Capital accumulation can spur catch-up growth. But capital accumulation becomes less potent as countries grow wealthier. How do we get more and better ideas?
The creation of new ideas is not random. Key ingredients that spur new ideas–they grow in the soil of good institutions. The flying shuttle improved looms.
John Kay invented his flying shuttle in 1733 and tried to acquire a lucrative patent on his device from the French government. Wikipedia explains:
In 1733, he received a patent for his most revolutionary device: a “wheeled shuttle” for the hand loom. It greatly accelerated weaving, by allowing the shuttle carrying the weft to be passed through the warp threads faster and over a greater width of cloth.It was designed for the broad loom, for which it saved labour over the traditional process, needing only one operator per loom (before Kay’s improvements a second worker was needed to catch the shuttle). 
Kay always called this invention a “wheeled shuttle”, but others used the name “fly-shuttle” (and later, “flying shuttle”) because of its continuous speed, especially when a young worker was using it in a narrow loom:
Check out this visual on how the flying shuttle works:
Kay had hostile opponents for the reasons mentioned in the video above–his invention was putting a lot of other businesses out of work.
Interesting history on competition.