Why must the rate of GDP growth be positive?
You would expect the rate of growth to be generally positive because inventing things or inventing more efficient ways of doing things, is generally a one way process - things don't get un-invented. So we would expect things that are made by machines to be made ever more quickly as the machines evolve and improve. Periods of negative growth are likely to correspond to some financial cock-up (e.g. asset bubbles) or increasing scarcity of some natural resources for which a replacement can not be found.