01 Apr

File:Correlation2x.png

‎Further Notes
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== Further Notes ==

== Further Notes ==

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On the molecular level, for instance, the isotropic-symmetry associated with liquid water may be '''broken''' by local translational pair-correlations (resulting in spherical reciprocal-lattice shells) as the liquid turns to polycrystal ice, and by both translational and rotational ordering (resulting in reciprocal-lattice spots) as the ice becomes a single crystal. A quasicrystal phase might have rotational without translational ordering, while a random-layer lattice might have rotational+translational ordering in one direction only. Thus even within a single layer of organization, broken symmetries play a role in the (at least temporary) development of order.
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On the molecular level, for instance, the relatively-featureless isotropy of liquid water may be '''broken''' by local translational pair-correlations (resulting in spherical reciprocal-lattice shells) as the liquid turns to polycrystal ice, and by both translational and rotational ordering (resulting in reciprocal-lattice spots) as the ice becomes a single crystal. A quasicrystal phase might have rotational without translational ordering, while a random-layer lattice might have rotational+translational ordering in one direction only. Thus even within a single layer of organization, broken symmetries play a role in the (at least temporary) development of order.

Hierarchical ordering in the layer just above a pair-correlated level is generally predicated on a higher-level symmetry-break, which in turn gives rise to processes that may select for inward-looking post-pair correlations as well as outward-looking pair-correlations on the next level up. Thus shared-electrons break the symmetry between in-molecule and extra-molecule interactions, bi-layer membranes allow symmetry between in-cell and out-cell chemistry to be broken, shared resources (like steady-state flows) may break the symmetry between in-tissue and external processes, metazoan skins allow symmetry between in-organism and out-organism processes to be broken, bias toward family breaks the symmetry between in-family and extra-family processes, membership-rules break the symmetry between in-culture and multi-cultural processes, etc.

Hierarchical ordering in the layer just above a pair-correlated level is generally predicated on a higher-level symmetry-break, which in turn gives rise to processes that may select for inward-looking post-pair correlations as well as outward-looking pair-correlations on the next level up. Thus shared-electrons break the symmetry between in-molecule and extra-molecule interactions, bi-layer membranes allow symmetry between in-cell and out-cell chemistry to be broken, shared resources (like steady-state flows) may break the symmetry between in-tissue and external processes, metazoan skins allow symmetry between in-organism and out-organism processes to be broken, bias toward family breaks the symmetry between in-family and extra-family processes, membership-rules break the symmetry between in-culture and multi-cultural processes, etc.

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