Balance

{Balance}

Balance is the middle touch and the core of being. It defines one's location in time and space. Balance in space seems to have more priority over balance in time. Evolution clearly displays the importance of territory. In physics, location (geometry) forms the backbone.

For example, hurricane takes it's vortex shape when a highly excited unstable locality brakes symmetry by collapsing and channeling energy in one angular direction. This direction is determined by the rotation of the earth. Spontaneous symmetry breaking is the mechanism used to make balance and define locality.

{OuterTouch, Balance, InnerTouch}

Balance uses inner and outer touch as its agents, when it evolves and differenciates more. Outer touch is the known touch, the screened interaction. Inner touch happens when allowed energy focus in the center. Brain performs the balancing function between these two touches. It mediates by correlating the inner to the outer.

Like reflection and refraction of light at a boundary. The boundary is closed for a being and the allowed energy makes patterns inside, creating an image of the outside. Energy comes in two modes; acoustic and electromagnetic or light. Acoustic energy gives an instant overview of the mechanics of the locality, if it is processed by an algorithm like FFT. Light energy is directional and provides 2D information. Acoustics is like gravity, globally felt. The inner brain develops ways to detect this dual energy pattern. Inner hearing and inner vision would evolve first. And then organs would evolve as the brain grows and differenciates.

{{Taste, Touch, Smell}, Balance, {Hear, InnerTouch, See}}

Then a similar splitting happens for both touch and inner touch, as the organism gets more complex and finds it's fundamental dual duality shape of the outer look. {Taste, See} and {Smell, Hear} correspondence demonstrates the level of correlation. See and Taste form the inner or local, while Smell and Hear form the outer territory. Dogs use smell and hear as the agents for defining outer territory.

Taste --> {Mouth, Stomach, Anus}
Smell --> {Nose, Lungs ? }
Hear --> {LeftEar, InnerEar, RightEar}
See --> {LeftEye, InnerEye, RightEye}

Then each sense splits to create it's organs. When organs split, they leave the boson of the relationship in the center as the mediator. InnerEar combines two sides to make a stereo image like model of the sound-scape outside. Duality in hearing gives depth, like also in seeing. I am not so sure about the nose-lung connection, in comparision to mouth-stomach. Maybe nose took dual role of mouth and anus at the same time, since it is only air.

{{Strong, Space, Weak}, Higgs, {Gravity, Time, Light}}

The energy expressed by gravity balances that of light. This is known but not integrated into physics properly yet. Potential/kinetic duality of energy comes from this. I suspect a similar thing is happening with {Strong, Weak}. {Light, Weak} and {Gravity, Strong} correlate strongly. The 3*2 symmetry of space is closely related to 3/2 symmetry of Strong. Higgs forms the background field which supports everything. Space is inner touch, time is outer touch.

Light --> {+ECharge, Light, -ECharge}
Strong --> {3 Color Charges, 3 Color Gluons}
Weak --> {W+, Z0, W-}

Then each field splits similarly to form an expanding tree, forming own charges. Strong seems to be like Taste. It branches deeper. Taste has mouth, stomach, anus, liver?, intestines...

Being, music and universe

ATON-M6 classification thus meets a serious challenge from a modular group like symmetry, {{a,b},{c,d}}, which is also in line with the new multifactorials and Zeta function formulation.











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Time/Space takes the center stage
as Not-Doing/Not-Being.









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A typical cycle of action;
{Feed,Feel,Think,Judge}
displays the 4/4 measure of being
as also done by musical conductors.
Christians do the same sign.





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Do/Be expanded to reveal
a model of nothingness or slumber.
My kind of model this one.

Mirror Set, rev-2

After discovering the multifactorials, or Barnes G-functions, a revision is necessary since G-functions are more general. Mirror Set maps pairs of naturals to rationals;





Where m,n are natural, G(m,n)=m!n is multifactorial of m to depth n. Revising and broadening Mirror Set previously defined as M(m)=M(m,2). This form is more general and combines G-functions and Zeta function. It has a ying-yang look and variables do not commute, G(m,n)=/G(n,m). Here are some small values;

M(1,1-4) = (1, 1/2, 1/3, 1/4)
M(2,1-4) = (2, 1/2, 2/9, 1/8)
M(3,1-4) = (6, 3/2, 8/9, 3/4)
M(4,1-4) = (24, 18, 4^4/3, 6^4)

Previously I took M(3,2) as the center. Now M(2,2) =2/4=1/2 takes the center, standing for time/space. {2,2/9}={light,gravity}, why 2/9 for gravity? (3/2,1/2}={strong,weak} is reasonable.

Applying continuity by setting m-->z and summing gives a harmonically weighed G-function. For G=1 it is the Zeta function;






Assuming continuity holds, G may be generalised to a function of 2 complex variables;






Where z!w stands for the multifactorial to depth w, G(z,w). The form of M seems to imply the extension of G but it remains to be seen if it can be made continuous. I think G works like a local correlation function.

Thus naturals take the center stage of ATON, instead of sets. Maybe not surprising. Don't they (mathematicians) consider number theory as the purest?

Multifactorials

Lately I found, to my great surprise, that ATON Exponential Set is in fact already defined in the number domain as the second multifactorial, also called Barnes G-function;

G2(z+1)=Gamma(z)*G2(z)
G2(1)=1
Gamma(z+1)=z*Gamma(z)

Higher multifactorials follow. To see how it works, expand 3 to depth 6;

G0(3) = 3 = 3*2^0
G1(3)=3.2.1.1 = 6 = 3*2^1
G2(3)=(3.2.1.1).(2.1.1).(1.1).(1) = 12 = 3*2^2
G3(3)=[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)] = 24 = 3*2^3

G4(3)={[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]} = 48 = 3*2^4

G5(3)={{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.

.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}} = 96 = 3*2^5

G6(3)={{{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.
.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.

.{{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.

.{{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.

.{{{[(1)]}}} = 192 = 3*2^6

Therefore Gn(3)=3*2^n.

Instead of multiplying, one could add the expanded elements (with no apparent benefits);

GS0(3)=3
GS1(3)=7
GS2(3)=14
GS3(3)=25
GS4(3)=41
GS5(3)=63
GS6(3)=92