Conventionalism in Reid’s ‘geometry of visibles’

The subject of this investigation is the role of conventions in the formulation of Thomas Reid’s theory of the geometry of vision, which he calls the ‘geometry of visibles’. In particular, we will examine the work of N. Daniels and R. Angell who have alleged that, respectively, Reid’s ‘geometry of visibles’ and the geometry of the visual field are non-Euclidean. As will be demonstrated, however, the construction of any geometry of vision is subject to a choice of conventions regarding the construction and assignment of its various properties, especially metric properties, and this fact undermines the claim for a unique non-Euclidean status for the geometry of vision. Finally, a suggestion is offered for trying to reconcile Reid’s direct realist theory of perception with his geometry of visibles.While Thomas Reid is well-known as the leading exponent of the Scottish ‘common-sense’ school of philosophy, his role in the history of geometry has only recently been drawing the attention of the scholarly community. In particular, several influential works, by N. Daniels and R. B. Angell, have claimed Reid as the discoverer of non-Euclidean geometry; an achievement, moreover, that pre-dates the geometries of Lobachevsky, Bolyai, and Gauss by over a half century. Reid’s alleged discovery appears within the context of his analysis of the geometry of the visual field, which he dubs the ‘geometry of visibles’. In summarizing the importance of Reid’s philosophy in this area, Daniels is led to conclude that ‘there can remain little doubt that Reid intends the geometry of visibles to be an alternative to Euclidean geometry’;¹ while Angell, similarly inspired by Reid, draws a much stronger inference: ‘The geometry which precisely and naturally fits the actual configurations of the visual field is a non-Euclidean, two-dimensional, elliptical geometry. In substance, this thesis was advanced by Thomas Reid in 1764 ...’² The significance of these findings has not gone unnoticed in mathematical and scientific circles, moreover, for Reid’s name is beginning to appear more frequently in historical surveys of the development of geometry and the theories of space.³Implicit in the recent work on Reid’s ‘geometry of visibles’, or GOV, one can discern two closely related but distinct arguments: first, that Reid did in fact formulate a non-Euclidean geometry, and second, that the GOV is non-Euclidean. This essay will investigate mainly the latter claim, although a lengthy discussion will be accorded to the first. Overall, in contrast to the optimistic reports of a non-Euclidean GOV, it will be argued that there is a great deal of conceptual freedom in the construction of any geometry pertaining to the visual field. Rather than single out a non-Euclidean structure as the only geometry consistent with visual phenomena, an examination of Reid, Daniels, and Angell will reveal the crucial role of geometric ‘conventions’, especially of the metric sort, in the formulation of the GOV (where a ‘metric’ can be simply defined as a system for determining distances, the measures of angles, etc.). Consequently, while a non-Euclidean geometry is consistent with Reid’s GOV, it is only one of many different geometrical structures that a GOV can possess. Angell’s theory that the GOV can only be construed as non-Euclidean, is thus incorrect. After an exploration of Reid’s theory and the alleged non-Euclidean nature of the GOV, in 1 and 2 respectively, the focus will turn to the tacit role of conventionalism in Daniels’ reconstruction of Reid’s GOV argument, and in the contemporary treatment of a non-Euclidean visual geometry offered by Angell ( 3 and 4). Finally, in the conclusion, a suggestion will be offered for a possible reconstruction of Reid’s GOV that does not violate his avowed ‘direct realist’ theory of perception, since this epistemological thesis largely prompted his formulation of the GOV.     

The Ter mutation in the dead end gene causes germ cell loss and testicular germ cell tumours

In mice, the Ter mutation causes primordial germ cell (PGC) loss in all genetic backgrounds. Ter is also a potent modifier of spontaneous testicular germ cell tumour (TGCT) susceptibility in the 129 family of inbred strains, and markedly increases TGCT incidence in 129-Ter/Ter males. In 129-Ter/Ter mice, some of the remaining PGCs transform into undifferentiated pluripotent embryonal carcinoma cells, and after birth differentiate into various cells and tissues that compose TGCTs. Here, we report the positional cloning of Ter, revealing a point mutation that introduces a termination codon in the mouse orthologue (Dnd1) of the zebrafish dead end (dnd) gene. PGC deficiency is corrected both with bacterial artificial chromosomes that contain Dnd1 and with a Dnd1-encoding transgene. Dnd1 is expressed in fetal gonads during the critical period when TGCTs originate. DND1 has an RNA recognition motif and is most similar to the apobec complementation factor, a component of the cytidine to uridine RNA-editing complex. These results suggest that Ter may adversely affect essential aspects of RNA biology during PGC development. DND1 is the first protein known to have an RNA recognition motif directly implicated as a heritable cause of spontaneous tumorigenesis. TGCT development in the 129-Ter mouse strain models paediatric TGCT in humans. This work will have important implications for our understanding of the genetic control of TGCT pathogenesis and PGC biology.     

An autoregulatory circuit for long-range self-organization in Dictyostelium cell populations

Nutrient-deprived Dictyostelium amoebae aggregate to form a multicellular structure by chemotaxis, moving towards propagating waves of cyclic AMP that are relayed from cell to cell. Organizing centres are not formed by founder cells, but are dynamic entities consisting of cores of outwardly rotating spiral waves that self-organize in a homogeneous cell population. Spiral waves are ubiquitously observed in chemical reactions as well as in biological systems. Although feedback control of spiral waves in spatially extended chemical reactions has been demonstrated in recent years, the mechanism by which control is achieved in living systems is unknown. Here we show that mutants of the cyclic AMP/protein kinase A pathway show periodic signalling, but fail to organize coherent long-range wave territories, owing to the appearance of numerous spiral cores. A theoretical model suggests that autoregulation of cell excitability mediated by protein kinase A acts to optimize the number of signalling centres.     

Generation and annotation of the DNA sequences of human chromosomes 2 and 4

Human chromosome 2 is unique to the human lineage in being the product of a head-to-head fusion of two intermediate-sized ancestral chromosomes. Chromosome 4 has received attention primarily related to the search for the Huntington's disease gene, but also for genes associated with Wolf-Hirschhorn syndrome, polycystic kidney disease and a form of muscular dystrophy. Here we present approximately 237 million base pairs of sequence for chromosome 2, and 186 million base pairs for chromosome 4, representing more than 99.6% of their euchromatic sequences. Our initial analyses have identified 1,346 protein-coding genes and 1,239 pseudogenes on chromosome 2, and 796 protein-coding genes and 778 pseudogenes on chromosome 4. Extensive analyses confirm the underlying construction of the sequence, and expand our understanding of the structure and evolution of mammalian chromosomes, including gene deserts, segmental duplications and highly variant regions.     

Synthetic biology: engineering Escherichia coli to see light

We have designed a bacterial system that is switched between different states by red light. The system consists of a synthetic sensor kinase that allows a lawn of bacteria to function as a biological film, such that the projection of a pattern of light on to the bacteria produces a high-definition (about 100 megapixels per square inch), two-dimensional chemical image. This spatial control of bacterial gene expression could be used to 'print' complex biological materials, for example, and to investigate signalling pathways through precise spatial and temporal control of their phosphorylation steps.     

WNT7b mediates macrophage-induced programmed cell death in patterning of the vasculature

Macrophages have a critical role in inflammatory and immune responses through their ability to recognize and engulf apoptotic cells. Here we show that macrophages initiate a cell-death programme in target cells by activating the canonical WNT pathway. We show in mice that macrophage WNT7b is a short-range paracrine signal required for WNT-pathway responses and programmed cell death in the vascular endothelial cells of the temporary hyaloid vessels of the developing eye. These findings indicate that macrophages can use WNT ligands to influence cell-fate decisions--including cell death--in adjacent cells, and raise the possibility that they do so in many different cellular contexts.     

Unexpected features of Drosophila circadian behavioural rhythms under natural conditions

Circadian clocks have evolved to synchronize physiology, metabolism and behaviour to the 24-h geophysical cycles of the Earth. Drosophila melanogaster's rhythmic locomotor behaviour provides the main phenotype for the identification of higher eukaryotic clock genes. Under laboratory light-dark cycles, flies show enhanced activity before lights on and off signals, and these anticipatory responses have defined the neuronal sites of the corresponding morning (M) and evening (E) oscillators. However, the natural environment provides much richer cycling environmental stimuli than the laboratory, so we sought to examine fly locomotor rhythms in the wild. Here we show that several key laboratory-based assumptions about circadian behaviour are not supported by natural observations. These include the anticipation of light transitions, the midday 'siesta', the fly's crepuscular activity, its nocturnal behaviour under moonlight, and the dominance of light stimuli over temperature. We also observe a third major locomotor component in addition to M and E, which we term 'A' (afternoon). Furthermore, we show that these natural rhythm phenotypes can be observed in the laboratory by using realistic temperature and light cycle simulations. Our results suggest that a comprehensive re-examination of circadian behaviour and its molecular readouts under simulated natural conditions will provide a more authentic interpretation of the adaptive significance of this important rhythmic phenotype. Such studies should also help to clarify the underlying molecular and neuroanatomical substrates of the clock under natural protocols.