Spectral Representation of Some Computably Enumerable Sets With an Application to Quantum Provability

We propose a new type of quantum computer which is used to prove a spectral representation for a class F of computable sets. When S in F codes the theorems of a formal system, the quantum computer produces through measurement all theorems and proofs of the formal system. We conjecture that the spectral representation is valid for all computably enumerable sets. The conjecture implies that the theorems of a general formal system, like Peano Arithmetic or ZFC, can be produced through measurement; however, it is unlikely that the quantum computer can produce the proofs as well, as in the particular case of F. The analysis suggests that showing the provability of a statement is different from writing up the proof of the statement.Comment: 12 pages, LaTeX2e, no figure

Human-AI Synergy in Creativity and Innovation

In order to maximize creative behavior, humans and computers need to collaborate in a manner that will leverage the strengths of both. A 2017 mathematical proof shows two limits to how innovative a computer can be. Humans can help counteract these demonstrated limits. Humans possess many mental blind spots to innovating (e.g., functional fixedness, design fixation, analogy blindness, etc.), and particular algorithms can help counteract these shortcomings. Further, since humans produce the corpora used by AI technology, human blind spots to innovation are implicit within the text processed by AI technology. Known algorithms that query humans in particular ways can effectively counter these text-based blind spots. Working together, a human-computer partnership can achieve higher degrees of innovation than either working alone. To become an effective partnership, however, a special interface is needed that is both human- and computer-friendly. This interface called BrainSwarming possesses a linguistic component, which is a formal grammar that is also natural for humans to use and a visual component that is easily represented by standard data structures. Further, the interface breaks down innovative problem solving into its essential components: a goal, sub-goals, resources, features, interactions, and effects. The resulting human-AI synergy has the potential to achieve innovative breakthroughs that either partner working alone may never achieve