The Second Hat-Shape Relationship and the hypothesis of innovation limits to growth The story of technological change and growth that is told by the theory of this chapter is one in which the technological revolution is a phenomenon of the TFA when the key resource ratios R/N and M/K are rising fairly fast to reach their optimum levels, and when the key growth rates n,, n, and a are temporarily significantly higher than their balanced growth magnitudes n and a*. The last two centuries are not the only ones when inventive activity, in terms of the inputs used, has been expanding faster than conventional activity. The history of science and technology provides ample evidence of significant bursts of inventive and innovative work in Europe in the Middle Ages, as well as in the ancient civilizations of the Middle East, China, and the Mediterranean. However, what makes the present technological revolution qualitatively quite unique is the circumstance that the growth rates n, n , , and n, have apparently all been much higher than ever before
over a prolonged period, giving rise to a correspondingly much higher innovation rate with profound implications for the pace of economic and social change in much of the world.