Index of Theorems 403 Cantor’s First Infinity Theorem — The infinite plane is the same infinity as the infinite line. 9. Known Unknowns Gédel’s Incompleteness Theorem — Mathematics involving simple logic is incomplete. Gédel’s Completeness Theorem -— First order logic is complete. Hilbert’s Completeness Theorem — Geometry is complete. 10. Turing’s Machines Entscheidungsproblem — The decision problem has no solution. Turing Thesis — All computers, once sufficiently powerful, are equally powerful. Non-Computability of Musict - That general musical compositions are non-computable. Non-Computability of Creativityt -— That general artistic creativity is non-computable. 11. Software Brooks’ Law — Adding resource to a late project makes it later. Law of Leaky Abstractions — However good the attempt to abstract complexity, complexity has a habit of leaking through. Software is Created} — writing software is a non-computable, creative task. Bug Hypothesist — Bugs are an inevitable consequence of trying to generalize software by mechanical means. 12. Hyper-Computing Adaptive Recurrent Neural Network Hypothesis — Hava Siegelmann’s proposal that ARNNs are capable of super-Turing computation. 13. Hyper-Communication Bandwidth Conjecturet — Person-to-person communication has infinite bandwidth and is non-symbolic. 14. Creativity Creativity Hypothesist — That all creative endeavor is a non- computable skill, analogue to theorem discovery. Wallas Model — A conceptual model for the way humans think creatively. HOUSE_OVERSIGHT_016093