The Generalised Liar Paradox: A Quantum Model and Interpretation

The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth-falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m)^m dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous 'time' dynamics is possible: typical truth and falsehood value oscillations are described by Schrodinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of 'truth-value by inference' projectors, (iv) time invariance of unmeasured state.Comment: 13 pages, to be published in Foundations of Scienc

The Tacit ‘Quantum’ of Meeting the Aesthetic Sign; Contextualize, Entangle, Superpose, Collapse or Decohere

The semantically ambiguous nature of the sign and aspects of non-classicality of elementary matter as described by quantum theory show remarkable coherent analogy. We focus on how the ambiguous nature of the image, text and art work bears functional resemblance to the dynamics of contextuality, entanglement, superposition, collapse and decoherence as these phenomena are known in quantum theory. These quantumlike properties in linguistic signs have previously been identified in formal descritions of e.g. concept combinations and mental lexicon representations and have been reported on in the literature. In this approach the informationalized, communicated, mediatized conceptual configuration—of e.g. the art work—in the personal reflected mind behaves like a quantum state function in a higher dimensional complex space, in which it is time and again contextually collapsed and further cognitively entangled (Aerts et al. in Found Sci 4:115–132, 1999; in Lect Notes Comput Sci 7620:36–47, 2012). The observer–consumer of signs becomes the empowered ‘produmer’ (Floridi in The philosophy of information, Oxford University Press, Oxford, 2011) creating the cognitive outcome of the interaction, while loosing most of any ‘classical givenness’ of the sign (Bal and Bryson in Art Bull 73:174–208, 1991). These quantum-like descriptions are now developed here in four example aesthetic signs; the installation Mist room by Ann Veronica Janssens (2010), the installation Sections of a happy moment by David Claerbout (2010), the photograph The Falling Man by Richard Drew (New York Times, p. 7, September 12, 2001) and the documentary Huicholes. The Last Peyote Guardians by Vilchez and Stefani (2014). Our present work develops further the use of a previously developed quantum model for concept representation in natural language. In our present approach of the aesthetic sign, we extend to individual—idiosyncratic—observer contexts instead of socially shared group contexts, and as such also include multiple idiosyncratic creation of meaning and experience. This irreducible superposition emerges as the core feature of the aesthetic sign and is most critically embedded in the ‘no-interpretation’ interpretation of the documentary signal

A Lorentz-Poincar\'e type interpretation of the Weak Equivalence Principle

The validity of the Weak Equivalence Principle relative to a local inertial frame is detailed in a scalar-vector gravitation model with Lorentz-Poincar\'e type interpretation. Given the previously established first Post-Newtonian concordance of dynamics with General Relativity, the principle is to this order compatible with GRT. The gravitationally modified Lorentz transformations, on which the observations in physical coordinates depend, are shown to provide a physical interpretation of \emph{parallel transport}. A development of ``geodesic'' deviation in terms of the present model is given as well.Comment: v1: 9 pages, 2 figures, v2: version to appear in International Journal of Theoretical Physic

A spatially-VSL gravity model with 1-PN limit of GRT

A scalar gravity model is developed according the 'geometric conventionalist' approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach 1957, Gruenbaum1973). In principle this approach allows an alternative interpretation and formulation of General Relativity Theory (GRT), with distinct i) physical congruence standard, and ii) gravitation dynamics according Hamilton-Lagrange mechanics, while iii) retaining empirical indistinguishability with GRT. In this scalar model the congruence standards have been expressed as gravitationally modified Lorentz Transformations (Broekaert 2002). The first type of these transformations relate quantities observed by gravitationally 'affected' (natural geometry) and 'unaffected' (coordinate geometry) observers and explicitly reveal a spatially variable speed of light (VSL). The second type shunts the unaffected perspective and relates affected observers, recovering i) the invariance of the locally observed velocity of light, and ii) the local Minkowski metric (Broekaert 2003). In the case of a static gravitation field the model retrieves the phenomenology implied by the Schwarzschild metric. The case with proper source kinematics is now described by introduction of a 'sweep velocity' field w: The model then provides a hamiltonian description for particles and photons in full accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972, Will 1993).Comment: v1: 11 pages, GR17 conf. paper, Dublin 2004, v2: WEP issue solved, section on acceleration transformation added, text improved, more references, same results, v3: typos removed, footnotes, added and references updated, v4: appendix added, improved tex

Quantum Experimental Data in Psychology and Economics

We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case the experimental data contain the effect referred to as the 'disjunction effect' in psychology. We identify different experimental situations in psychology, more specifically in concept theory and in decision theory, and in economics (namely situations where Savage's Sure-Thing Principle is violated) where the disjunction effect appears and we point out the common nature of the effect. We analyze how our theorem constitutes a no-go theorem for classical probabilistic weight structures for common experimental data when the disjunction effect is affecting the values of these data. We put forward a simple geometric criterion that reveals the non classicality of the considered probabilistic weights and we illustrate our geometrical criterion by means of experimentally measured membership weights of items with respect to pairs of concepts and their disjunctions. The violation of the classical probabilistic weight structure is very analogous to the violation of the well-known Bell inequalities studied in quantum mechanics. The no-go theorem we prove in the present article with respect to the collection of experimental data we consider has a status analogous to the well known no-go theorems for hidden variable theories in quantum mechanics with respect to experimental data obtained in quantum laboratories. For this reason our analysis puts forward a strong argument in favor of the validity of using a quantum formalism for modeling the considered psychological experimental data as considered in this paper.Comment: 15 pages, 4 figure

On a modified-Lorentz-transformation based gravity model confirming basic GRT experiments

Implementing Poincar\'e's `geometric conventionalism' a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate space-time and momentum-energy scaling ("normalization") relative to a nondynamical flat background geometry according to an isotropic, nonsingular gravitational `affecting' function Phi(r). Elimination of the gravitationally `unaffected' S_0 perspective by local composition of space-time GMLT recovers the local Minkowskian metric and thus preserves the invariance of the locally observed velocity of light. The associated energy-momentum GMLT provides a covariant Hamiltonian description for test particles and photons which, in a static gravitational field configuration, endorses the four `basic' experiments for testing General Relativity Theory: gravitational i) deflection of light, ii) precession of perihelia, iii) delay of radar echo, iv) shift of spectral lines. The model recovers the Lagrangian of the Lorentz-Poincar\'e gravity model by Torgny Sj\"odin and integrates elements of the precursor gravitational theories, with spatially Variable Speed of Light (VSL) by Einstein and Abraham, and gravitationally variable mass by Nordstr\"om.Comment: v1: 14 pages, extended version of conf. paper PIRT VIII, London, 2002. v2: section added on effective tensorial rank, references added, appendix added, WEP issue deleted, abstract and other parts rewritten, same results (to appear in Found. Phys.

Brassica juncea chitinase BjCHI1 inhibits growth of fungal phytopathogens and agglutinates Gram-negative bacteria

Brassica juncea BjCHI1 is a plant chitinase with two chitin-binding domains. Its expression, induced in response to wounding, methyl jasmonate treatment, Aspergillus niger infection, and caterpillar Pieris rapae feeding, suggests that it plays a role in defence. In this study, to investigate the potential of using BjCHI1 in agriculture, Pichia-expressed BjCHI1 and its deletion derivatives that lack one or both chitin-binding domains were tested against phytopathogenic fungi and bacteria. Transplastomic tobacco expressing BjCHI1 was also generated and its extracts assessed. In radial growth-inhibition assays, BjCHI1 and its derivative with one chitin-binding domain showed anti-fungal activities against phytopathogens, Colletotrichum truncatum, C. acutatum, Botrytis cinerea, and Ascochyta rabiei. BjCHI1 also inhibited spore germination of C. truncatum. Furthermore, BjCHI1, but not its derivatives lacking one or both domains, inhibited the growth of Gram-negative bacteria (Escherichia coli, Ralstonia solanacearum, Pseudomonas aeruginosa) more effectively than Gram-positive bacteria (Micrococcus luteus and Bacillus megaterium), indicating that the duplicated chitin-binding domain, uncommon in chitinases, is essential for bacterial agglutination. Galactose, glucose, and lactose relieved agglutination, suggesting that BjCHI1 interacts with the carbohydrate components of the Gram-negative bacterial cell wall. Retention of chitinase and bacterial agglutination activities in transplastomic tobacco extracts implicates that BjCHI1 is potentially useful against both fungal and bacterial phytopathogens in agriculture

Episodic Source Memory over Distribution by Quantum-Like Dynamics – A Model Exploration

In source memory studies, a decision-maker is concerned with identifying the context in which a given episodic experience occurred. A common paradigm for studying source memory is the ‘three-list’ experimental paradigm, where a subject studies three lists of words and is later asked whether a given word appeared on one or more of the studied lists. Surprisingly, the sum total of the acceptance probabilities generated by asking for the source of a word separately for each list (‘list 1?’, ‘list 2?’, ‘list 3?’) exceeds the acceptance probability generated by asking whether that word occurred on the union of the lists (‘list 1 or 2 or 3?’). The episodic memory for a given word therefore appears over distributed on the disjoint contexts of the lists. A quantum episodic memory model [QEM] was proposed by Brainerd, Wang and Reyna [8] to explain this type of result. In this paper, we apply a Hamiltonian dynamical extension of QEM for over distribution of source memory. The Hamiltonian operators are simultaneously driven by parameters for re-allocation of gist-based and verbatim-based acceptance support as subjects are exposed to the cue word in the first temporal stage, and are attenuated for description-dependence by the querying probe in the second temporal stage. Overall, the model predicts well the choice proportions in both separate list and union list queries and the over distribution effect, suggesting that a Hamiltonian dynamics for QEM can provide a good account of the acceptance processes involved in episodic memory tasks