MDMD(1): Forbidden Symmetries

[jporter]

It seems appropriate to me that the tale begins on page 5, but that the
first page actually numbered is 6....something definitely going on here in
the play between the numbers 5 and 6, perhaps related to his more obvious
use of the Symmetry concept.

>From the study of crystallography (without getting too New Age) fivefold
symmetry is "forbidden,"  because of the lack of *translational symmetry*
in fivefold patterns, [Look it up, Penrose does a pretty good job in: The
Emperor's New Mind] whilst  2, 3, 4, and coincidentally 6-fold symmetry
patterns are permitted for crystals. This use of the "verboten" theme is
reinforced later in the novel with the five pointed star, "ears up" on the
gunstocks of certain muskets.

While fivefold symmetry is naturally "forbidden" in crystal formation, as
Penrose points out, certain quasicrystalline structures, have been
discovered  which are based on fivefold symmetry. Penrose states: "...a
remarkable feature of the quasicyrstalline tiling patterns...is that their
assembly is necessarily *non-local*" Meaning that there has to be some way
in which the evolving pattern (which is aperiodic!) is "known" many atoms
ahead of where the structure has already formed.

pick up styx,

jody