In the last fortnight I have asked more than 400 members of the general public if I could take a look at their penises. Bar none, they have all acquiesced. That’s not surprising; I’m very persuasive. But what did take me aback was how similar all their offerings were; they either looked like a three-dimensional chimney or dot-to-dot sausage.

I should explain: the penises in question had been drawn by members of the audience in my Edinburgh Fringe show Double Art History — a jolly one-hour romp through all the modern art movements. At the beginning of each show, as a bit of an ice-breaker and as a way to elicit the audience’s art historical knowledge, I ask them to draw a phallus in the style of a modern art movement. As an aide-mémoire I hold up a large white board that lists 25 movements from Impressionism to Conceptual art from which they can choose. Ninety-five per cent plump for either Cubism or Pointillism (hence the 3-D chimney and dotty sausage). This is remarkable. Not just because of the narrowness of selection but also the art historical inaccuracy of their renderings. (The Cubists flattened the third dimension so they could show the back of the box too. And Pointillism is about colour theory and the careful placing of different colours next to each other whereby the viewer mixes the paints and not the artist). Yet despite the gaps in their understanding, the general public are extremely interested in the art of their time, which has rarely been the case in the past.

And that’s what has made doing the show so exciting. To have the audience’s genuine enthusiasm for learning about modern art, combined with the irreverence of the Fringe has created a sort of teaching alchemy. The audience assiduously take pages of notes during the show and then in the exam that they have to sit at the end, they have achieved an incredible average pass mark of 90 per cent (which is about 90 per cent more than they would have achieved at the beginning, judging by their penises).

About half the audience rip their notes out of their exercise books. The other half are far too polite and leave them behind. In the following three paragraphs you can read a digested Twitter-like version of their jottings.

Impressionism — painting outside of a studio with quick, loose brushstrokes to capture an evocative impression of their subject. Van Gogh was an Impressionist but wanted to express how he felt about what he saw so he distorted the subject. This helped to lead to Expressionism practised by artists from Edvard Munch through to Francis Bacon. The Fauves (wild beasts) expressed themselves by painting with bright colours. Jackson Pollock did it by throwing or dripping paint on a canvas. His paintings were abstract — Abstract Expressionism.

Cézanne was very important. He began as an Impressionist but then started to look at a subject from two different perspectives to represent how we see. Picasso and his friend Georges Braque were very impressed and started to paint subjects from lots of different views. This is Cubism. Marcel Duchamp was a Cubist but then changed art for ever. He said the idea is more important than the medium and refused to stick with the limited choice of canvas or stone. So he chose everyday objects and called them art because he had altered their context. This led to Conceptual Art where the idea becomes the medium.

The Dadaists were very cross. They blamed the horrors of the First World War on the Establishment’s reliance on rational and reasoned thought. They radically opposed rational thought and became nihilistic — the punk rock of modern art movements. Dada plus Sigmund Freud equals Surrealism. The Surrealists were fascinated by the unconscious mind, as that’s where they thought truth resided. Piet Mondrian thought he could paint everything he knew, felt and saw by using two lines placed at rectangles and three primary colours. This was called Neo-Plasticism and was inspired by Cubism. So was Futurism, which is Cubism with motion added. Vorticism is the same as Futurism, but British. The Minimalists might represent the real truth because they weren’t trying to represent anything. Performance Art is Dada live.

But it’s not just my audience who have been learning; I have too. I have been amazed by how my audience have immediately regressed to schoolchildren just because the show is site-specific and set in a lecture room. And I had never fully grasped the huge difference there is between the performing arts and all the other art forms. A book, a painting, a piece of recorded music and even a film are fixed — they don’t change. But the performing arts are not just live; they are alive. So, although the content may remain the same, the delivery of it and the response to it are totally dependent on the mood of the performers, the audience and the relationship between the two, which changes significantly every day.

So, in future I’m going to change my policy to live arts: if I have loved the show, great and I’ll leave it at that. But if I’m not sure about it, I’ll go back again because there’s every chance it’s a real gem. Which helps to explain why it is so terrifying being a performer; you simply never know what’s going to happen.

Will Gompertz is a director of the Tate Gallery. His Double Art History is sold out — but may be coming to London

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