Progressive educationalists like Robinson frame existing knowledge as the enemy of new ideas. But at the most basic level, all of our new ideas are made up of old ones: to imagine a winged horse, you first need to be familiar with the ideas of horses and wings; to create a smartphone you need to know about computers and phones.

Here are the key takeaways: New problems worth solving come from old solutions. There is always an old way. Innovation is fundamentally about causing a switch from the old way to a new way. The best way to cause this switch is by anchoring new solutions against problems caused by old solutions—i.e., breaking the old way.