Five Answers on Randomness

Five brief and highly biased answers to five questions on rand omness posed by Hector Zenil: Why were you initially drawn to the study of c omputation and randomness? What have we learned? What don’t we know (yet)? W hat are the most important open problems? What are the prospects for pro g ess? 1 Why were you initially drawn to the study of computation and randomness? The topic is so all-encompassing and sexy. It helps to formal ize the notions of Occam’s razor and inductive inference [9, 36, 10, 37, 12, 19], which a re at the heart of all inductive sciences. It is relevant not only for Artificial Inte lligence [7, 30, 28, 33] and computer science but also for physics and philosophy [14, 18 , 20]. Every scientist and philosopher should know about it. Even artists should, as th ere are complexity-based explanations of essential aspects of aesthetics and art [16 , 15, 32]. 2 What have we learned? In the new millennium the study of computation and randomnes s, pioneered in the 1930s [5, 39, 8, 36, 9, 12], has brought substantial progress in the field of theoretically optimal algorithms for prediction, search, inductiv e nference based on Occam’s razor, problem solving, decision making, and reinforcemen t l arning in environments of a very general type [7, 23, 25, 26, 21, 30, 28, 33]. It led to a symptotically optimal universal program search techniques [6, 22, 33] for extreme ly broad classes of problems. Some of the results even provoke nontraditional predi ctions regarding the future of the universe [14, 18, 20, 29] based on Zuse’s thesis [40, 41 ] of computable physics [14, 18, 19, 27]. The field also is relevant for art, and for cla rifying what science and art have in common [16, 15, 17, 24, 31, 32].