Peter Marcer, Peter Rowlands
A definition of intelligence in terms of the computational principles by which a sentient being may make sense of a universe structured according to the nilpotent universal computational rewrite system (NUCRS), with an infinite universal alphabet as discovered by Rowlands and Diaz, is briefly set out. This alphabet defines the semantics of quantum mechanics in terms of a universal grammar, such that the nilpotent generalization of Dirac's quantum mechanical equation is the computational machine order code. Investigations underway show that this discovery not only provides a fundamental semantic foundation for universal quantum computation, but is the likely keystone of a fundamental computational foundation for mathematics, quantum physics, the genetic code / molecular biology, neuroscience and an evolutionary cosmology. The NUCRS is a universal organizational principle, which provides well determined testable models, some already in agreement with experiment. These show that the structure of the cosmos, the genetic code, the human brain, and human language, correspond to quantum mechanics, as determined by the generalized nilpotent Dirac equation D(N) and the complementary semantic theory of quantum holographic pattern recognition specified by the 3 dimensional nilpotent Heisenberg Lie Group. The two nilpotent representations correspond to the required division of the universal nilpotent quantum mechanical state space (NQM) into its Clifford / fermionic and Lie / bosonic parts, where the 3D Heisenberg Lie algebra defines NQM Heisenberg uncertainty and, remarkably, a dual so that under the right circumstances this duality is the means by which to compute holographically, as, for example, in magnetic resonance imaging machines (MRI). We postulate that the NUCRS's power to be able connect to such significant ideas as nonstandard analysis over the surreal numbers fields, Wheeler's meaning circuit, the cosmological holographic principle, quantum holography, anticipatory computation and quantum thermodynamic machines, shows it to be an Evolutionary Anthropic Semantic Computational Principle, by means of which a sentient being is able to comprehend the rules by which Nature is apparently structured.
Subjects: 9. Foundational Issues; 9.3 Mathematical Foundations
Submitted: Jan 23, 2007