Thorndike's replacement theory was not correct. He was wrong in thinking that only the superficial elements of a task needed to match.

An idea, as an abstract concept, can influence your thinking more on a broader range of problems than only memorising some steps in a procedure.

Learning ideas are useful to a point. To make a general idea useful, some key obstacles need to be overcome:

• We need to notice the idea in other contexts. Research found that people tend not to apply patterns they learn to different domains unless prompted.
• We need to change the idea to suit our current purposes.
• Knowing about an idea is not the same as using it.

Ideas help, but it is just the start. Easy ideas in a field may be the only visible tip of deeper knowledge.

People that develop expertise in multiple areas are able to solve a wide range of problems.

The key is to gain broadly valuable skills:

• Breadth comes from specificity. General skills are built from large libraries of specific knowledge.
• Deeply understanding more abstract ideas extends the range of your knowledge.
• Visible knowledge is built on invisible ones. The easy facts depend on skills that are harder to spot.
• Practice in various real situations because knowledge is not always expressed.