On the Origins of Randomness

This presentation discusses the definition of randomness, the sources of randomness in the physical system (the Universe) as well as in the formal mathematical system. I discuss how randomness, through nonlinearity and chaos, the second law of thermodynamics, the quantum mechanical character of small scales, and stochasticity, is an intrinsic property of nature. I then move to our mathematical system and show that even in this formal system we cannot do away with randomness, and that the randomness in the physical world is consistent with the origins of randomness suggested from the study of mathematical systems. Many examples are presented ranging from pure mathematical processes, to natural processes, to social processes, and to life in general, which clearly demonstrate how the combination of rules and randomness produces and explains the world we live in. Finally, a possible explanation is provided as to why rules and randomness cannot exist by themselves but instead, they have to coexist.