There's a battle of the giants going on. In one corner, Ray Kurzweil, AI pioneer & inventor, businessman, leading philosopher and acclaimed author. In the other corner, Stephen Wolfram, Ph.D at the age of 20, multi-millionaire creator of Mathematica, fundamental influence in the field of complexity.

The debate? Wolfram's new book which he's spent over 10 years writing, ambitiously titled A New Kind of Science.

Wolfram essentially believes that repetitively applying simple computational transformations can cause very complex phenomena. He believes this concept is the fundamental source of complexity in the world. He takes as an example his Cellular Automata Rule 110, which generates non-repetitive, yet not random patterns. The book looks into ways of applying this to biology, physics, perception, computation, mathematics, and philosophy -- this reveals the depth of the book nicely!

Kurzweil thinks that these rules of Class 4 are limited to an order of complexity, and can't go beyond that. He believes humans for example, are much more complex in nature, which these rules cannot capture. In theory, he admits the "hardware" at the base of cellular automata allows any computation to be performed, any problem to be solved. But Wolfram's software that uses this hardware is limited, to an order of complexity. Kurzweil believes that introducing the concept of evolution into the mix will potentially resolve this limitation (being the true source of complexity).

Anyway, Kurzweil AI has the review in question; Reflections on Stephen Wolfram's 'A New Kind of Science'. It should explain things in more depth than the paragraphs above!