In 2008, GKO+Melax + Dean Ferrel recorded this piece which had been fixed in GKO's mind since the death of his sister Vivan in 1995.  So here is Vivaldi for Vivan.

Laude Purre, Psalm 112, by Antonio Vivaldi

The Lorentz-Möbius Torsion Theorem presented in this paper establishes a rigorous connection between special relativity, spacetime torsion, and the hydrodynamic interpretation of quantum mechanics. By demonstrating that the integral of the Lorentz factor over all normalized velocities equals π/2, the theorem reveals an underlying angular normalization analogous to the quantization in spin fields. This result reflects the cumulative effects of relativistic transformations, where integrating over velocities yields a discrete angular measure akin to the quantized spin values in quantum mechanics. The theorem is explored in the context of Lorentz transformations and Möbius mappings, connecting these to physical phenomena such as rapidity, the behavior of spinors under boosts, and the intrinsic spin in quantum fields. Additionally, the discussion extends to the implications of spacetime torsion, as predicted by the Einstein-Cartan theory, and its unifying role in describing particles, black holes, and potential dark matter candidates through the lens of the holographic principle. This unified framework highlights how local spin-induced torsion can influence gravitational behavior, aligning with observations that suggest non-trivial topologies and quantum effects at cosmic scales.

The Lorentz-Möbius Torsion Theorem

Patre is based on the Icelandic national anthem. Written by GKO in 1984, it adheres to every stricture of copyright and the statutes applying to the Icelandic National Anthem. It is GKO’s ode to his country and countrymen. The piece was originally recorded in the Elgar Sessions with Björk in 1987. The text is read by Megas with words taken from GKO’s comments on magic numbers and Platonic polyhedra - along with additional words from a poem by one of Björks boyfriends (Þór Eldon)

Patre, Track #4 from the album "Dense Time" (2006)

Mjötviður til Fóta was a CD album released in 2001 by GKO and HOH, to celebrate the 20 year anniversary of the proper version of the band ÞEYR (1981-1983), and is a compilation from the albums "Mjötviður Mær" and "Iður til Fóta", both released in 1981. The tracks for this album were selected with universality in mind, so the more "local" tracks that addressed Icelandic audience were not included. This album was printed in 1500 units, and sold out in 2010 and has not been reissued - while we will possibly do a vinyl version in 2021 to celebrate the 40 year anniversary of the said proper band ÞEYR.

The Lorentz-Möbius Torsion Theorem

Alessandro Rizzo

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