How Hockney got me thinking about four dimensional chairs

It’s all a matter of perspective

Earlier this week, we went to the David Hockney immersive exhibition at Lightroom for my wife’s birthday. (For birthdays, we often take the day off and visit an exhibition, accompanied by a nice leisurely lunch – this time with a newborn in tow).

Lightroom is an amazing new venue, and worth a visit if you’re in London (I now regret missing the previous exhibit on the moon landings). But one idea jumped out for me in particular about the Hockney show, because I hadn’t seen it before at previous exhibition of his.

It was an idea that starts with a chair. If you were asked to draw a chair, you might produce something like the following (except probably better):

In other words, it’s a drawing as if you’re standing looking at the chair. But Hockney made the point that this isn’t how we actually see chairs. We don’t walk up to the chair with eyes closed, open them up for a static moment like a camera shutter, then walk off again. We see it from one angle as we approach, then another as we depart.

In his 1984 piece The Perspective Lesson, Hockney therefore suggests that if we want to capture in a single drawing the chair as we actually see it, we’d end up like something like this:

Hockney contrasted the traditional single-viewpoint perspective in Western artwork with alternative approaches, like Chinese painting, where the perspective tracks across the image. Earlier movements like cubism also showed objects from multiple angles in the same piece, in an attempt – through abstraction – to get closer to the real experience of being there with the object.

Ultimately its a problem of dimension: how to convert a three dimensional world into a two dimensional drawing. One of the most familiar examples of this problem in daily life is with map projections, which attempt to compress a 3D globe onto a 2D page:

Source: Justin Kunimune, Strebe via Wikipedia

But the Hockney exhibit got me thinking whether it’s just a three-to-two dimension problem. It seems our perception of a chair, or globe – or any other object – is actually more like four dimensions, because we observe it from multiple angles. Although the chair itself is three dimensional, and our brains combine two slightly different 2D images from each eye to produce a single 3D perception, the information needed for a person to observe and understand it has an extra dimension: time.

The idea that we perceive objects in terms of both space and time felt a bit obvious once I’d thought about it (and had a sit down). But that’s one of the nice things about art: it reveals things we might have seen before but not properly appreciated.

As Hockney put it: ‘The world is very very beautiful if you look at it, but most people don’t look very much.’