked, regardless of what was fashionable and what was supposed to be important and what would allegedly sell. In that regard, Hockney was old school.

He broke all the other rules, which may account for his popularity especially with the British, the most classified and repressed people on Earth. He painted universal things, sights and objects so familiar and common – the intricacies of a houndstooth jacket, a splash in a pool, the geometry of a building or field, a winding road, the dresses of a mother – that most of us gradually forget to notice them, whereupon they become hidden and lost to us. Hockney's talent for seeing glory and importance in the ordinary and everyday has only intensified with age; the older he gets, the more heartfelt his painting is. This can make you wish the Tate's curators had started the show at the end of his life, and worked backward, toward the beginning, so that we might see right away what the rewards of aging are. Alas life, and the Hockney exhibition, don't work that way.

The show is organized chronologically instead, so a 90-minute tour requires strict discipline. You can take in the message of its opening salon, Play Within a Play, dedicated to Hockney's lifelong themes – his preoccupation with wringing three-dimensional feeling and thinking out of two-dimensional surfaces – by looking at any one picture, instead of all of them. This will save precious minutes: That theme doesn't change.

Skip the early paintings, too. I realize how barbaric that sounds, but Hockney's life has given us a lot to look at. Many of the early works date to the infamous 1962 Young Contemporaries show at the Royal College of Art, Hockney's alma mater. That was where he demonstrated at the age of 25 that he could paint in any style, whether it was blocky abstract expressionism or amphetamine strokes such as Francis Bacon's, even as he toyed with the pop art of Andy Warhol and his American contemporaries. (The alpenglow in a picture called Flight into Italy – Swiss Landscape 1962, for instance, is a parody of the work of Morris Louis, the famous op artist who worked in stripes.) The paintings from that time have more at stake, emotionally, than Warhol's: Hockney's homosexual relationships were a frequent theme, though homosexual acts were still criminal offences in Britain.

Go directly to the third room, instead. It's here, where Hockney moves to Los Angeles in 1964, allegedly for the light and the fit young men, and switches to acrylic paintings of precisely gridded modern buildings and swimming pools and lawn sprinklers and naked men climbing out of the pools, that things get recognizably Hockneyed. These are the paintings that made Hockney famous in North America, and L.A. famous in Britain: He thought of himself as L.A.'s chronicler, its first Piranesi. (One of his paintings, A Bigger Splash, ended up as the cover of Reyner Banham's famous book, Los Angeles: The Architecture of Four Ecologies, and was used as the title of an excellent 2015 film starring Tilda Swinton and Ralph Fiennes.)

The 30-ish Hockney loves to paint surfaces, coolness itself: glass, water, pools, shadows made by water on the bottom of pools and the flickering, naked, mostly anonymous young men climbing out of them. Hockney does not apologize for his fascination with the superficial; this is what he sees. But you can't look at a surface Hockney has painted without thinking about the idea of what a surface is, and what lies underneath it and how the one becomes the other. These pictures are still, even static, but your mind swims as you look at them. He more or less stops painting male nudes, incidentally, after homosexuality is decriminalized in Britain in 1967: Once something is permissible and above board and in the open, in Hockney's world, it can't be longed for in the same way. It loses its singularity.

We've hurried into room four of the exhibition now: As a general rule, British gallery-goers are better behaved than Canadian ones, and seldom roll up and park themselves between a painting and another looker who is already there. Manners matter more in the motherland, so you can move faster.

Over time, his Los Angeles paintings become warmer and more naturalistic. He begins to paint couples, skillfully and faithfully. (Hockney started using a Pentax camera's photographs as references for his paintings when he moved to L.A.). But the couples in Hockney's paintings don't interact so much as they occupy separate spaces next to each other. You can, if pressed for time, get away with looking at two high points in room four: Hockney's tragic painting of his friend Peter Schlesinger watching an underwater swimmer in a pool, painted while his relationship with Hockney was falling apart; and the even more famous portrait (again, a double) of his parents – his calm mother gazing warmly at the painter, his antsy father deeply distracted by a picture book. (Hockney's father was an amateur painter himself.) The title of a large-format art book on the tool chest (!) between them is visible to the onlooker, Chardin. Hockney claims he painted it there simply because he liked the word "Chardin." (What he likes, he paints.) But Teilhard de Chardin, the theologian, once said that "what paralyzes life is lack of faith and lack of audacity." Whatever he has been painting and however he has been painting it, Hockney has never lacked faith that what he is doing is worth it, however audacious – such as making "homemade prints" on fax and colour Xerox machines, to list just two of his more unexpected artistic products. Genius may be 2-per-cent inspiration and 98-per-cent perspiration, as both Edison and Einstein said, but it is 100-per-cent confidence as well. You can feel Hockney's daring in every room of the show.

Gallery-goers feel a strong urge to speed through the next room, which contains examples of Hockney's drawing over the years. Try not to skip it: Hockney has always been a brilliant and obsessive draftsman, capable of sketching in a range of styles that stretched from Ingres and van Gogh to Hopper and Saul Steinberg. But there is a lot to fall into in this room, drawings that will sneakily pickpocket your limited time, so move as quickly as you can. This will make you sad, as if you are missing opportunities to experience a unique artist's point of view, but this feeling is unavoidable in an important artist's retrospective, unless you go back and back and back again – and who can do that these days?

It's the next room, A Bigger Photography, where the heart of Hockney's work, and the key to his success as a postpostmodernist, resides. Hockney has had a love-hate relationship with photography: "I do not think the world looks like photographs," he once observed. "I think it looks a lot more glorious than that." The problem, Hockney feels, is that while photographs claim to be accurate depictions of reality, they actually lack the dimension of time. They are most often simply the moment of their taking, whereas a painting is made over time and reflects that physical reality of its making, as well as the continuing way it is taken in by a human observer.

So Hockney set out to make photographs that contained the dimension of time by giving them more than one point of perspective and perception, as Picasso and the Cubists did in their creations.

Hockney begins his artistic destruction of photography modestly, using Polaroids to expand portraits into spaced and separated and multiply focused parts. He later moves on to more elaborate collages of lab-developed pictures. His masterpiece is Pearblossom Hwy., 11-18th April 1986 #1, a photographic collage of a desert intersection. Instead of one shot of a road that vanishes in the distance, Hockney takes many shots of each detail in the picture, thereby ripping off the straitjacket of traditional perspective and bringing every element to the foreground, into the present of the picture. The distant green roadside sign designating California Route 138 is as prominent as the nearby crushed Pepsi can littering the roadside. Hockney needed nine days to take the photographs, and several more to assemble them into a single image. The result, Hockney once told the journalist Lawrence Weschler, is "a more vivid way of depicting space and rendering the experience of space." You no longer think, I could walk into that picture, as you do with traditional photographs. In Pearblossom Hwy., you're instantly surrounded by it.

Hockney then applied everything he figured out in his re-perspectived photographs to his depiction of space in paintings. He was going slowly deaf at the time, which may have had an influence on how he painted space. In the next room, in images such as Mulholland Drive: The Road to the Studio (1980) – the winding commute he made most days – and Large Interior: Los Angeles, an acrylic of a living room, the vanishing points in the pictures – and there are many – change as your eye moves around them, just as it does in the real, artistically unmediated world. The effect isn't simply a trick, but a remaking of the project of art. If the point of infinity in a painting, the vanishing point to which all the lines of perspective drive, is suddenly reversed, and is in front of the painting rather than behind it, the viewer becomes the point of infinity – becomes God. This is the transformation Hockney has been attempting all his working life.

As he gets older – we are almost trotting now, because time is running low, from a room called Experiences of Space to the next two, Experiences of Place and The Wolds – Hockney gets more nostalgic and more personal. The ideas behind the paintings – about form and perspective and colour, about what is real and what is not, about how we depict what we want others to see – are now balanced by the depth of his feelings for his subjects (friends, landscapes, parents, dogs). In 2004, he moved back to his native Yorkshire, and the intensity of his affection for that landscape, and for Los Angeles when he returned there again in 2014, informs his work to the present day. He begins to paint outdoors more and more, in the plein air tradition of Turner and van Gogh (a tradition made possible by the invention of tube paints in the 1840s, but which Hockney makes steroidally new again by creating huge, multipanel paintings 12 feet wide). Working outdoors, he becomes attached to specific views and objects, sometimes the same ones over and over again: trees (Six Part Study for Bigger Trees, say, or Woldgate Woods, which sold at auction for $11.7-million [U.S.] last year), bendy country roads, planted fields, explosions of hawthorn blossoms – massive canvases composed in separate (six, nine, 12, even as many as 60) panels.

This is where you have to spend most of your time in the Tate's retrospective: amid massive multipart paintings of the Yorkshire countryside, of woods and wolds but also of the Grand Canyon, paintings that attempt to shimmer, with their colour and form, as much as they move, perspectivally. Hockney has been faulted by critics of these later-life paintings, and accused of giving in to nostalgia and the lure of prettiness, just as he was accused early in his career of being apolitical, of not painting the darker side of life. But that's the shallowest possible interpretation of David Hockney's work.

Yes, Hockney has always made formal investigations of art and painting, and how they work (including Secret Knowledge, his bestselling book about the until-then-unknown use of lenses in hyper-realistic Renaissance and later painting). But he has also always painted human longing – our fascination not just with what is there in front of us, with what we like and desire and use and notice, but also with what is not there, with what we can't easily have (such as the homosexual encounters of his early work) and thus learn to miss or even willfully ignore (logging is taking place all over Britain, the English landscape is altering quickly, we are less and less in touch with what is in front of us, distracted as we are by our screens, by the technology that transports us somewhere else). The subjects in Hockney portraits are always pausing, watching and waiting; the lobbies he paints are always empty; his sitters are drawn carefully, but within a random emptiness of white and nothingness. Human existence is even more precarious than a tree's.

As for technology, Hockney is too gifted to simply lament it. Instead he uses it to try to bring us back to something bigger and more human than technology. In the second-to-last room of the exhibition, Four Seasons, he abandons painting altogether, and attaches nine high-definition video cameras, each aimed at a slightly different part of the scene than the others, to the back of his Land Rover, which he then drives slowly through one of Yorkshire's tree-arched country lanes, at the peak of each of the four seasons. The results are projected simultaneously onto the four walls of the gallery. The effect is electric and kinetic: You can't stop looking everywhere at once.

Finally, with 10 minutes to spare, if you have literally run from room to room, you arrive in the shattering last room of Tate Britain's Hockney retrospective. It's not the work that's heartbreaking: Hockney has always embraced new technologies, and, just as he embraced acrylics and photography, has most recently been drawing on an iPad, which makes a recording of the picture as it progresses. Many artists would avoid that revelation, preferring to preserve the potentially sausage-like mysteries of creation. Not Hockney: Watching his iPad drawings come together on the screen as he drew them, you still shake your head at his sheer skill, at his unerring eye.

There is no such thing as a failure in these drawings: Every line becomes something that can be used. He binds some of the sketches together into composite multiscreen works, or "prints" them. There is an exhibit of his free-standing iPad sketches as well: wall sockets promiscuously stuffed with converters and plugs, cars on the interstate, a fern in a pot in a mirror, scenes from anyone's day. He has also been making "photographic drawings" (digital photographs recomposed on screen), notably of dancers, a motif Matisse and Degas loved, and card players, a favourite subject of Cézanne. And of course there are the paintings of his own back garden, the view from his bedroom and his studio, where, according to the accompanying literature on the show, Hockney spends a lot of time these days.

That's the heartbreaking part: David Hockney, the sketcher of the world, is 79 now. He had a small stroke in 2012, but continues to work, vigorously. Now living in Los Angeles again, he still paints and iPads pictures and portraits alike. Just as his encroaching deafness in 1979 caused him to sometimes depict space as a function of what he could and could not hear, he refuses to stop looking and drawing, even as his years make it harder to move around and find new things to see, which means he must find new ways of seeing the old stuff.

His art becomes a declaration of the purpose of human existence – to record what we notice, and what moves us, whatever our circumstances. That relentless gaze, that refusal to stop looking for a fresh angle, is the real reason we admire him. Why be conventional, he seems to ask with every picture. It's not as if we have time to spare.

David Hockney is at Tate Britain in London through May 29 (tate.org.uk).