From Osher Doctorow

So how does the universe come to distinguish between parts of
noncommutative codes like L1L2L3 versus L3L2L1?

Arguably, a clue is in our reconciling the Frenet-Serret formulas and
the spaces/curvature tensors/scalars of General Relativity. For the
latter, it proved decisive that locally spacetime is "flat" which
enabled solving many specific problems of importance. For the former,
recall the orthogonal vector "coordinate" triple at each point:

1) tangent, normal, binormal

In a way, GR's local "flatness" is similar to being guided by the
tangent vector to a curve/path in the sense of curvilinear motion,
while homogeneous/isotropic expansion-contraction is similar to being
guided by the normal vector and torsion generalization/modifications of
GR are similar to being guided by the binormal vector. Non-homogeneous
non-isotropic expansion-contraction is arguably similar to being guided
by all three vectors: tangent, normal, binormal.

In three dimensional Cartesian coordinates, the normal, tangent
(plane), and binormal have interesting 1 and 2 and 3 dimensional
priorities. The tangent and binormal form a plane, the tangent and
normal form a plane, and so on. The gradient vector is
"inward-outward" from a surface in a 3-dimensional sense.

Osher Doctorow

From Osher Doctorow

Another indication of priority comes from the physics and geometry of
life, in which curvilinear motion or even "non-motion" often lose
priority to intrusion of external objects or stimuli on/in local
neighborhoods of a point or little string. In simpler language, there
is especially priority with regard to the direction of danger/threat or
sought after stimuli from various "outside" directions which impinge on
or relate to local small neighborhoods of an organism. In avoiding or
seeking the external stimulus, most organisms make use of curvilinear
as well as expansion-contraction and rotation motion. If the z
coordinate is taken to be in the direction of the external stimulus,
LzLxLy or LzLyLx seems to be the noncommutative preferred type of
length/distance subcode with z being "highest priority causal".

Osher Doctorow