The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g., does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g., what is the role played by randomness?, are computers capable of handling the infinity...

The Second International Conference on Unconventional Models of Compu UMC'2K, organized by the Centre for Discrete Mathematics and The tation, oretical Computer Science, the International Solvay Institutes for Physics and Chemistry and the Vrije Universiteit Brussel Theoretical Physics Division was held at Solvay Institutes from 13 to 16 December, 2000. The computers as we know them today, based on silicon chips, are get ting better and better, cheaper and cheaper, and are doing more and more for us. Nonetheless, they still give rise to frustrations because they are unable to cope with many...

The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook....