Where Do New Ideas Come From? How Do They Emerge? Epistemology as Computation (Information Processing) [chapter]

Gordana Dodig-Crnkovic
2007 Randomness and Complexity, From Leibniz to Chaitin  
Preface Human beings have a future if they deserve to have a future! Gregory J. Chaitin This book is offered with admiration and affection to Gregory J. Chaitin 1 on the occasion of his 60th birthday (25 June 2007 ). Gregory J. Chaitin, together with Ray Solomonoff and Andrei N. Kolmogorov, are the founding fathers of the subject called Algorithmic Complexity, Kolmogorov Complexity, or Algorithmic Information Theory (AIT). 2 R. Solomonoff and G. Chaitin at NKS2003 (photo by David Reiss) 1 Greg
more » ... or friends. 2 Chaitin coined the name AIT; this name is becoming more and more popular. VI During its history of more than 40 years, AIT knew a significant variation in terminology. In particular, the main measures of complexity studied in AIT were called Solomonoff-Kolmogorov-Chaitin complexity, Kolmogorov-Chaitin complexity, Kolmogorov complexity, Chaitin complexity, algorithmic complexity, program-size complexity, etc. Solovay's handwritten notes [22] 3 , introduced and used the terms Chaitin complexity and Chaitin machine. 4 The book [21] promoted the name Kolmogorov complexity for both AIT and its main complexity. 5 The main contribution shared by AIT founding fathers in the mid 1960s was the new type of complexity-which is invariant up to an additive constant-and, with it, a new way to reason about computation. Founding fathers' subsequent contributions varied considerably. Solomonoff's main interest and results are related to inductive inference, see [19]. Kolmogorov's main contributions to AIT were mainly indirect 6 -through the works of his students, P. Martin-Löf, L. Levin, V. Uspenskij. 7 Chaitin's contributions-spanning over four decades-on plain and program-size complexity, algorithmic randomness (finite and infinite sequences), applications to Gödel incompleteness, and concrete versions of AIT (hands-on programming), are central for the field. One can appreciate their lasting impact by inspecting the forthcoming monograph [17] which also includes the boom of results obtained in the last decade (due in part to the renaissance of Recursion Theory focussed on AIT). While Chaitin's main contributions are in AIT, he was engaged in other research projects as well. His first paper [5]-published when he was 18-was in automata theory. It significantly improves a theorem by Moore, which later became very important for modelling quantum phenomena with automata, see [24]. In fact, Chaitin was interested in the relation between computation and quantum physics since the early 1960s; he even wrote an APL2 course outline for 3 During the research for my book [1]
doi:10.1142/9789812770837_0015 fatcat:hhtjs3z765chpebraxckg3p4hu