How Intelligence Evolved?

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. A semantic model of computation Success in science is measured by agreement between the predictions of the particular mathematical language description used and experiment, and the language’s interdisciplinary breadth. Syntactic correctness of the language is thus a necessary but not necessarily sufficient condition. It may only guarantee a combinatorial explosion of possible correct solutions, as now, for example, appears to be the case in string theory according to the admission of one of its originators, Leonard Susskind (Susskind, 2005). It supports Peter Woit’s argument that string theory is, in Pauli’s famous phrase, ‘not even wrong’ (Woit, 2006), because correct syntax is not accompanied by correct semantics, as in a semantic language model of computation, such as the rewrite systems synonymous with computing / information processing, which specify a grammar as well as a syntax appropriate to the problem needing solution. Thus, the theory of nilpotent quantum mechanics outlined below, may be able, we hypothesize, to give physicists their much sought after ‘Theory of Everything’ in the form of this NUCRS foundational universal organization principle. Rewrite systems concern the languages in which programs are rewritten as symbols for computing hardware to interpret. The NUCRS (Rowlands and Diaz, 2002, Diaz and Rowlands, 2005) is of particular significance, since its subset alphabets emerge in a minimal way and not only have a mathematical interpretation as algebra, but concern the nilpotent Dirac algebra, with which one can generalize Dirac’s well known quantum mechanical equation, so as include not only mass and electric charge, but also the strong and weak charges, and, implicitly, the property of spin (Rowlands, 2004, 2005, 2006). The NUCRS has a universal grammar in the sense that it delivers the entire infinite alphabet of symbols in one step, when presented with zero, in a simplified presentation, as the initial subset alphabet. (In a more technical extended presentation the need to start with anything at all can be dispensed with.) This universal system, we conjecture, has a minimum of two rewrite rules or productions (which it turns out are dual): i) a creation operation, delivering a new symbol at each invocation, where this new symbol may be a single character of the alphabet, a subset alphabet, or the entire alphabet, and ii) a conserve / proofreading operation, which examines all currently existing symbols to ensure that the bringing into existence of a new symbol or subset alphabet, etc., produces no anomalies. The NUCRS differs from traditional rewrite systems, of computational semantic language description with a fixed or finite alphabet, in that the rewrite rules allow new symbols to be added to the initial alphabet. As already stated, we start with just one symbol representing ‘nothing’ and two fundamental rules: create, a process which adds new symbols, and conserve, a process that examines the effect of any new symbol on those that currently exist, to ensure ‘a zero sum’ again. In this way at each step a new sub-alphabet of an infinite universal alphabet is created. However the system may also be implemented in an iterative way, so that a sequence of mathematical properties is required of the emerging sub-alphabets; and we have shown that one such sequential iterative path proceeds from nothing (as specified by the mathematical condition nilpotent) through conjugation, complexification, and dimensionalization to a stage in which no fundamentally new symbol is needed. At this point the alphabet is algebraically congruent with the nilpotent generalization of Dirac’s famous quantum mechanical equation, showing that this equation defines the quantum mechanical ‘machine order code’ for all further (universal) computation corresponding to the infinite universal alphabet. The property of the universal nilpotent rewrite system that a new symbol can stand for itself, a sub-alphabet or the infinite universal alphabet, allows NUCRS to rewrite itself, so as to enable it to describe the ontological structure at a higher (hierarchical) level in terms of those at lower levels, beginning with the fundamental level. This rewrite system with its nilpotent bootstrap methodology from ‘nothing / its empty state’ thus defines the requirement for universal quantum computation to constitute a semantic model of computation with a universal grammar. It is also significant that, though the universal rewrite system generates both number systems and algebras, it is not confined to these systems, and does not depend on the preexistence of numerical or algebraic concepts, or any of the ideas of set theory, and the zero is not confined to being that of the empty set. The mathematical structure generated derives rationals from reals, not reals from rationals; and shows that complexification logically precedes discrete numbering, a result that cannot be derived from any form of set theory (Rowlands and Diaz, 2002, Diaz and Rowlands, 2005). Such a nilpotent computional rewrite system describing both arithmetic and geometric properties must describe what is called universal computer construction, i.e. such nilpotent quantum computation will be both computer universal in the sense of arithmetic and constructor universal in the sense of geometry. That is, it includes both universal digital computation as discovered by Turing (Turing, 1936) in the form of the universal Turing Machine model, and universal computer construction or self replication as revealed by Von Neumann (Von Neumann, 1966). Scientific perspectives on semantic computation From the above it would appear that: i) both theoretical physics and mathematics, grounded in nilpotent quantum physical process action, are single, possibly equivalent, bodies of human linguistic / semiotic knowledge emergent from the human brain, a quantum physical semantic machine, as the evolutionary result of the semantic natural physical law NUCRS describes; and ii) that, as proposed by Langlands, mathematics is indeed (in this new computational NUCRS foundation) a single inseparable body of knowledge, where theoretical physics will be the same thing as mathematics, thus explaining what is often referred to as ‘the unreasonable effectiveness of mathematics in relation to physics’ (Chapline, 1999). That is, the NUCRS describes the basis for two new foundational disciplines, the computational foundations of physics and mathematics. Thus, this law’s semantic mathematical language description would be expected, in addition to correct syntax, to provide the description of such properties as: i) a measure, metric and Hamiltonian / Lagrangian for each variable, process and system respectively described (examples, Fatmi and Resconi, 1988; Schempp, 1992); and ii) thermodynamic principles in relation to quantum measurement, where information becomes a physical resource such as entropy production, as occurs in magnetic resonance imaging (MRI) machines, where the real and virtual imagery of 3 + 1 relativistic space-time physical structures, exist independently of the presence of any observer. This is the fact that natural radiation of any kind, incident on any object it illuminates, shows to be the case; for, as is known and can be demonstrated holographically, any such incidence will, quite independently of any observer, effect local changes of the radiation’s amplitude and phase, so as to capture the 3 + 1 relativistic space-time image of the illuminated object as appropriate to the nature of the incident radiation. All the evidence, we have so far, supports the hypothesis that nilpotent quantum mechanical language description, NUCRS, constitutes ‘Nature’s rules’ in accordance with the Premise and M