A population of breakthrough scientists is considered to trace the development of science in both old Arabic-Islamic and Western civilisations. A statistical method is used to trace variation in the scientist population over several centuries. The analysis shows that the following: 1) There has been growth in Arabic-Islamic sciences for a period of three centuries, which was then followed by a period of decline. The decay time is approximately eight centuries. 2) The growth of science in Western civilisation started in (...) approximately 1200 AD and continues to grow. The behaviour of the curve can be attributed to different historical events, particularly those events that may have affected scientific development. (shrink)