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For me, the greatest lesson of the cool Google Arts and Culture selfie-match app, the one that matches your picture to a similar-looking portrait in an art bank (only recently available in Canada) is that I need to trim my beard. I took a selfie that somehow exaggerated the bushiness of the mustache, and so all the images I got back were of dudes with enormous drooping handlebars. Apparently I look like an ad for zeppelin-flying, circa 1905. This must be rectified.

In other words, the impulse to see what famous portrait-sitter I resembled was an essentially self-regarding one: I want to see not so much what paintings look like, but what I look like.

The selfie-search function of the Arts and Culture app is only a tiny part of it (albeit by far the most popular part – it was the most downloaded free app for iOS and Android last week). The app suggests museums to explore, links paintings by colour palette and shows you through "street view" the interiors of art galleries around the world. By now it has banked photos of the contents of 1,500 cultural institutions in 70 countries, and is adding more.

The selfie-match function is the result of incredible technology. It uses facial-recognition software – something I remember as a menacing sci-fi concept 20 years ago. The search, through hundreds of thousands of images, takes only a second. The capacity of this thing is staggering.

Before you give your likeness to the bunkers of machines at Google, to do with it whatever they want, they do provide you with a quick reassurance that they will not store your face or use it for any purpose other than this. Okay, Google! This silly little party game is too much fun for it to make anyone worry about the surveillance possibilities offered by the facial analysis of millions of volunteers.

The more serious objection to the app has been about its limited racial representation. People of colour have discovered, not very much to their surprise, that they are not very well-represented in the museums of Europe and the United States. Images found to match people of African descent are particularly few, and they tend to be either of racial stereotypes (servant, entertainer) or ancient tribal sculptures. Google says it is trying to rectify this by adding ever more museums outside Europe to its roster, but undoing centuries of Eurocentrism in art is going to be a long project.

A milder objection is that no matter who uses the app, they are going to find it is not terribly accurate. It focuses on crude shapes, posture and other superficial distractions such as facial hair. A white guy in a beard, according to these algorithms, looks pretty much exactly like every other white guy in a beard in the history of Western art. (One of my matches was someone from 1752 "in Turkish garb" with a beard the size of my cat; I don't resemble him in any way. But I get the message about the beard, Google.)

Most people are not going to bother looking up the detailed history of each of the artworks found – there are quite a few links to go through to get to the hosting museum's descriptions, and those may be in other languages. Again, the point here is not so much to explore art as to learn what feature of your own physiognomy stands out the most to a computer program. It is a primitive robot caricaturist, one that seems to snicker at you.

Not that looking at lots of little-known portraits of long-forgotten figures isn't fun in itself. Artworks that make it to museums tend to be accomplished. They look nice on incandescent screens. We now have access to high-definition, brightly coloured, glowing reproductions of the most beautiful art in the world.

But consider this puzzle: We could in theory furnish our houses with these. We could put up flat screens on our walls and have our favourite paintings in high definition in our homes – a Matisse here, a Gainsborough there. We could change this exhibition daily. Why do people not do this? Why do people instead put up on their living-room wall their aunt's rather clumsy landscapes?

Of course your aunt's amateur painting is nicer than near-perfect LCD reproductions. Your painting is literally duller: It reflects light rather than emitting it. But it is unique and original. You have a connection to it. Above all it is hand-made. The brushstrokes you can make out are the traces of a moving body. Screens, no matter how advanced, will always screen: Whatever you see on them is mediated by pixels. You will always know they are not real.

This is why the new accessibility of millions of beautiful historical images will not herald a new era of art appreciation. The tiny pictures are useful references to real things, like encyclopedia entries, but they won't have the draw of objects. Other than that, they will be useful in indicating that you need a shave.