10.
11.
12.
13.
14,
Index of Theorems 403
Cantor’s First Infinity Theorem — The infinite plane is the same infinity as the infinite line.
. 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.
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.
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.
Hyper-Computing
Adaptive Recurrent Neural Network Hypothesis — Hava Siegelmann’s proposal that ARNNs are capable of super-Turing computation.
Hyper-Communication Bandwidth Conjecturet — Person-to-person communication has infinite bandwidth and is non-symbolic.
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