Shai Spilberg currently studies science at Vanier College in Montreal, Canada. He is interested in the philosophical and practical implications of the ideas presented in A New Kind of Science. In particular, he is interested in questions regarding the foundations of mathematics. Examples of such questions:
- Is mathematics just a symbolic game?
- Are there other possible mathematics?
- Why is mathematics so useful?
- Which axiom systems are universal?
- How do consistency and completeness vary across different axiom systems?
Aside from science and mathematics, his other hobbies include reading, violin playing, and biking.
Project: Determining Powerful Theorems in Axiom Systems
Page 817 of NKS lists all the theorems of propositional logic in order of increasing complexity. Theorems that cannot be proved from previous theorems in the list are called “powerful.” The question is, what are the powerful theorems of alternative axiom systems?
Favorite Three-Color Cellular Automaton