Prime Toroidal Universe of Number Patterns

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......"The only thing that interferes with my learning is my education"....A Einstein....

Our finite, occupied space reality{ Observed Time } is based on, or associated with, the self-stabilizing trinary set as follows;

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 etc. see two lines inside inferred, toroidal tube below, as occupied space reality{ Observed Time }

Ex 3 fundamental kinds of electron, quark neutrino and 3 kinds of anti-electron, quark and neutrino.

.....1......................5............7......................11..........13........................17.......19....................23.......25..............outer peak positive surface
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0...................................6....................................12....................................18...............................24..................inside toroidal tube
................3.....................................9.........................................15.................................21.................................inside toroidal tube
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...........2..........4........................8.........10.............................14........16...................20..........22.................26........inner peak negative surface.

Here below is another way to view the above inferred torus as (  ) Space - vTime^ - Space )(

---------(  ) Gravitational Space via positive outer surface curvature of torus (  )-----------------------
.........................incoming photon..v..at top peak of wave...........
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/ Observed Time aka reality inside torus tube
..........................incoming photon...^...at bottom peak of wave................
----------)( Dark Energy Space via negative inner surface curvature of torus )(----------------------------

In this latter set above we may begin to consider scenario to explain how radiation{ photon } is a constant speed irrespective of the observers speed.

What is important to realize in the above is that our reality is resultant of the inversions  --photonic in the above scenario--- from peak of positive Gravitational (  )  curvature and peak of negative )( Dark Energy curvature.

Here is another trinary set to consider as seen in  first previous set of four lines level above on this page.

1, 3, 4--> this sum-total set of six integers is only set with a shared nuclear prime number{ 3 }
2, 3, 5 ---> and is also the only trinary set of prime numbers and the only set of 4{ tetrahedral } prime numbers in the hexagonal set

4, 6, 7
5, 6, 8

7, 9, 10
8, 9, 11

11, 12, 14
10, 12, 13

13, 15, 16
14, 15, 17

17, 18, 20
16, 18, 19

19, 21, 22
20, 21 23

23, 24, 26
22, 24, 25---> this is the first trinary set that has no prime number and instead has number 25

So above we have 15 trinary lines that have a prime number.
And we have 7 hexagonal sets of that contain a prime number.

However, remmeber that 25 is composed of 5 prime number fives{ 5 } 5 * 5
--------------------------------------------------------------------------------------------------------------------

Lets look again a these quasi-helical, irregular hexagonal sets and remmeber that this pattern of positions  is as if,  we are inside the 3D tube and see this repeating, overlapping, seemingly 2D hexagonal pattern approaching us

.....1.....................5P............7P.................11P.......13P.....................17P.......19P..............23P.......25..............outer peak positive surface
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0.................................6....................................12....................................18..............................24....................inside toroidal tube
................3P...................................9....................................15...............................21................................27....inside toroidal tube
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...........2P.........4........................8.........10........................14........16...................20..........22.................26........inner peak negative surface.


0, ..1, ..5P,... 6, ..4, ...2P with nuclear 7th position as 3P

..3P, 5P, .7P,.. .9, ..8,.... 4 with nuclear  7th position as 6

.....6, ..7P, 11P, .12, .10, ...8  with a nuclear 7th position as 9 

.......9, ..11P, 13P, .15, .14, 10 with a nuclear 7th position as 12

.......12,..13P,...17P,..18....16,..14 with a nuclear 7th position as 15

..........15,.17P,...19P,....21,...20,...16 with a nuclear 7th position as 18

.............18,.19P, ..23P,.. 24,.. 22, ...20 with a nuclear 7th position as 21

................21,.23P,..25,......27,...26,....22 with a nuclear 7th position as 24


24 = 3 * 8 or 4 * 6 or 2 *12

25 = Phi-ration five times
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God { ess }-ence is the graviton and my explorations conclude, that, the graviton has both Gravity { gravitonic ] and Dark Energy { darkion } properties//aspects.

Putting aside the specific dynamic shapes that we may presume accompany all occupied space I use Euclidean simplification to present the topology of what shape we can assign to the Graviton//Darkion.

Most recently Ive tried to take an older concept I never developed much and apply it to my newer prime number torus as defined by a four level line numerical sequence in regards to the shape of the graviton//darkion.

I believe the graviton//darkion is associated with the shape of truncated { on two ends } di-pyramid i.e. two tetrahedron sharing a common triangle. See LINK

The link above is not a truncated di-pyramid. By truncating a di-pyramid in two ends we create three triangle openings ---i.e. 9 points//vertexes//nodes--  ergo, a tube, and I believe to be one tubular section of my numerical torus.

However, in introducing some dynamic activity to this truncated di-pyramid scenario and the exact reason why we have a seemingly finite quanta iis having these three triangles expand-contract in a such a fashion so as to create a pulse a unit-of-wave. <><><><><><><>

More details of this di-pyramid the next post.
 


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Ok, so di-pryamid { <> or as <|> } as graviton//darkion needs to be altered to fit into my geodesic, prime numerical inverting torus scenario.

We must truncate the di-pyramid on two of its diametrically opposing ends, Doing so now gives us three triangle openings just like the central middle-girth triangle.

Now we have a tube, as defined by three triangles --ergo 9 points//vertexes//nodes--- and to have a quanta, then we have to have closure of the two ending triangles.

Those nine points on my numerical torus are the outer and inner surface points, 1, 2, 4 --- 5, 7, 8 --- 10, 11, 13. See in pattern that follows.

.....1......................5............7......................11..........13........................17.......19....................23.......25..............outer peak positive surface
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0...................................6....................................12....................................18...............................24..................inside toroidal tube
................3.....................................9.........................................15.................................21.................................inside toroidal tube
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...........2..........4........................8.........10.............................14........16...................20..........22.................26........inner peak negative surface.

So these 9 points ---3, 3, 3--  have 9 surface, lines-of-relationship.  However, we also have internal { body } criss-crossing, lines-of-relationship
ship between the two ending sets of 3-points and that is an additional 9 body lines-of-relationship. Total 18. Or is it? See Fullers formula below.

Next I also consider the number { points//nodes } 3, 6, 9 and 12, inside { the body } my toroidal tube that fall between 1 and 13.

So this is total of 9 { surface } points//nodes + 4 internal { body } points//nodes and that totals as 13 points//nodes.

So we use Fullers lines-of-relationship formula to discover the number of relationships n^2 - n, divided by 2. see LINK

So 9^2 = 81.  81 - 9 = 72.  72 / 2 = 36 --twice as many as my given 18 above--   and there exists 36 kinds { flavor//aggregates } of quark. 18 quark and 18 anti-quark.

And those internal set as 4^2 = 16.  16 - 4 = 12.  12 / 2 = 6 is internal-only, body-only, lines-of-relationship.

However, exponentially { synergetically? } we get a larger number than just those two above added.

13^2 = 169.  169 - 13 = 156.  156 / 2 = 78 lines-of-relationship.

78, minus  36-lines-of-relationship, leaves 42-{ internal body }- lines-of-relationship.

The above numbers are new to me, so have not drawn any other conclusions, however, if want to get back to gravition//darkion as an integral quantum unit, then I believe we need to introduce that the dynamic idea of closure.

So I see the internal 4 points//nodes as being a integral, quanta-pulse-resultant of the contraction  of a triangle set 1, 2, 3,,then as expansion as 5, 7, 8 and closure of  10, 11, 13. However we have one extra point//node not acounted for. Pu that unaccounted node//point to the side for the moment and consider the following.

If we want to consider Jacob Bekensteins concluding thoughts ..."we appear to 2D creatures having an illusion of 3D"...  then we express the above as follows;

1, 2, 3 points//nodes exist and  have internal #4 node//point ergo we have subdivide triangle with 6 lines-of-relationship and this is the same as  a 3D tetrahedron that is now just flattened into seemingly 2D and as it moves forward over time, it expands as 5, 7, 8, with internal #6, then contracts again as 10, 11 13 with internal #12.

Ok, except #9 is apparrently left out of this pulsating, 2D-only, quantum scenario. What the heck is going on!

.....1......................5............7......................11..........13........................17.......19....................23.......25..............outer peak positive surface
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0...................................6....................................12....................................18...............................24..................inside toroidal tube
................3.....................................9.........................................15.................................21.................................inside toroidal tube
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...........2..........4........................8.........10.............................14........16...................20..........22.................26........inner peak negative surface.

Two things come to mind.

1} In Fullers book Synergetics 1 and 2 he mentions how calculations done by hand in old days were double checked/verified or done quicker by using by the "crossing-out of nines procedure ergo it it became apparrent to Fuller that #9 and non-counting #0 are intimately correlated,

2} with the strong sub-nuclear gluonic force{ gluons }, we mathematically have 9 possible flavors//kinds of gluon but only 8 are manifest.

Leave the above at that for consideration, for now.












 


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1} In Fullers book Synergetics 1 and 2 he mentions how calculations done by hand in old days were double checked/verified or done quicker by using by the "crossing-out of nines procedure ergo it it became apparrent to Fuller that #9 and non-counting #0 are intimately correlated,

...."BUT WAIT! See LINK Sometime during the development of this condensation trick, someone, blesstheir soul, found out that adding 9, or any combination of digits whichadd to nine, does not influence a digit sum.
Ex: The digit sum of 34 is 7.

Now let's add the digit 9 to make43. Its digit sum is 4+3=7, so we have another digit sum of 7.Adding that 9 did not change the digit sum.
Nowlet's add several combinations of numbers which add to nine and somemore nines to the 34: 34+2+7+4+5+9+9=70. Notice the new digit sum isSTILL 7.
Quitefrankly, they found that you can add as many nines or, combinationsof numbers that add to nine, as you want, and it wontchange the digit sum.
Takea look at 543,994. Here we get 5+4+3+9+9+4=34. And then 3+4=7. Againwe arrive at a digit sum of 7.
ellif nines don't change a digit sum, then by golly, let's just assign a value of ZERO to them and forget aboutthem, or shall we say CAST THEM OUT of the digit sum completely!
Itbecomes lightning FAST to find the digit sums of most numbers once youare good at CASTING OUT THOSE NINES."...

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1} so we see how #9 is likened to zero in last post { LINK }, via the casting out of nines, math procedures

2} 9 gluons should exist mathematically, yet  only eight gluons are manifest, that we know of,

3} we see that there exist 78 lines-of-relationhship that define one graviton//darklon quantum, as located within my  four level/line,  numerically sequential, toroidal pattern.

We also see how three sets of outer surface 2D  triangle is a subdivided 2D triangle { 4 triangles//tetrahedron } when we place the 4th point//node inside { internal } to it ergo;

1, 2, 4 with nuclear #3 --- 5, 7, 8 and nuclear #6 ---10, 11, 13 with nuclear #12 that leaves isolated {9}

....1......................5............7......................11..........13........................17.......19....................23.......25..............outer peak positive surface
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0...................................6....................................12....................................18...............................24..................inside toroidal tube
................3...................................-9-.........................................15.................................21.................................inside toroidal tube
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...........2..........4........................8...........10.............................14........16...................20..........22.................26........inner peak negative surface.

|  |  | = profile form side of three subdivided triangles{ 12 points//nodes } that define a 3D tube having 36 surface lines-of-relationship

|  |  {9}  | = three subdivided triangles and the isolated and internal #9 point//node

|* |* {*} |* = three 2D triangles { not subdivided } and the four internal points//nodes{ * } with isolated {*}  #9

{0}..|* |* {*} |* = includes zero{ internal to overall tube } outside of this graviton//darkion as the complement to #9 inside the set and internal to graviton//darkion quantum as one section of longer//greater toroidal tube.
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|* |* {*} |* = three 2D triangles { not subdivided } and the four internal points//nodes{ * } with isolated {*}  #9

| = 1, 2, 4 as triangle set  and  * as the internal #3 nodal point

| = 5, 7, 8 as a triangle set  and the * as the internal #6 nodal point

| = 10, 11, 12 as a triangle set the * as the internal #12 nodal point

{*} = the isolated i.e outside of any triangle set, #9 nodal point

So this is a total of 13 nodal points or as 13 vertexes. Aha! The nucleated cubo{6}-octa{8}hedron aka the Vector Equlibrium{ VE } in Fullers Synergetics,  there is 12 peripheral vertexes and a 13th nuclear vertex.

....1......................5............7......................11..........13........................17.......19....................23.......25..............outer peak positive surface
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0...................................6....................................12....................................18...............................24..................inside toroidal tube
................3...................................{9}.........................................15.................................21.................................inside toroidal tube
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...........2..........4........................8...........10.............................14........16...................20..........22.................26........inner peak negative surface.

|  |  | = profile from side of three subdivided triangles{ 12 points//nodes } that define a 3D tube having 36 surface lines-of-relationship

|  |  {9}  | = three subdivided triangles and the isolated and internal #9 point//node

|* |* {*} |* = three 2D triangles { not subdivided } and the four internal points//nodes{ * } with isolated {*}  #9

{0}..|* |* {*} |* = includes zero{ internal to overall tube } outside of this graviton//darkion as the complement to #9 inside the set and internal to graviton//darkion quantum as one section of longer//greater toroidal tube.

8 days later

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{0}..|* |* {*} |*...14  = the truncated di-pyramidal set of 13 points//nodes plus the non-counting #0 { inside tube not di-pyramid } and, the counting #14 { outside of tube, on inner surface of torus.

In review, we have the following lines-of-relationship that define the graviton//darkion quanta as based on Fullers formula;

Sum-total of 13^2 = 169  >  169 - 13 = 156 >  156 / 2 = 78 vectorial lines-of-relationship that define  graviton//darkion quanta

Outer and inner only is 9^2 = 81.  81 - 9 = 72.  72 / 2 = 36 lines-of-relationship
....there exists 36 kinds { flavor//aggregates } of quark. 18 quark and 18 anti-quark.......

Inside the di-pryamidal quanta 4^2 = 16.  16 - 4 = 12.  12 / 2 = 6 lines-of-relationship { internal-only }, to the di-pyramid quanta.

And again, we remind ourselves of and expontial { synergetic? } gain  in the number of lines-of-relationship i.e. when adding those lines-of-relationship seperately we only get a total 42 lines-of-relationship.



....1.....................5P............7P...................11P..........13P.......................17P.......19P..................23P.......25..............outer peak of positive surface
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{0}.................................6....................................12.......................................18...................................24..................inside toroidal tube
................3...................................{9}.........................................15.....................................21....................................inside toroidal tube
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...........2..........4........................8...........10...........................{14}......16.......................20..........22....................26........inner peak of negative surface.

|* = 1, 2, 4 as triangle set  and  * as the internal #3 nodal point

|* = 5, 7, 8 as a triangle set  and the * as the internal #6 nodal point

|* = 10, 11, 12 as a triangle set the * as the internal #12 nodal point

{*} = isolated #9 inside the di=pyramidal quanta { graviton//darkion }

{0}..|* |* {*} |*...14  = the truncated di-pyramidal set of 13 points//nodes plus the non-counting {0}  inside tube not di-pyramid  and, the counting {14} outside of tube, on inner surface of torus.

So this total of 13 nodal points and we may associate indirectly, with the 13 vertexes of the the nucleated cubo{6}-octa{8}hedron aka the Vector Equlibrium{ VE } in Fullers Synergetics, i.e.  there is 12 peripheral vertexes and a 13th nuclear vertex aka one-in-the-oven { cosmic pregnancy } 12-around-1. See LINK

I take note here that when the VE as jitterbug  ---only 12 vertexes-- transforms to the double-sine-wave pattern, or a few others, its nucleus becomes 4 vertexes. So here we may see association to the 4 nodes//points inside the truncated di-pyramid.

However, the VE//jitterbug will have only 8 around 4, whereas the truncated di-pyramid will have 9 around 4.

20 days later

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In this LINK I see that the cosmic minimum 7-color surface limit LINK takes three line sections to make one revolution around the tube, not the around the whole torus.

#7 occurs as follows in relation to Pi;

31.00 62 7 66  and that is #7 in the overall 7th position as found in Pi^3{ XYZ } 31.00

24.35 22 7 27 and that is #7 in 7th position as found in  Pi^4/4{ re-normalization } aka Pi-Time { 66.4 }
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The ratio Pi { 3.14 } is close to three and it takes three line segments to complete revolution around the tube, not the whole torus.

What to do, to arrive at cosmic baseline reference value that can then be used to find mass values.

Divide Pi by three? 1.0471975511965977461542144610932

Divide Pi-Time by three 66.4 / 3 = 22.13

#1, #2-4  and inside reality nucleus #3 is surface set nodal points of three 

5-7..8 with reality nucleus #6 is 2nd set of nodal points of three within the quanta graviton/darkion set of

10..11-13 with reality nucleus #11 is third set of nodal points that total  12, however, that is still no sum-total.

We have to add #9 in there to sum-total for graviton/darkion.