Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

A universal primer for isolation of fragments of a gene encoding phytoene desaturase for use in virus-induced gene silencing (VIGS) studies

We have been using Virus-Induced Gene Silencing (VIGS) to test the function of genes that are candidates for involvement in floral senescence. Although VIGS is a powerful tool for assaying the effects of gene silencing in plants, relatively few taxa have been studied using this approach, and most that have are in the Solanaceae. We typically use silencing of phytoene desaturase (PDS) in preliminary tests of the feasibility of using VIGS. Silencing this gene, whose product is involved in carotene biosynthesis, results in a characteristic photobleaching phenotype in the leaves. We have found that efficient silencing requires the use of fragments that are more than 90% homologous to the target gene. To simplify testing the effectiveness of VIGS in a range of species, we designed a set of universal primers to a region of the PDS gene that is highly conserved among species, and that therefore allows an investigator to isolate a fragment of the homologous PDS gene from the species of interest. We report the sequences of these primers and the results of VIGS experiments in horticultural species from the Asteraceae, Leguminosae, Balsaminaceae and Solanaceae.

Universal scaling of production rates across mammalian lineages

Over many millions of years of independent evolution, placental, marsupial and monotreme mammals have diverged conspicuously in physiology, life history and reproductive ecology. The differences in life histories are particularly striking. Compared with placentals, marsupials exhibit shorter pregnancy, smaller size of offspring at birth and longer period of lactation in the pouch. Monotremes also exhibit short pregnancy, but incubate embryos in eggs, followed by a long period of post-hatching lactation. Using a large sample of mammalian species, we show that, remarkably, despite their very different life histories, the scaling of production rates is statistically indistinguishable across mammalian lineages. Apparently all mammals are subject to the same fundamental metabolic constraints on productivity, because they share similar body designs, vascular systems and costs of producing new tissue.

On the universal TRO of a JC*-triple, ideals and tensor products

In a development from material introduced in recent work, we discuss the interconnections between ternary rings of operators (TROs) and right C*-algebras generated by JC*-triples, deducing that every JC*-triple possesses a largest universally reversible ideal, that the universal TRO commutes with appropriate tensor products and establishing a reversibility criterion for type I JW*-triples.

Universal and language-specific patterns of categorisation

Previous work on object classification preferences shows that speakers of languages that lack morphological plural marking (like Yucatec and Japanese) display a tendency to match objects by common material, while speakers of languages with morphological plural marking (like English) display a tendency to match objects by common shape. The present paper compares categorisation preferences of English and Japanese speakers with those of Greek speakers. Greek resembles English in that it has morphological plural marking, but contrasts with English in that mass nouns typically do not resist pluralization. Results show that all groups distinguish significantly between countable objects and non-countable substances, but the degree to which they do this differs and conforms to language-specific grammatical patterns. It is argued that the effects of grammatical structure on categorisation preferences are finer-grained than earlier studies have assumed, thus providing a more precise account of the extent and nature of linguistic influence on cognition.

Evidence of a universal scaling relationship for leaf CO2 drawdown along an aridity gradient

The leaf carbon isotope ratio (δ13C) of C3 plants is inversely related to the drawdown of CO2 concentration during photosynthesis, which increases towards drier environments. We aimed to discriminate between the hypothesis of universal scaling, which predicts between-species responses of δ13C to aridity similar to within-species responses, and biotic homoeostasis, which predicts offsets in the δ13C of species occupying adjacent ranges. The Northeast China Transect spans 130–900 mm annual precipitation within a narrow latitude and temperature range. Leaves of 171 species were sampled at 33 sites along the transect (18 at ≥ 5 sites) for dry matter, carbon (C) and nitrogen (N) content, specific leaf area (SLA) and δ13C. The δ13C of species generally followed a common relationship with the climatic moisture index (MI). Offsets between adjacent species were not observed. Trees and forbs diverged slightly at high MI. In C3 plants, δ13C predicted N per unit leaf area (Narea) better than MI. The δ13C of C4 plants was invariant with MI. SLA declined and Narea increased towards low MI in both C3 and C4 plants. The data are consistent with optimal stomatal regulation with respect to atmospheric dryness. They provide evidence for universal scaling of CO2 drawdown with aridity in C3 plants.

A universal agro-hydrological model for water and nitrogen cycles in the soil-crop system SMCR_N: critical update and further validation

Agro-hydrological models have widely been used for optimizing resources use and minimizing environmental consequences in agriculture. SMCRN is a recently developed sophisticated model which simulates crop response to nitrogen fertilizer for a wide range of crops, and the associated leaching of nitrate from arable soils. In this paper, we describe the improvements of this model by replacing the existing approximate hydrological cascade algorithm with a new simple and explicit algorithm for the basic soil water flow equation, which not only enhanced the model performance in hydrological simulation, but also was essential to extend the model application to the situations where the capillary flow is important. As a result, the updated SMCRN model could be used for more accurate study of water dynamics in the soil-crop system. The success of the model update was demonstrated by the simulated results that the updated model consistently out-performed the original model in drainage simulations and in predicting time course soil water content in different layers in the soil-wheat system. Tests of the updated SMCRN model against data from 4 field crop experiments showed that crop nitrogen offtakes and soil mineral nitrogen in the top 90 cm were in a good agreement with the measured values, indicating that the model could make more reliable predictions of nitrogen fate in the crop-soil system, and thus provides a useful platform to assess the impacts of nitrogen fertilizer on crop yield and nitrogen leaching from different production systems. (C) 2010 Elsevier B.V. All rights reserved.

The impracticality of a universal drought definition

This paper demonstrates the impracticality of a comprehensive mathematical definition of the term `drought' which formalises the general qualitative definition that drought is `a deficit of water relative to normal conditions'. Starting from the local water balance, it is shown that a universal description of drought requires reference to water supply, demand and management. The influence of human intervention through water management is shown to be intrinsic to the definition of drought in the universal sense and can only be eliminated in the case of purely meteorological drought. The state of `drought' is shown to be predicated on the existence of climatological norms for a multitude of process specific terms. In general these norms are either difficult to obtain or even non-existent in the non-stationary context of climate change. Such climatological considerations, in conjunction with the difficulty of quantifying human influence, lead to the conclusion that we cannot reasonably expect the existence of any workable generalised objective definition of drought.

Reflection iii: Transnationalisation, Television Formats and the Universal

This reflection argues that, despite various good reasons for approaching the notion of the ‘universal’ with caution, cultural theorists should give up their resistance to the universal. The prominence of formats in today’s television suggests that the time is ripe to do. Intentionally or not, accounts of difference implicitly also often reveal sameness; the more we probe heterogeneity, the more likely we are to encounter something that remains consistent and similar. Thus, it is time to collaborate with scholars from the numerous disciplines for which the universal has long had validity and pertinence.

Global forecasting of thermal health hazards: the skill of probabilistic predictions of the Universal Thermal Climate Index (UTCI)

Although over a hundred thermal indices can be used for assessing thermal health hazards, many ignore the human heat budget, physiology and clothing. The Universal Thermal Climate Index (UTCI) addresses these shortcomings by using an advanced thermo-physiological model. This paper assesses the potential of using the UTCI for forecasting thermal health hazards. Traditionally, such hazard forecasting has had two further limitations: it has been narrowly focused on a particular region or nation and has relied on the use of single ‘deterministic’ forecasts. Here, the UTCI is computed on a global scale,which is essential for international health-hazard warnings and disaster preparedness, and it is provided as a probabilistic forecast. It is shown that probabilistic UTCI forecasts are superior in skill to deterministic forecasts and that despite global variations, the UTCI forecast is skilful for lead times up to 10 days. The paper also demonstrates the utility of probabilistic UTCI forecasts on the example of the 2010 heat wave in Russia.

Introducing "ecoputation": a universal systems design process

A universal systems design process is specified, tested in a case study and evaluated. It links English narratives to numbers using a categorical language framework with mathematical mappings taking the place of conjunctions and numbers. The framework is a ring of English narrative words between 1 (option) and 360 (capital); beyond 360 the ring cycles again to 1. English narratives are shown to correspond to the field of fractional numbers. The process can enable the development, presentation and communication of complex narrative policy information among communities of any scale, on a software implementation known as the "ecoputer". The information is more accessible and comprehensive than that in conventional decision support, because: (1) it is expressed in narrative language; and (2) the narratives are expressed as compounds of words within the framework. Hence option generation is made more effective than in conventional decision support processes including Multiple Criteria Decision Analysis, Life Cycle Assessment and Cost-Benefit Analysis.The case study is of a participatory workshop in UK bioenergy project objectives and criteria, at which attributes were elicited in environmental, economic and social systems. From the attributes, the framework was used to derive consequences at a range of levels of precision; these are compared with the project objectives and criteria as set out in the Case for Support. The design process is to be supported by a social information manipulation, storage and retrieval system for numeric and verbal narratives attached to the "ecoputer". The "ecoputer" will have an integrated verbal and numeric operating system. Novel design source code language will assist the development of narrative policy. The utility of the program, including in the transition to sustainable development and in applications at both community micro-scale and policy macro-scale, is discussed from public, stakeholder, corporate, Governmental and regulatory perspectives.