

A Conversation Between Jonathan Gorard and Stephen Wolfram (September 1, 2023)
13 snips Sep 12, 2023
Jonathan Gorard joins Stephen Wolfram to discuss ongoing science research. They explore the concept of rulial relativity, the distinction between normalizing and strongly normalizing systems in term rewriting, decidability and primitive recursive functions, non-terminating rewriting sequences, evolutionary perception and course screening, regular patterns and proof theory, observers in computation, randomness and complexity, primitive recursive functions and limited number systems, linear logic and sub-integer set theory, state and event canonicalization in multi-way systems, gravitational radiation and bronchial space, defining fluid velocities, and functoriality with a geometrical interpretation.
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Tractable Hypo-ruliad
- A tractable example exists within the hypo-ruliad (primitive recursive functions).
- This allows for hands-on exploration, unlike the hyper-ruliad.
Decidability vs. Termination
- Decidable theories, like Boolean algebra, guarantee a finite computation for truth/falsity.
- This doesn't mean all computational paths within the theory terminate.
Boolean Algebra Example
- Stephen Wolfram and Jonathan Gorard explore Boolean algebra's computational behavior.
- They demonstrate that not all paths terminate, even in decidable theories.