C. S. Calude, G. Paun (eds.). Finite vs Infinite, Contributions to an Eternal Dilemma, Springer-Verlag, London, 2000, ISBN: 1-85233-251-4. £45.00 March 2000, x + 372 pages softcover.

The finite-infinite interplay is central in the human thinking, from ancient philosophers and mathematicians (Zenon, Pythagoras), to modern mathematics (Cantor, Hilbert) and computer science (Turing, Goedel). Recent developments in mathematics and computer science suggest radically new answers to classical questions such as:

• Does infinity exist?
• Where does infinity come from?
• How can we reconcile the finiteness of the human brain with the infinity of ideas it produces?

• What is the role played by randomness?
• Are computers capable of handling the infinite through unconventional media of computation?
• How can one approximate efficiently the finite by the infinite, and conversely the infinite by the finite?

Well-known authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to this volume. While mathematical in spirit, contributions have many connections with computer science, cognitive science, linguistics, philosophy, physics, biology and semiotics.

• Preface
• Tribute to Professor Solomon Marcus
• Umberto Amato, Dan Tudor Vuza
  Smoothing Data: When Finite and Infinite Dimensional Help Each Other
• Hari Bercovici
  Rearrangements of Real Functions Derived from the Combinatorics of Young Tableaux
• Massimo Borelli, Andrea Sgarro
  A Possibilistic Distance for Sequences of Equal and Unequal Length
• Cristian S. Calude, Helmut Jürgensen, Shane Legg
  Solving Problems with Finite Test Sets
• Cezar Câmpeanu, Kai Salomaa, Sheng Yu
  State Complexity of Regular Languages: Finite Versus Infinite
• Gregory J. Chaitin
  A Century of Controversy over the Foundations of Mathematics
• Florin Diacu
  Finite Versus Infinite in Singularity Dynamics
• John Ewing, Ciprian Foias
  An Interesting Serendipitous Real Number
• Rudolf Freund, Alexandru Mateescu, Arto Salomaa
  Algebraic Representations of Regular Array Languages
• Salvatore Greco, Benedetto Matarazzo, Roman Slowinski
  Rough Set Processing of Vague Information Using Fuzzy Similarity Relations
• Tom Head
  Relativized Code Concepts and Multi-Tube DNA Dictionaries
• Lucian Ilie, Ion Petre, Grzegorz Rozenberg
  Uniformly Scattered Factors
• Vincenzo Manca
  Splicing Normalization and Regularity
• Carlos Martín-Vide
  Infinitely Many Infinities
• Georges Nicolas
  Finite and Infinite in Geography
• Piergiorgio Odifreddi
  Ultrafilters, Dictators, and Gods
• Sergiu Rudeanu
  On the Behaviour of Semiautomata
• Jouko Seppänen
  Infinity - An Outline of Conceptions in Mythology, Cosmology and Natural Philosophy
• Hava T. Siegelmann
  Finite Versus Infinite Neural Computation
• Dan A. Simovici, Szymon Jaroszewicz
  On Information-Theoretical Aspects of Relational Databases
• Robert M. Solovay
  A Version of W for Which ZFC Cannot Predict a Single Bit
• Ludwig Staiger
  On the Power of Reading the Whole Infinite Input Tape
• Victor Vianu
  Finite and Infinite in Logic