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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

THE NUMBER LINKAGE. “It is clear that if the shear, twist and Ricci tensor vanish, the geodesic congruence is convergent, i.e., θ(τ) < 0 at every τ for θ(0) < 0. This is the case of spontaneous jamming, and is independent of any assumed symmetries of spacetime, spherical or otherwise.” https://lnkd.in/dusKMKM View in LinkedIn

POLYNOMIAL COMPLEXITY IN EXPONENTIAL TIME. “What does this have to do with black holes? We will see shortly.” https://lnkd.in/dByfCJV View in LinkedIn

The mechanical wonder is now an electrinic marvel. View in LinkedIn

ARTIFICIAL STABLE SILICON DOUBLE BOND. “While carbon–carbon double bonds are common in organic chemistry, at the heart of countless chemical transformations, silicon–silicon double bonds are much rarer. Despite silicon sitting just below carbon in the periodic table, silicon double bonds are much less stable than those involving carbon.” https://lnkd.in/dvvPbnC View in LinkedIn

NON-COMPUTABILITY. “As we will see the argument also goes in the other direction: If the universal quantum computer produces greater than polynomial complexity in exponential time, then certain hard problems (PSPACE-complete) cannot be solved in polynomial time by a quantum computer.” https://lnkd.in/dByfCJV View in LinkedIn

c(N). “Let us suppose that a universal quantum circuit, when run for exponential time failed to produce complexity greater than polynomial in the number of qubits. Consider some problem which is classically hard, i.e., it takes exponential time ∼ c(N) to solve it. It follows that there is a way to get to the answer in a polynomial number of steps running the computer as a quantum computer.” https://lnkd.in/dByfCJV View in LinkedIn

QUITE THE ANSWER. “The result was a theorem (mainly due to Aaronson) connecting the growth of complexity with certain plausible properties of complexity classes.” Originated from black hole quantum circuits. https://lnkd.in/dByfCJV View in LinkedIn