Global population growth is described over practically the whole of human history by assuming self-similarity as the dynamic principle of development. Nonlinear growth is proportional to the square of the number of people due to a collective interaction of an informational nature. Estimates of the beginning of human development 4 – 5 million years ago and of the total number of people who have ever lived since then 100 billion are made. Large scale cycles, defined by history and anthropology, are shown to follow an exponential pattern of growth, culminating in the demographic transition. A veritable revolution, when global population growth is to stabilize at 10 – 12 billion in the foreseeable future.