To understand one of the secrets of creativity, just peek into an art classroom in Denver, Colorado. The teacher asks her pupils to imitate the style of Vassily Kandinsky. The students mimic Kandinsky’s geometric abstractions, mastering brushwork and learning colour theory.

If that was all there were to the lesson, it would be a hands-on class in art history. But the art teacher asks the students to cut up their paintings and build 3D sculptures out of the pieces. They have all started with the same source, but their works all end up looking extremely different: some rise straight up in a column, while others are a jigsaw of different forms and angles. The students learn to treat the past not as a landing point, but as a launching pad.

Creativity does not emerge out of thin air. Instead, it is a process of derivation and extrapolation. No idea is ever wholly original; there is always a link from the known to the new. We rely on culture to provide us with a storehouse of raw materials which we then transform. Each generation adds another layer to the cliffside of history.

One of the keys to fostering inventiveness is not to treat the past as sacred. Artists and musicians sometimes earn reputations as provocateurs for their irreverent treatment of history – but they are actually doing what is necessary: putting culture on to the workbench and remodelling it.

Beethoven didn’t write symphonies because he thought there was anything wrong with Mozart’s. Picasso didn’t paint variations on canvases by Velásquez and Manet because he rejected the old masters, but rather because he revered them. While we sometimes tinker with the imperfect, we also remake what we love, showing our admiration for the past by passing down its DNA.

Sometimes inventors attempt to cover their tracks. Stravinsky denied that The Rite of Spring, his revolutionary ballet about pagan Russia, included any actual folk tunes, but scholars found a volume of them in his library after his death.

It took Apple seven years to acknowledge that the iPod was based on schematics created by inventor Kane Kramer two decades earlier. But whether it’s obvious or obscured, new ideas always have a family tree.

Creative minds always start from a precedent and move from there, but how far should they go? The challenge is that staying too close to the familiar can dissatisfy, while wandering too far can fail to find followers. As a result, inventive people cover the spectrum from the incremental to the disruptive.

Thomas Edison made small changes to the telephone, dramatically improved the lightbulb – and at the far end imagined underwater cities powered by solar energy.

The designer Norman Bel Geddes designed a host of practical products, such as cocktail shakers and furniture – but he also ranged much further, sketching flying cars and houses in which the walls rose up into the ceiling like garage doors.

Beethoven’s Diabelli Variations illustrate the same principle of covering the spectrum from familiar to novel: the first few variations stay recognisably close to what’s come before, and then Beethoven gradually drifts further away until we barely recognise the theme any more.

The DNA of the original is still there, but by the end it has evolved to something new. Each of us is creating our own variations on themes passed down to us. We’re at our most inventive when we summon history not to limit our imaginations, but to launch them. That’s a lesson that can start young – and that never ages.

The Runaway Species: How Human Creativity Remakes the World by Anthony Brandt and David Eagleman is published by Cannongate at £20. To order a copy for £17, go to guardianbookshop.com