From Osher Doctorow

Is the universe code of form M1M2M3L1L2L3T1T2T3F1(F2) commutative or
noncommutative? If it is noncommutative, then dimensional analysis
itself for the universe as a whole would be in general noncommutative
(unlike its classical and even sometimes nonclassical forms) but would
still have some commutative specializations such as apparently in our
common classical universe (or parts of it).

The genetic code in DNA and RNA is noncommutative, which is at least
suggestive that the universe code is not always or even overwhelmingly
commutative.

Where would a noncommutative code arise? Probable Influence/Causation
as well as the Influence/Causation set which is (A--B) = (AB' )' = A'
U B is fundamentally noncommutative in the sense that (A--B) = (B--A)
iff A' U B = B' U A which is equivalent to (AB' )' = (BA' )' = (A'B)'
so that AB' = A'B which means that AB' = A'B = N when N is the null set
so the universe is composed of AB and A'B' and hence A = B.

This doesn't mean that two set/events or processes can't equally
influence each other by the measure of causation/influence that is
Probable Influence/Causation (PI), namely:

1) P(A--B) = P(B--A) = 1 + P(AB) - P(A) = 1 + P(AB) - P(B)

which holds iff P(A) = P(B). An interesting thing about the latter
equation P(A) = P(B) is that it is not equivalent to A = B because two
distinct events or processes can have equal probabilities. P(A) =
P(B) is more like "equal orbits", and the universe is divided into
"equal orbit" sectors which hypothetically (although somewhat unlikely)
could contain one-element orbits as well as more than one element
orbits.

If the universe did begin in a singularity or in close proximity to a
singularity (whether cyclic or not), then from the beginning it had a
"choice" of (a) noncommutativity via causal/influence
sets/events/processes, or (b) commutative "orbits" via probabilities of
arbitrary sets/events/processes or even via probabilities of
causal/influence sets (using set for short as set/event/process).

Osher Doctorow

From Osher Doctorow

In classical dimensional analysis, the dimension of Length, L, is
ordinarily distinguished from Lx, Ly, Lz if some event (short here for
set, process, event) if not spatially or directionally homogeneous. In
the absence of such homgeneity, L is enough. When the direction such
as x, y, z or other directions make a difference, then one or more of
Lx, Ly, Lz are used depending on which directions are relevant to the
problem.

What exactly the state of "only containing one event" is, is very
difficult to conceive of. The Big Bang or "Almost-Big-Bang" seems
roughly analogous to the idea that "a light wave 'sees' its entire
past, present, and future simultaneously". In the case of the Big
Bang, it would also presumably 'see' its entire spatial past, present,
and future extents and masses/energies and forces.

It is not difficult to see why F. Tipler became Spiritual even without
PI with such Big Bang or Near-Big-Bang scenarios apparent to him,
including his zero-point ideas discussed also by David Deutsch.

Once more than one event existed in the universe, however, and indeed
in the process of the universe "getting" more than one event, a curious
thing must have happened which comes from the very nature of events
which are sets (even processes as "generalized" sets). In losing its
unity or unification, the universe immediately had to 'discover' both
similarities ("commutative" in a sense) and dissimiliarities
("noncommutative" in a sense), the second from sets, the first from
probabilities or measures of sets or more specifically orbits
characterized by P(A) = P(B) = ....

When we treat the universe via classical dimensional analysis, we are
using dimensions as an abelian (commutative) group under multiplication
with positive and negative and zero exponents.

In the genetic code, we have perhaps an "ultimate" type of
noncommutative treatment in a sense, with everything noncommutative in
the code.

All this does not require the universe to be "conscious" in the human
sense, but it does indicate that it is correct to use the words
"discrimination" (ability to distinguish between two (or more) stimuli)
and "integration" (ability to find what is similar or common to two (or
more) stimuli) in regard to the universe.

When we discriminate and integrate (sometimes called "correctly
generalize" for the latter), we are "true to the universe" in a rather
profound sense. Both are arguably equally and highly valuable.

Osher Doctorow

From Osher Doctorow

So we come to the question of what it means for the universe code to be
noncommutative in regard to M1M2M3L1L2L3T1T2T3F1(F2).

The most interesting thing is that a clue is available from metrics and
of all things additively-subtractively! From ds^2 = dx^2 + dy^2 +
dz^2 - dt^2 or its negative, we get an additive noncommutativity
distinguishing time from space. So already whether the triple
("codon") L1L2L3 is to the left or to the right of T1T2T3 arguably
makes a difference.

So we already have two "strings" of characters in the universe code:

1) L1L2L3T1T2T3M1M2M3F1(F2)
2) T1T2T2L1L2L3M1M2M3F1(F2)

The first string is correctly described as the representation of our
"time is causal" non-black-hole universe. The second string arguably
describes the reversal of time and space in black holes. Triples to
the left of other triples are "causes" of the right triples.

I suppose that Sir Roger Penrose's twistor theory might roughly be
described by:

3) M1M2M3T1T2T3L1L2L3F1(F2)

since his twistors are used to attempt to create "space-time" geometry
(time, distance, etc.), while a more usual approach with spacetime
either on an equal footing or causing matter and so on would have the L
and T parts to the left of the M and maybe F parts or else would be
commutative which wouldn't discriminate the orders.

Notice that an infinite number of dimensions is neither out of the
question nor indicative of nonlocality. In fact, even a Mickey
Mouse-like balloon which expands differently in different directions
gives us an idea of the general nature of expansion-contraction which
involves an enormous number and arguably an infinite (even uncountably
infinite!) number of directions/dimensions of L type but "tied to" each
local point or little string. This does not yet mean that those are
all dimensions in the same sense as L1, L2, L3 since arguably dimension
and direction aren't the same.

Osher Doctorow