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BRIDGING TO SAND. “Trapping is characterized by the horizon radius at which the spatial length (given by the metric) may actually diverge. This spatial distance (within a particular frame) is taken to correspond to the correlation length in the phase transition description of ‘spontaneous’ jamming.” https://lnkd.in/dusKMKM View in LinkedIn

THE BLACK HOLE. “In particular, an isotropically jammed state in granular matter corresponds in the analogue gravity description to the formation of a trapped surface in gravitational collapse, with the envelope of such trapped surfaces being a horizon.” https://lnkd.in/dusKMKM View in LinkedIn

THE CORE ANALOGY. “General Relativity is well-known to be inherently non-linear, and to admit a great many time-dependent solutions (like gravitational collapse solutions) which, from a statistical standpoint correspond to distinctly non-equilibrium processes. In many cases though, constant-time spatial slices do reveal steady state aspects of such solutions.” https://lnkd.in/dusKMKM View in LinkedIn

The most beautiful of all the ancient Greek coins, signed by Kimon. " " https://lnkd.in/dzZypJq View in LinkedIn

SURREALIST LEONORA CARRINGTON. “She sought to capture fleeting scenes of the subconscious where real memories and imagined visions mingle. In Carrington’s rich universe, ethereal beings enact rituals with unknown purposes; these creatures have characteristics of women and animals, and seem to be somewhere between humans and beasts.” https://lnkd.in/d8TMTkF View in LinkedIn

BALANCED SYMMETRIES. “The proposal naturally embodies the local translational and rotational symmetries corresponding respectively to force and torque balance in the standard approach to grain interactions, but with a Riemannian-geometrical description in terms of spatial curvature replacing the standard Newtonian force paradigm.” https://lnkd.in/dusKMKM View in LinkedIn

REDUCTIONISM HAS FAILED. “Zen is holism, carried to its logical extreme. If holism claims that things can only be understood as wholes, not as sums of their parts, Zen goes one further, in maintaining that the world cannot be broken into parts at all. To divide the world into parts is to be deluded, and to miss enlightenment.” https://lnkd.in/dmfn9qW View in LinkedIn

SO ENDS this first of two weekends focused on a fearlessly imaginative essay linking William Blake’s grain of sand not just to the world, but to black holes, relativity and the very fabric of the universe, spacetime. It should be an Exemplar for students in the tradition of Darwin’s excavating earthworms, photonic crystals in beetle wings, and peacock feather Iridescence. Looking is not enough, but observing keenly with a primed mind is how science is built. https://lnkd.in/dusKMKM View in LinkedIn

THE ANALOGY. “On the other hand, for initially unjammed states with θ(0) = 0, but with non-vanishing shear, while the rotation still vanishes, there is still convergence θ(τ ) < 0, corresponding to shear jamming in granular matter, provided, we use the Einstein equation " "Rμν = (8πG/c4)(Tμν−(1/2)gμνT) (where T ≡ gμνTμν) with non-negative energy density Tμνnμnν ≥ 0. The presence of an external stress-energy tensor exacerbates jamming, if the analogy holds.” https://lnkd.in/dusKMKM View in LinkedIn

BLACK HOLE MASS. “For example, according to the calculations of Spera et al, a star of mass ≃90M⊙ will be required to produce a remnant of mass mbh = 30 M⊙ if its metallicity is Z/Z⊙ = −0.5. A more metal poor star (−1.5) will need to be only ≃33M⊙ to produce a 30 M⊙ BBH remnant.” (BBH = binary black hole; M⊙ = unit of stellar mass in suns). https://lnkd.in/d8Jh7TB View in LinkedIn