The Synthesis and Decoding of Meaning

Thinking machines must be able to use language effectively in communication with humans. It requires from them the ability to generate meaning and transfer this meaning to a communicating partner. Machines must also be able to decode meaning communicated via language. This work is about meaning in the context of building an artificial general intelligent system. It starts with an analysis of the Turing test and some of the main approaches to explain meaning. It then considers the generation of meaning in the human mind and argues that meaning has a dual nature. The quantum component reflects the relationships between objects and the orthogonal quale component the value of these relationships to the self. Both components are necessary, simultaneously, for meaning to exist. This parallel existence permits the formulation of ‘meaning coordinates’ as ordered pairs of quantum and quale strengths. Meaning coordinates represent the contents of meaningful mental states. Spurred by a currently salient meaningful mental state in the speaker, language is used to induce a meaningful mental state in the hearer. Therefore, thinking machines must be able to produce and respond to meaningful mental states in ways similar to their functioning in humans. It is explained how quanta and qualia arise, how they generate meaningful mental states, how these states propagate to produce thought, how they are communicated and interpreted, and how they can be simulated to create thinking machines.

Probability estimates for Shor's algorithm

Let N be a (large) positive integer, let b be an integer satisfying 1< b < N that is relatively prime to N, and let r be the order of b modulo N. Finally, let QC be a quantum computer whose input register has the size specified in Shor's original description of his order-finding algorithm. In this paper, we analyze the probability that a single run of the quantum component of the algorithm yields useful information---a nontrivial divisor of the order sought. We prove that when Shor's algorithm is implemented on QC, then the probability P of obtaining a (nontrivial) divisor of $r$ exceeds $.7$ whenever N \ge 2^{11} and r\ge 40, and we establish that $.7736$ is an asymptotic lower bound for $P$. When $N$ is not a power of an odd prime, Gerjuoy has shown that $P$ exceeds 90 percent for $N$ and $r$ sufficiently large. We give easily checked conditions on N and r for this 90 percent threshold to hold, and we establish an asymptotic lower bound for $P$ of 2\Si(4\pi)/\pi ~0.9499 in this situation. More generally, for any nonnegative integer $q$, we show that when QC(q) is a quantum computer whose input register has $q$ more qubits than does QC, and Shor's algorithm is run on QC(q), then an asymptotic lower bound on P is 2\Si(2^{q+2}\pi)/\pi (if N is not a power of an odd prime). Our arguments are elementary and our lower bounds on P are carefully justified.

RELATIVISTIC QUANTUM FIELD THEORY FOR CONDENSED SYSTEMS-(III): AN EXPLICIT EXPRESSION OF ATOMIC SCHWINGER–DYSON METHOD

A new explicit expressions of self-energies Πμν and Σ are introduced for photons and electrons based on the particle-hole-antiparticle representation (PHA) of Atomic Schwinger–Dyson formalism (ASD). The PHA representation describes exactly the physical processes such as particle-hole excitations (electron-hole) and particle-antiparticle excitations (electron-positron). The self-energy Σ includes both the quantum component and the classical component (classical external field and Coulomb's field), which are divided into the scalar part Σs and 4-dimensional vector parts Σ0, Σj. The electron propagators are composed of the particle part, hole part and antiparticle part in PHA representation. The general representation of photon self-energy Πμν with 16 elements is expressed in terms of only two components (transverse and longitudinal) Πt and Πl. The general form of the photon propagators are written in terms of free propagator D0 and two independent propagators Dl and Dt, which include two independent photon self-energies. The tensor part of the electron self-energy does not appear in ASD formalism which makes perfectly the closed self-consistent system, when we take the bare vertex approximation, Γμ→γμ.