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And by a prudent flight and cunning save A life which valour could not, from the grave. A better buckler I can soon regain, But who can get another life again? Archilochus

Wednesday, April 30, 2025

Forbidden Symmetries and Alchemical Mysteries

from Google AIi:
Penrose tilings exhibit "forbidden" symmetries, particularly 5-fold and 10-fold symmetry, which are not possible in traditional repeating crystal structures. This was a revolutionary discovery that opened new avenues in crystallography and quasicrystal research, ultimately leading to Dan Shechtman's 2011 Nobel Prize. Penrose tilings, with their non-repeating patterns, also demonstrate the potential for aperiodic structures to exhibit mathematical properties related to quantum error correction
Parmenides, Meet Heraclitus!

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