Between Kepler and Newton: Hooke’s ‘principles of congruity and incongruity’ and the naturalization of mathematics

ABSTRACT

Robert Hooke’s development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke’s ‘Principles?…?of Congruity and Incongruity of bodies’ represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke’s ‘Uniform Geometrical or Mechanical Method’ was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world.     

Champsodontidae (Pisces: Trachinoidei) in the Eastern Mediterranean: how many species are there?

ABSTRACT

Three marine fish species of the Indo-Pacific genus Champsodon were reported as invasive species in the Eastern Mediterranean between 2009 and 2012; Champsodon nudivittis, C. vorax, and C. capensis. These are presumed to invade through the Suez Canal, but only C. nudivittis is known from the Red Sea, so the presence of C. vorax and C. capensis is surprising. To test the validity of the taxonomic identification of these two species, this study combined traditional morphology, genetic barcoding, and photography investigation. Our results demonstrate that only one species, C. nudivittis, has migrated into the Eastern Mediterranean.     

Neocortical excitation/inhibition balance in information processing and social dysfunction

Severe behavioural deficits in psychiatric diseases such as autism and schizophrenia have been hypothesized to arise from elevations in the cellular balance of excitation and inhibition (E/I balance) within neural microcircuitry. This hypothesis could unify diverse streams of pathophysiological and genetic evidence, but has not been susceptible to direct testing. Here we design and use several novel optogenetic tools to causally investigate the cellular E/I balance hypothesis in freely moving mammals, and explore the associated circuit physiology. Elevation, but not reduction, of cellular E/I balance within the mouse medial prefrontal cortex was found to elicit a profound impairment in cellular information processing, associated with specific behavioural impairments and increased high-frequency power in the 30-80?Hz range, which have both been observed in clinical conditions in humans. Consistent with the E/I balance hypothesis, compensatory elevation of inhibitory cell excitability partially rescued social deficits caused by E/I balance elevation. These results provide support for the elevated cellular E/I balance hypothesis of severe neuropsychiatric disease-related symptoms.     

Virus-mediated inhibition of natural cytotoxicity receptor recognition

Natural killer (NK) cells are a part of the innate immune system that functions mainly to kill transformed and infected cells. Their activity is controlled by signals derived from a panel of activating and inhibitory receptors. The natural cytotoxicity receptors (NCRs): NKp30, NKp44, and NKp46 (NCR1 in mice) are prominent among the activating NK cell receptors and they are, notably, the only NK-activating receptors that are able to recognize pathogen-derived ligands. In addition, the NCRs also recognize cellular ligands, the identity of which remains largely unknown. In this review, we summarize the current knowledge regarding viruses that are recognized by the NCRs, focusing on the diverse immune-evasion mechanisms employed by viruses to escape this detection. We also discuss the unique role the NCRs have in regulating NK cell activity with particular emphasis on the in vivo function of NKp46/NCR1.     

Quantum nonlinear optics with single photons enabled by strongly interacting atoms

The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantum-by-quantum control of light fields, including single-photon switching, all-optical deterministic quantum logic and the realization of strongly correlated many-body states of light.