Duality, quantisation and symmetry in BWV-999

I just love BWV-999, the Dm Prelude to the lute works by Bach. It is relatively simple to get started and there is ample potential to improve. It seems to be written to be played fast. As usual with Bach, it should be played very balanced to make the different parts stand together coherently. Speed and balance in a piece with very difficult chord transitions. A piece for life.

Measure is the most outstanding aspect of a musical piece. BWV-999 has 3/4, with each quarter further divided into 4, giving 12 sixteenths. Bach chooses special numbers with religious and mystical qualities, 2, 3, 4, 12. No surprises here. 2 comes from bass and treble duality.

Measure also happens to be the most outstanding aspect of any physical entity. Life is made of cells. Matter is made of atoms. Light is made of photons.

The first beat of all measures belongs to bass. Although it is the opening shot of the measure, it also closes the previous measure. This linking, or chaining, is very elementary and comes from the scales;
(C,D,E,F,G,A,B,(2C),2D,2E,2F,2G,2A,2B,3C)
When a two octave scale is played, one can hear the dual role of the root C. It is both the ending of the previous and the beginning of the next. This dual property of the root is central to music.

Life also displays this property of ever becoming.

Bass and treble make a 3+3 pattern with bass twice slower. Bass has 2+1 pattern with 2 completing to 3 in the next measure.

Another duality comes from the bass-treble interaction. Chords act as vertical glue to bind bass and treble. The first quartet (D,2D,2F,2A) sets out the dual vertical pattern.
((D,2D),(2F,2A)) and (D,(2D,2F,2A))
The 2+2 pattern arises since D and 2D attract each other, being the same.
The 1+3 pattern is due to bass and treble duality. Treble flock together.

The ambiguity in meaning is what makes the bonding between parts. He then plays with harmony, in the rest of the peace, to explore the interactions between dualities. The quantum, or measure, is the one that carries all these dualities. Reminding the uncertainty principle.

Dual ambiguity gives us depth in our vision and hearing.

There is also a spine of the piece, formed out of 6 alternate 16ths. Bass and treble are bonded to aech other around a spine. When played fast it sounds like a tremelo. As if the whole thing is like a DNA piece, with bass and treble dancing around each other around a spine. Even the numbers of bases match (2+2). We enjoy music because, it seems, the patterns of the mind match that of music.

Measurement and Consciousness

Consciousness is awareness of being. It comes as a mediated duality;
{nothingness,self,other}
(0,1,infinity}
Whole existence is defined on the concept of being one. Awareness of anything requires the concept of nothingness. It is the canvas. When there is picture on the canvas, it always has two aspects;
{detail,overall}
Eyes have two modes of operation (also less obviously ears);
{focus,anti-focus}
Anti-focus is the way of paying attention to overall aspects.

The dual split in the brain reflects this duality. The 'eye' in the brain makes it's own scenery by analysing and feeling at the same time. Feeling provides the context for analysing. Thinking is based on feeling.

Thinking takes it's symmetry from Space-Time, since ST is the arena of reality;
{temporal,local,spatial}
{analytic,existential,emotional}
{algebra,number theory,geometry}
{melody,rythm,harmony}
Thinking is an act of measurement, or observation, of this duality in the brain, therefore it obeys the law of uncertainty;
dx.dp >= h/4*pi
'dx' for spatial, 'dp' for temporal, h/4*pi for local. The limit of focusing in the brain is neuron. Locality definition, or quantisation, is the prime act of any being.

Atom

All entities are made of a smallest unit, an atom.
Chemical elements are made of atoms.
Carbon based life is based on cells, the atoms of life.
Species are made of individuals.
Galaxies are made of stars.
Universe is made of galaxies.

Atoms are made of a core, a shell and a core-shell relationship.
Cell core is made of genetic material.
Cell shell or skin is made of porous tissue made of proteins that allows bothways filtration.
Cell's inside is a dynamic environment, reflecting it's outer environment, that digests the food eaten, defends against invaders, does maintenance, creates heat and many other tasks.
The know-how is stored in the core, which is in a periodic swirling motion like a beating heart.
This motion is both inwards and outwards so that there is loop.

Like galaxies, all atoms spin in a preferred direction, left or right handed.
This spin creates a moment and allows atoms to line up to make networks.
Higher spins create inner moments.

For contained smooth motion to exist, a minimum of 2 dimensions are required.
The smallest sphere is a circle.
This is demonstrated by the closure of complex numbers by 2 dimensions {+-1, +-i}.
Contained motion defines the entity, e^i*a.
The first motion that emerges is that of communication or exchange.
i*i = -1
Sqrt[-1] = i

In the wild, all populations have predators until the top ones.
Even the top ones have predators in another context.
A relatively contained Predator/Prey relationship oscillates around a mean and defines both species.
Without a predator, a species would not evolve as fast and becomes extinct easily.
Predator eats the weak and the sick and thus refines the genetic pool of the prey.
Thus a good PP relationship defines an entity out of it's base.

Art in nature

Some humans are artier than others.
The artiest humans are usually the strangest.
Marginal thinking is just that, marginal.
Most humans prefer to think nothing.
Thinking is painful for them.
They would rather exist in a fantasy land secured for them by the bullies.
The bully worshipping is typical for many monkey species.
When a new bully takes over the clan, he first encounters resistance.
After a while the bully becomes accepted and loved.
The bullies of the society scare the wits of any potential challengers early in life.
Like ants, most of us get programmed in childhood by the politics of power into subserviance.
This happens in many ways at the same time for each individual.
Freedom to create is one's best asset.
The ultimate feeling is that of the creative moment.
Some people are almost impossible to oppress in any society.
They will protect their freedom at any cost.
The most important thing for them is the freedom to create.
Scientists are artists, they just use a different palette.
Musicians and mathematicians are the most blessed and cursed individuals of them all.
Blessed by the creative pleasure, while cursed by the obsession to create.
The creative people are always in the minority for any time or society.

Creativity in animals is rarely acknowledged.
We like to think they have no feelings or thoughts.
Otherwise how can we eat them?
Have you seen the Bowerbird art?
A bird obsessed in blue easthetics.
Bird songs are usually in tune and some very melodic.
Heard male cats singing the cat-sex blues?
I once heard a song lasting minutes.
It was unbelivable, a musically interesting song improvised on the spot by a horny cat!
Seen cats courting?
Birds courting?
Usually animals dance and sometimes sing in courting rituals.
Sexual and social selection may have shaped humans, but it is also very noticable in many animals.
My cat Rupty likes to posture like an equal member of the household.
And she does that with considerable style.
Cats have definite style for every individual.
I also noticed from her growing, that she has creative moments.
She slowed down in playing now but I can still see her having fun moments.
I believe all life have feeling and thought in the full spectrum.

We humans are about to enter the post natural evolution stage, if we survive the coming energy/climate singularity.
Humans most probably will survive anything, we are tough creatures.
If we can find the theory of the universe, then nothing can stop us, except the aliens.
One wonders why there aren't any definite contact.
Hard to believe we are alone in this gigantic universe.
Maybe there is a universal code of ethics about not contacting lower forms of life, until they have to.
We keep listening to e/m radiation from space, but who said they would use that form of communication anyway?
They would have mastered gravity and zero point energy.

Resolution

Resolution, or the smallest/largest ratio is the first aspect of an entity.
,/{}
Matter is made of atoms.
All plants and animals are made of cells.
All living populations are made of individuals.
The universe is made of galaxies.
Galaxies are made of stars.
In fact the universe is an atom fractal.
TV screen is made of pixels which are made of 3 colors.
The retina of the eye is also made of smallest units.
This fact is known as quantisation in quantum field theory.

Cells differentiate from stem cells to form different tissues.
Embryo is the ultimate stem cell and in it's growth it summarizes the evolution of the it's species.
Ontogeny recapitulates phylogeny. (Ernst Haeckel)
Thus an embryo traces a compacted tree fractal in it's growth.

The smallest unit is like nothingness.
It is made to be taken for granted, yet it makes the entity.
Atoms are nothingness to a cell.
What atoms make the atoms, Higgs?

The universe has an astounding resolution.
We don't even know yet what the smallest part is.
It could be Planck's constant, h.
The smallest/largest ratio is what gives measure to an entity.
Measure is the first thing that enables an entity to exist.
All senses are based on measure, they have degrees.
Measure is not sensed since it is the foundation.
Like water has no taste.
It makes the nothingness for taste.
Air makes the nothingness for smell.
A slave is nothingness in a farm, yet it makes the farm run.
Space/time is like nothingness for matter and energy.

All entities exist in a shell of nothingness.

Why 3 colors?

There are 3 primary colors;
{yellow,blue,red}
And there are 2 intensity limits;
{black,white}
Perception of color shifts to white in high intensity, to black in low intensity.
3/2 symmetry of color reflects the quark/gluon and space symmetry.
Space has 3 dimensions, each dimension with forward/backward duality.
Quark/gluon symmetry determines the space symmetry,
and space symmetry determines the symmetry of color perception.

Color perception would evolve from intensity (black and white) perception.
With humans, color perception has a full octave spectrum.
Unlike sound, color has only one cycle, infra-red to ultra-violet.
But within one cycle, sound also reflects color.
{C,D,E,F,G,A,B}
can be compared to white and 3 colors;
{White,Yellow,Orange,Red,Purple,Blue,Green}
Black would be silence.
Tree top living would enforce a 3D phase (state) space in the mind.
Moving around in a 3D grid requires an inner simulation of this grid for fast response.
Essentially it is about 3D pattern recognition.
Color identification of each space locality is the result of this inner mapping.
Like the RAM (Random Access Memory) address in computers,
color is a fast indexing mechanism to label space.

Charge and field

The elementary particles come in two types, charge and field.
Mass is charge, gravity is field.
(+) and (-) electrical charges, light or electric and magnetic fields.
Quarks are color charges, gluons are color fields.

Algebra is like charge, geometry is like field.
Algebra operates in the boundary provided by geometry.

Analytical brain performs algebra, while emotional brain provides geometry.
Although the brain hemispheres tend to specialise to a degree, they can perform both tasks.
Like the elementary particles, brain hemispheres also divide into parts.
The frontal lobes are for higher functions like planning.
The higher functions form a weak field of influence on the brain.
They only control the available free parameters, thus acting like a donkey leading a camel herd.
Mass/Gravity are the higher functions of the universe, forming it's overall shape.

A town is like charge, it's villages are like field.

A cat in the wild holds it's territory by random inspections, thus forming a field of influence.

In ATON, charge is like ESet, field is like HSet.

Lateral of lateral is opposite

Self of self is self,
opposite of opposite is self,
lateral of lateral is opposite.
Or,
(+)*(+)=(+)
(-)*(-)=(+)
(i)*(i)=(-)
This shows the "sign" aspect of "i".
The 1st one stands for a cycle of modularity 1, the 2nd for 2, and the 3rd for 4.
(+)^n=(+,+,+,+,...)
(-)^n=(+,-,+,-,...)
(i)^n=(+,-,-i,+i,...)
(i)^n shows a circular cycle, i^n=e^(i*n*pi/2), of modularity 4.
Circular rotation comes with the "lateral" concept.
It allows us to go beyond the logic of opposites and introduces us to cycles.
In a rotating system, self becomes lateral first, before it becomes opposite.
According to a point, there are two kinds of motions, along and lateral.
Lateral motion allows a system to change smoothly, without disturbing the distance between the observer and the observed too quickly.
In physics this duality is translational and angular momentum.

In biped walk, the action of the arms is like lateral motion.
It balances the upper body against the (+,-) action of the legs.
On 4 leg walk, where 2 leg one comes from, there are few modes of motion like horse's trot and gallop.
Gallop involves a smoother circular action to go fast.
Running comes naturally to 4 leg movers, 2 leggers like us lost it when we decided to use our front legs exclusively for other purposes.

The lateral motion for electric field is magnetic field.
Light action shows the symmetry of the 4 leg moving.

In electrical engineering time comes with the imaginary or lateral, e^(i*w*t), where 'w' is angular frequency.
I heard in special relativity time is lateral as well.
Time has to be lateral to space since it is not manifested explicitely like 3 space dimensions.
Space dimension, Real numbers, couples laterally to time dimension, i^2=-1.
Space is always one dimensional for motion, and time couples to it laterally.
Translational motion happens on a line, and angular motion happens around a line.
Time makes it possible for space to reflect itself smoothly along a polarised line by having a lateral motion, like a spiral.
Therefore as far as space-time is concerned, together they make 1 complex dimension.
What makes space look 3 dimensional is the 3/2 symmetry of quark/gluon.

SU(2)

SU(2) is the symmetry of the weak force and has a base of 3 2*2 complex matrices with unit determinant;
((0,1),(1,0))
((0,-i),(i,0))
((1,0),(0,-1))
They all square to the unit matrix;
((1,0),(0,1))
SU(2) is like an extention to complex numbers.

SU(2) compares to E2/H2={,{}}/{,{,{}}} with the state quotient SE2/SH2=2/4=1/2.
Consider the collapsing iteration of H2;
{,{,{}}}
[,{,{}}]+[{,{}},]
[,[,{}]]+[,[{},]]+[[,{}],]+[[,{}],]
The collapse of {} gives only one state [], like +1-1=0.
H2 has a 2*2 form when collapsed, like a 2*2 matrix.
As I noted before, E2=H1={,{}} compares to Complex numbers.
{,{}}
[,{}]+[{},]
Thus E2/H2 is interpreted as "E2 for given H2".

Modular group has also 2*2 form and obeys a condition similar to unit determinant.
((a,b),(c,d)) with ad-bc=1.
DNA has a similar form with 2*2 bases.

Light and complex numbers

I previously compared C to H2={,{,{}}} and Light to E1/H1={}/{,{}}.
There is a mistake since the symmetry of light is U(1), the circle group, or the complex unit circle, e^(i*x).
Therefore C has to be like H1={,{}} and R like H0={}.
In fact, it works better if {} is interpreted as {-1,0,+1}, reflecting dual nature of {}.
0 is the content and -1, +1 are the boundary.
Boundary determines the content and vice versa;
+1-1=0
Quantum Mechanics has a similar form as Bra and Ket vectors.
Then C is obtained by an iteration on R;
x^2=-1
x={+i,-i}
Like magnetic field is obtained from electric field.
A complex number can be written in two dual formats;
a+i*b=Sqrt(a^2+b^2)*e^(Arctan(b/a))
Reflecting the collapse;
{,{}} -> (,())+((),)

It is interesting to see that C closes so quickly.
The reason for this is that, {,{}} is the last common form to E and H sets.
E0=,
E1={}
E2={,{}}
H0={}
H1={,{}}
E1=H0 and E2=H1.
After that they diverge.

E1/H1={,}/{,{}} reflects electrical-charge/light duality.
Electrical charge comes with (+,-) duality, like integers.
Light comes with two dualities, (+,-) and (electric, magnetic).

E3/H3={,{},{,{}}}/{,{,{,{}}}} reflects strong-charge/strong-field duality.
SE3/SH3=3!2!1!0!/2^3=6*2/8 indicates 2*6 quarks and 8 gluons.

Evolution

Evolution is the adaptive process that has led to the current situation.
The rate of evolution changes from species to species, time to time and place to place.
It is usual for a species to change to another species in a relatively short time, like a revolution.
This kind of rapid change happens in highly excited localities, through Spontaneous Symmetry Breaking, like lightnings.
When early humans got down from tree tops and stood up, tail lost it's utiliterian balance and other functions (like hiding your privates), and got clipped off in a short time.
Standing up and freeing hands would have happened in a short time as well.
Once the direction is set, previously stored energy builds the momentum for sustained change.
An excited system develops an outward force on it's boundary, like heating water in a closed container.
When a system bursts it's boundary, it settles to lower entropy, therefore a simpler arrangement.
Like many legs of early life forms finally ended up just 2.
The general pattern of evolution is like a river flowing down to ocean through a series of ponds, lakes and fast streams.
First it accumulates and developes inner tension, then it bursts it's boundary and settles to a new form.
This pattern comes right from the beginning of the universe.
All existence imitates this blueprint, M6.
Ontogeny recapitulates phylogeny. (Ernst Haeckel)
M6 is in fact an act of evolution (of form and content) in 7 stages.
The last stage is that of art, or creation.
Humans are very close to that.
A singularity in our culture is fast approaching.
It is hard to tell what happens after that.
We will be able to create life.
Maybe in the end we will find that, a hunter gatherer life style is the most interesting of them all.
And probably we will create simulations to experince that life.
Maybe we are simulations after all.
What is a good simulation?
One that is very hard to figure out.

Spontaneous Symmetry Breaking

SSB happens when a highly excited system discards some action and settles to lower entropy.

Before a tossed coin hits the ground and collapses to one side, it has full entropy, say 1.
{,{}}
When it collapses it displays a definite side with probability (entropy here) 1/2, since sides are marked. When a sequence of tossings are considered, the state becomes a mixture of two. Like in quantum mechanics.
(,())+((),)
Thus we get a collapse of a duality by SSB. A tossed coin in air represents a highly excited system.

Stopping walk is SSB, like coin tossing. While you are walking, it is an excited system, and freezes upon stopping.

Standing on 2 legs and freeing up hands was SSB in evolution. 4 legs is good if you are always on ground. Spend less energy by discarding the balancing on 2 legs. But if you are also doing things with your hands, like on trees, it becomes a highly excited system that wants to split. Hands are freed up from walking thus reducing the entropy of walking and manipulating.

When a locality of atmosphere becomes highly excited, it discards energy as lightning and reduces entropy. A state of a system has a geometry that defines it's boundary. The action within this geometry is determined by it. Like water in a cup. Bit of shaking makes it to prefer the lower ground. For lightning, the boundary is the ionisation potential. When the e/m energy in the system gets out of hand, it tears the boundary and gets out. Clouds convert some of their kinetic energy into e/m energy. E/m energy is always present in kinetic environments since atoms do not always behave neutral.

When the early universe was an excited cloud in the mother universe, it was tossing it's options around, and decided to make a big spark in 7 phases and made all fields and their associated charges, and settled into a lower entropy.

DNA

DNA comes with 4 bases in 2 pairs,
((A,T),(G,C))
that make two strands that spiral around each other by using Hydrogen bonds of the pairs.
Thus one strand determines the other.
This makes it very easy to split for cloning.
After the split, the second strands are rebuilt in their own cells.

Complex numbers also come in a similar form,
((-1,+1),(-i,+i))
also forming a rotating cross like DNA bases.
Complex numbers can be represented by two equivalent forms, cartesian and polar,
a+ib=Sqrt(a^2+b^2)*e^(i*arctan(b/a))
where a,b are real.
The unit circle e^(i*a) is isomorphic to U(1), the symmetry group of light.
Light traces a double helix form as it moves in space.

Modular group is also isomorphic to unit circle,
((a,b),(c,d)), ... a*d-b*c=1

All this shows that M2 is a universal set.

SU(3)

SU(3) is the symmetry of quark and gluon interactions.
It consist of 3*3 complex matrices with determinant 1.
SU(3) is in fact the symmetry of the 3D space.
Quark-Gluon symmetry determines the number of space dimensions.
Not surprising since atoms are balanced around heavy quarks.
In MSet language 3/2 is the number that corresponds to SU(3).
SM3=SE3/SH3=12/8=3/2
3 colors, 2 color/anti-color.
3 dimensions, 2 opposite directions.
3 inter-dependent complex numbers.
12 for the number of quarks, 6 quarks, 6 anti-quarks.
8 for the number of gluons.

Atom fractal

This chapter is superceded;
http://a-theory-of-nothingness.blogspot.com/2006/11/music-and-universe.html

Consider the mapping of M6;

SM0=1 ... Higgs ... Higgs
SM1=1/2 ... Light ... Atom (+/-)
SM2=1/2 ... Weak ... Cell (Male/Female)
SM3=3/2 ... Quarks ... Planet (Full energy spectrum)
SM4=18 ... Leptons ... Star
SM5=1080 ... Space-Time-like ... Galaxy
SM6=12150 ... Mass-Gravity-like ... Universe

The atom fractal,
{Higgs,Atom,Cell,Planet,Star,Galaxy,Universe}
includes all objects with atomic symmetry.
An atom always has skin, flesh and nucleus.
Planet has atmosphere, biosphere and rocksphere.
This classification puts cell (life) right in there with the great players in cosmology.
There seems to be correspondence between the weak symmetry SU(2) and life.
Life obeys the modular group in many ways.
SU(2) has three irreducable complex 2*2 matrices as it's base.
These matrices all have determinant 1, like the modular group condition ad-bc=1.
Another aspect of this mapping is that it puts planet in the center.
Not surprising in a way since a planet provides the widest spectrum of matter and energy.
The application of 1/2 symmetry to atom (+/-) and to cell (male/female) is also interesting, increasing the strength of the mapping.

Higher numbers are curious.
18; Since a star is in plasma state, leptons are free to roam and express their symmetry.
1080; Maybe the next meltdown happens with Space-Time, in the form of a black hole.
Assuming ST is some kind of a frozen state like an atom.
Then you get a horizon appear, to seperate the hot ST plasma from ST.
12150; Then the next meltdown is with Mass-Gravity.
This would represent a higher class black hole, a universe.
Then the atom fractal starts to look like a black hole fractal.

3 boundaries

The purest moment is the Creative Moment.
It comes out of nowhere.
Or does it?
"For every action, there is an opposite and equal reaction."
The master said.
What is the intention reacting to?
What caused the big spark that made it rain matter in Big Bang?
What causes the lightning that leads to rain?
CM is like Symmetry Breaking.
SB happens when a highly excited system settles to lower entropy, by discarding the extra action.
Lower entropy brings a new boundary.
Boundary transition happens through SB.

Boundary has two irreducable elements, Inner Boundary and Outer Boundary .
{,}
When two things are the same, there is no need to separate them.
{,}={}
Life has two boundaries.
OB is skin, IB is cell skin.
In fact everything has two boundaries, in any context.
Atoms have leptons as OB, and quarks as IB.
Atmosphere's outer is space, inner is earth.
Birth is IB, death is OB.
Time is IB, space is OB.

What was first, IB or OB?
IB seems to be the first to appear, to be followed by OB in it's due time.
Nature prefers things to start small and grow to make OB.
There is a third boundary that is invisible.
It is the boundary that appears before the first boundary, nothingness.
Simply put, "," can only be written in an empty space.
Disturbance needs something to disturb.
Our universe must also be sitting in some environment that acts like nothingness.

Thus there are three boundary types, inner, middle, outer.
{,}
IB is ",", MB is {}, OB is Infinity.
Thus we go back to the triplet;
{0,1,I}

When a boundary forms, it comes with Surface Tension.
ST forms as the flattening surface forces particles to line-up in a grid made by inter-particle forces.
This grid imposes secondary dynamics within a gradual skin-depth.
ST allows water bugs to navigate the surface by using it like a trampoline.
They can also use ST gradients to climb menisci at the edges.
As the universe cooled, it would also have settled into boundaries with ST.

Sex, mathematics and politics

Sex evolved from a sexually neutral being;
{male,hermaphrodite,female}
Sexual polarisation is a low entropy solution to many ways of reproductive interactions within a localised and differentiated population.
Many ways of reproduction is still observed in nature, from hermaphrodites to humans.
The success of sexual reproduction comes from the differentiated merging, which opens up a larger territory for the species.

Mathematics has a similar mediated duality;
{algebra,probablity,geometry}
When something is totally unintelligible, like white noise with infinite band-width, there can be no means of analysis.
Therefore probability, as a method, can only arrive after some differentiation in the phase space, like white noise acquiring a spectral shape like Gaussian distribution.
To have probability, one has to have both algebra and geometry to measure it.
In Gaussian, numbers provide geometry and the exponential provides algebra.
Only when total chaos settles, we get mathematics.

Politics also settles into a mediated duality when things are stable;
{socialist,pragmatist,capitalist}
It is amusing to see that these days socialist aint socialist.
Things can never settle down to absolute zero.
Therefore there is always change.
The moment the labor movement became a political commodity, it attracted the attention of the capitalist, to find out ways of manipulation.
Labor is no longer labor, if it ever really was anyway.
Tony Blair can pursue "our way of life" with surprising acceptance from voters.
USA democrats are also practically indistinguishable from the republicans.
This shows that there is a political vacuum emerging fast.
The reason is that capitalists acquired total power, reflecting the exponential increase in global consumption.
But now the order is about to turn into chaos.
It is unavoidable since there are more than one singularities approaching.
There is not enough time or resources for a benign political revolution.
Petrol is running out.
Climate is changing alarmingly fast.
Nasty global epidemics seem to be around the corner.
Water is running out.
Species are dying too fast.
And as an indication what is to come, we got Iraq.
Like cats, humans become violently territorial when resource conflicts arise.

If there is no miracle soon, we are all doomed, most probably within a decade or two.
There is only one miracle left that is possible;
A theory of the universe.

Brain

All brains come in dual form;
{,{}}
(right,left)=(emotional,analytical)
Sometimes this mapping is flipped;
(right,left)=(analytical,emotional)
Like the split in mathematics;
(Algebra,Geometry)
Algebra for analytical, geometry for emotional.
Like the split in computers;
(Programs,Operating System)
Programs for algebra, OS for geometry.
Emotions set the overall mood by using hormones.
Thus the material base for the dual split is science;
(Physics, Chemistry)
Chemistry sets the geometry for physics (electricity) to operate in.

An M6 brain should unite around M3, like ETT.
M3=E3/H3
SE3/SH3=3!2!1!0!/2^3=12/8=3/2
Would 3/2 symmetry correspond to color perception?
Basically there is only one color to start with;
{gray}
Then it seperates into a mediated duality;
{gray} -> {black,gray,white}
Then white seperates into 3 colors;
{white} -> {yellow,blue,red}
Each color pair also get their own mediation;
{yellow,orange,red}
{yellow,green,blue}
{red,purple,blue}
Thus 3/2 colors, {yellow,red,blue}/{black,white}, define a 3D coordinate system, 3D space.
Each color gets an axis, and {black,white} gives intensity like {-,+}
Like the universe, a brain that perceives 3 colors obeys M3.

Although the color symmetry obeys 3/2, it doesn't necessarily mean light is essential for a brain to evolve.
As ETT shows, sound also obeys the same symmetry.
It seems the brain opens up a seperate 3D phase-space to solve each problem.
3D aspect of hearing is clearly visible in the conic spiral shape of cochlea in ear.
Then there must be other 3/2 modules in the brain to deal with other cognition tasks.
Sense comes in 5 types;
{see,hear,taste,touch,smell}
I think consciousness has to be added in this list.
Even then I think there is one missing, considering M6.
Taste has 3 colors;
{sweet,sour,salty}
With taste intensity we again get 3/2 symmetry.
I regarded 'bitter' as extreme sour.
Touch has 3 colors?
{elastic,stick,inelastic}
Smell comes from taste, therefore obeys the same symmetry.

Vertebrate body

The most obvious aspect of an animal body is that of mouth-stomach-anus or head-body-tail mediated duality.
Mouth-stomach-anus aspect would be the first to evolve for any living entity.
Life starts with birth and then eating and growth follow.
If you can't eat, you can't grow, very simple.
Eating can be as simple as in and out of a simple tube, like worms suggest.
A particular eating action evolves as a low entropy solution to many types of action that a differentiated population would use.
An eating action would have to controlled from the front since sensors would be there.
The first sense for an animal to experience would be taste.

The second most obvious aspect is left-middle-right mediated duality.
L/R seperation is necessary since most movements would have to be in a plane for a water-land margin living entity.
With head/tail and left/right setup, we are ready to navigate a plane.
A certain type of head/tail, left/right oscillation would be enough to move.
This motion would be the one that splits the first animal brain.
Then we get many appendages appear, as worm evolution shows, and these settle to head/tail, left/right and arms/legs configuration for vertebrates.

These steps map to M0-2;
SM0=1/1=1 ... mouth/anus (head/tail)
SM1=1/2 ... left/right
SM2=2/4 ... arms/legs

To continue.

M3

Above are 3 visualisations of M3 with no perspective. It is a shape I found while playing with equal length bamboo sticks. Previously I called it Bion. I decided to call it just M3. Now I aso don't divide the outer cubes. It's outer aspect is the 3 interlaced cubes like the Escher's. Inside, it has a cube made of two reflected tetrahedrons. The number of total faces of the outer cubes is 18. The tetrahedrons have 8 triangle faces. Note the resemblance to some ancient Asian yantras, specially Shri Yantra.

I found it when I was admiring the beauty of a tetrahedron made using 6 equal length sticks. Then I rotated it pi/2 and added them to each other making a cube made of two reflected tetrahedrons. This is a cube made by it's diagonals. The diagonals of the cube make two interlaced tetrahedrons. Then I wondered what would happen if I kept this iteration of making a transformation and adding it to the parent shape. I rotated the cube pi/2 and translated it by 1/2 in each of the 6 face directions and added them all to each other. Then I completed the manifested cubes and also divided the cubes to into 8 equal pieces.

There may be more things one can do to Bion with equal length sticks as suggested by M6. There is already a large octahedron inside. I expect all the Plato's polyhedrons to appear in some iteration of Bion. I had enough of playing with sticks, too tedious.
I am thinking about a little program to experiment with Bion. Someday it may happen. It would be wonderful to make a full connection with M6.

In the middle there are two interlaced Tetrahedrons, made by rotating one of them pi/4 and adding. Each T is made of 6 sticks representing the edges. T+T(pi/4) has 2*6=12 sticks. There are 6 crosses making the faces of a cube. There are 8 corners made by the tips of Ts. Thus we got our;
12/8=3/2=E3/H3={,{},{,{}}}/{,{,{,{}}}}
T^2 is a cube made by it's diagonals.

The outer layer of Bion has 3 cubes made by sticks at the edges. There are 3*6=18=SE4/SH4 faces.