Search Results (5)

We develop a symmetry-based reconstruction of the vacuum impedance and the fine-structure constant. Hyperbolic geometry and discrete sectorization of the electromagnetic field plane are the only input assumptions. The construction identifies a unique integer-square hyperbolic selector that fixes the electric–magnetic partition without adjustable parameters. This yields the geometric part of the vacuum impedance when combined with the quantum scale $h/e^2$. The same discrete structure provides a normalization for the fine-structure constant through a universal sector angle $\pi /24$. We discuss how discrete rotational and modular symmetries, commonly realized in crystalline metals and layered heterostructures, provide experimentally accessible settings to probe the proposed geometric structure through electromagnetic and transport measurements. Full article

This article describes the relationship between spatial perception and temporal experience, emphasizing the limitations of linear frameworks in understanding these phenomena for contemporary students of design. Drawing on recent literature in neuroscience, the author argues for wider recognition of how our brains represent space through an awareness of non-Euclidean geometries, particularly hyperbolic models that more holistically reflect the complexity of lived experience. Through the lens of personal narratives, including reflections on living in a militarized landscape in Hawai‘i, the paper emphasizes the importance of various cultural and sensory interpretations of time—such as “Hawaiian Time” and “Turtle Time”—which offer unique perspectives on what it means to exist in these built environments. Ultimately, it advocates for a pedagogical shift in design education that encourages students to embrace and integrate more diverse temporal experiences in their work, fostering a richer awareness of their present as they engage with the conceptualization and design of built space. Three key assertions are described. First, multiple, different perceptions of time coexist in the same universe and reality, offering various sensations and registrations of existence. Second, these diverse views on the passage of time, like Island Time, emphasize a slower, more direct engagement with life’s vicissitudes, in contrast to mechanical time, for example. Lastly, by acknowledging the presence of differing states of temporal perception, design students are aided in more holistic and rational conceptualization of built space and therefore in their own movement into complex and indeterminant futures in design. Full article

Double-spiral galaxies are common in the Universe. It is known that the logarithmic double spiral is a Maximum Entropy geometry in hyperbolic (flat) spacetime that well represents an idealised spiral galaxy, with its central supermassive black hole (SMBH) entropy accounting for key galactic structural features including the stability and the double-armed geometry. Over time the central black hole must accrete mass, with the overall galactic entropy increasing: the galaxy is not at equilibrium. From the associated entropic Euler–Lagrange Equation (enabling the application of Noether’s theorem) we develop analytic expressions for the galactic entropy production of an idealised spiral galaxy showing that it is a conserved quantity, and we also derive an appropriate expression for its relativistic entropic Hamiltonian. We generalise Onsager’s celebrated expression for entropy production and demonstrate that galactic entropy production (entropy production corresponds to the intrinsic dissipation characteristics) is composed of two parts, one many orders of magnitude larger than the other: the smaller is comparable to the Hawking radiation of the central SMBH, while the other is comparable to the high entropy processes occurring within the accretion disks of real SMBHs. We conclude that galaxies cannot be isolated, since even idealised spiral galaxies intrinsically have a non-zero entropy production. Full article

Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the directions of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface theory’s isometric immersion recipe, with the spacetime metric being induced by an ambient parent. We note, in this paper, that the indefinite signature of the Lorentzian metric perhaps hints at the lesser known equiaffine hypersurface theory as being a possibly more natural, i.e., less customized beyond minimal mathematical formalism, description of our universe’s extrinsic geometry. In this alternative, the ambient is deprived of a metric, and the spacetime metric becomes conformal to the second fundamental form of the ordinary theory, therefore is automatically indefinite for hyperbolic shapes. Herein, we advocate investigations in this direction by identifying some potential physical benefits to enlisting the help of equiaffine differential geometry. In particular, we show that a geometric origin for dark energy can be proposed within this framework. Full article

Universal hyperbolic geometry gives a purely algebraic approach to the subject that connects naturally with Einstein’s special theory of relativity. In this paper, we give an overview of some aspects of this theory relating to triangle geometry and in particular the remarkable new analogues of midpoints called sydpoints. We also discuss how the generality allows us to consider hyperbolic geometry over general fields, in particular over finite fields. Full article