(Page 0801) historically been made to get an axiom system that somehow describes definite kinds of objects. But now the main way this has been done is by progressively adding ...

(Page 0806) So if one makes a list of all possible axiom systems -- say starting with the simplest -- where in such a list should one expect to see axiom systems that ...

(Page 0825) simple underlying rules -- can generate at least as much complexity as we see in the components of typical living systems. Yet despite all this, we do not in our ...

(Page 0836) And there is certainly in general no lack of radio signals that we receive from around our galaxy and beyond. But the point is that these signals typically seem ...

(Page 0838) humans have historically developed ultimately covers only a tiny fraction of what is possible -- notably leaving out the vast majority of systems that I have ...

(Page 0859a) Notes for: The Foundations for a New Kind of Science | An Outline of Basic Ideas Mathematics in science The main event usually viewed as marking the beginning of ...

(Page 0861a) Notes for: The Foundations for a New Kind of Science | An Outline of Basic Ideas Complexity and theology Both complexity and order in the natural world have been ...

(Page 0912c) Notes for: Systems Based on Numbers | Mathematical Constants Digit sequence properties Empirical evidence for the randomness of the digit sequences of Sqrt[n] , ...

(Page 0929h) Notes for: Two Dimensions and Beyond | Cellular Automata Other geometries [for cellular automata] Systems like cellular automata can readily be set up on any ...

(Page 0953a) Notes for: Starting from Randomness | Randomness in Class 3 Systems Probabilistic estimates [of cellular automaton properties] One way to get estimates for ...