{The Sphere [continued (10)]}[24th July 1988]

[Redbook5:224-225][19880724:1443j]{The Sphere [continued (10)]}[24th July 1988]

19880724.1443

[continued]

Pascal[‘s Triangle] Stage n=2,* associated with the Circle (by me!), makes possible an interesting explication of the favourite current **theory of unification of forces, in its simplest terms – bearing in mind ***the slight skew in relationship terms which is apparent in Pascal’s Triangle (above)**** used for this purpose, and also in the first circle of Archetypes (giving attributes – slightly different from now) which I can trace in my notes# (and which is evident in the fiction in the closer relationships of +C and +M on the one hand, and +K and +Mk on the other).

(Either the cross or the arrows may be distorted, according to the major purpose of the diagram.)#*

[Text on the ms rough working diagram shown above is too complex to be properly represented in tables here at present.]

This fits with the general direction of the Circles: i.e. from relative singleness and ‘strength’ on right hemisphere through Distraction to relative plurality and ‘weakness’ on left hemisphere (or reversed thro’ Diversity, of course), i.e. dropping off forces on the way.#**

This would allow for the fact that going away from Energy at the bottom,#*** the Weak [Nuclear] Force gets weaker and the Stronger [sic] [Strong Nuclear] force gets stronger (i.e. as Hawking describes it, but in the direction of ‘Time’).

*[i.e. level. Ref e.g. [Redbook5:222][19880724:1443g]{The Sphere [continued (7)]}[24th July 1988]]

**(cf II [[Redbook2:159A(-W)][19791021:2000]{Fundamental Forces}[21st October 1979]], ff [– probably])

***ref II.[[Redbook2:71C][19750913:0000]{Destruction}[13^th September 1975],] 71C [– apparently]

****ref [[Redbook5:222][19880724:1443g]{The Sphere [continued (7)]}[24th July 1988],] 223

#[reference not yet found]

#*‘The basic idea of [Grand Unification Theories]... is as follows: ... the strong nuclear force gets weaker at high energies[;] … the electromagnetic and weak forces [...] get stronger at high energies. At some very high energy, called the grand unification energy, these three forces would all have the same strength and so could just be different aspects of a single force.’ (per Hawking, ibid ['A Brief history of Time', Bantam, 1988], p73)

(The E[lectro-]M[agnetic] and Weak forces are already shown to be unified at a lower temperature)

#**(The W[eak ]N[uclear ]F[orce] is conventionally shown as leaving the E[lectro-]M[agnetic ]Force mainstream, but when only [those] 2 [forces] are left[;] I do not know why this should be so.)

[cf [Redbook4:151][19871021:1425c]{Superstrings and Fundamental Forces [continued (3)]}[21st October 1987]]

#***or at the top? – if Time runs down the diagram? <880730>

[continues]

[PostedBlogger20092018]

{The Sphere [continued (9)]}[24th July 1988]

[Redbook5:223][19880724:1443i]{The Sphere [continued (9)]}[24th July 1988]

19880724.1443

[continued]

I guess that the further down the [Pascal’s] Triangle* you go, the less distinct or noticeable are the boundaries between levels – if only because of the greater or absolute number of items originating in higher levels.**

*[See last two previous entries; & [Redbook5:218-239][19880722:2307]{The Sphere}[22nd July 1988]]

**It should also be obvious that the number of items [on each level of Pascal’s Triangle]* does not restrict the number of Individuals – except, I guess, in levels n=0, & n=1(?)

[continues]

[PostedBlogger17for19092018]

{The Sphere [continued (8)]}[24th July 1988]

[Redbook5:223][19880724:1443h]{The Sphere [continued (8)]}[24th July 1988]

19880724.1443

[continued]

Is the [Pascal’s] Triangle* cumulative downwards? – i.e. does each level include the previous level in itself, or as (a) separate level(s)? In this context, it depends how you look at it. If you look only at your level, only the items of that level exist. But if you see the triangle (or [the] ‘cone’)** as a whole, the higher levels exist concurrently with your own.

----

*[See last previous entry; & [Redbook5:218-239][19880722:2307]{The Sphere}[22nd July 1988]]

**[sic – not necessarily referring (or referring only) to Pascal’s Triangle, but possibly (or possibly also) to the Cone discussed earlier, e.g. [[Redbook3:211-214][19870419:1050h](THE STRUCTURE OF TOTALITY)[19th April 1987],ff].]

[But cf [Redbook5:226-227][19880724:2355c]{The Sphere [continued (15)]}[24th July 1988], final fn]

[continues]

[PostedBlogger17for18092018]

{The Sphere [continued (7)]}[24th July 1988]

[Redbook5:222-223][19880724:1443g]{The Sphere [continued (7)]}[24th July 1988]

19880724.1443

[continued]

*Pascal’s Triangle and the Octet Rule** (Stability of 8)[:]

(1) Although each level is relatively stable, being 8 or a multiple/factor, the cumulative total at each level is always one short of 8, encouraging a change to the next (or last!) level.

(BUT (2) It is arguable that 8 (level n=3) is the most stable and that other levels will always tend up or down towards that.

There is, I believe, some kind of qualitative change in the nature of the expansion (in the context considered) which occurs at about n=4 ((n=3 gives 8)).

Big Pascal:

(Amended 880725ff)

[{cf III.220} from level n=3-4 above]***

[{VI.152} from level n=3-4 above]****

[Text on the ms rough working diagram shown above is too complex and has been too much amended to be properly represented in tables here at present.]

*(ref [[Redbook5:221][19880724:1443e]{The Sphere [continued (5)]}[24th July 1988]] 221)

**[See last previous entry]

***{III.[[Redbook3:217-222][19870502:1025](EVOLUTION OF PATTERNS OF SYMBOLS)([&] DIAGONAL PERSONALITIES) [2nd May 1987],] 220

****{VI.[] 152}

[continues]

[PostedBlogger16for17092018]

{The Sphere [continued (6)]}[24th July 1988]

[Redbook5:222][19880724:1443f]{The Sphere [continued (6)]}[24th July 1988]

19880724.1443

[continued]

Note:

[Cum = cumulative. Text &c on the ms rough working diagram shown above is too complex to be properly represented in tables here at present. ]

(I would not expect the Atomic Shell Model to be linked directly to the Tarot Pack, or vice versa!)

This is interesting, but inconclusive.

________

[continues]

[PostedBlogger16092018]

{The Sphere [continued (5)]}[24th July 1988]

[Redbook5:221][19880724:1443e]{The Sphere [continued (5)]}[24th July 1988]

19880724.1443

(Originally inspired) Attempts to develop a new structure for the booklet(s),* at the same time as contact in various ways with Pascal’s Triangle, have led to a renewed consideration of the two together, mostly in note form on notes for the booklets plan, from which some of this is taken:)**

Too little space! See [[Redbook5:218-239][19880724:1443#]{The Sphere [continued(7)]}[22nd July 1988]] page 223

[Text on the ms rough working diagram shown above is too complex and has been too much amended to be properly represented in tables here at present.]

*Particularly explication of the structure of the Circles

**(& see [[Redbook5:218-239][19880722:2307]{The Sphere}[22nd July 1988]] 219 above.)

[continues]

[PostedBlogger14for15092018]

{The Sphere [continued (4)]}[22nd July 1988]

[Redbook5:220][19880722:2307d]{The Sphere [continued (4)]}[22nd July 1988]

19880722.2307

[continued]

The ‘Stretchy Wriggle’* which, rather than a Point, is taken to represent an individual on the Circles (in a particular context) might seem merely a device for avoiding precision – until it is appreciated that a similar image or representation underlies the Wave-Particle duality consequent upon Heisenberg’s Uncertainty Principle which gives rise to Quantum Mechanics.

*ref [[Redbook5:112][19880324:2307]{The Stretchy Wriggle}[24th March 1988]] 112

[continues]

[PostedBlogger14092018]

{The Sphere [continued (3)]}[22nd July 1988]

[Redbook5:219-220][19880722:2307c]{The Sphere [continued (3)]}[22nd July 1988]

19880722.2307

[continued]

*But I am also intrigued by the loose similarity of the (x+y)ⁿ basis** to the equation for the circle: x² + y² = r²*** (via Pythagoras’ Theorem).****

#

Taking in also the simple equations for the Cardinal Polarities (or Cartesian axes):

Vertical ‘y’ axis/polarity: x=0

Horizontal ‘x’ axis/polarity: y=0

and the diagonals (which may not be necessary):

Top left to bottom right: y=-x (and x=-y)

Bottom left to top right: y=x (and x=y)

(on the convention that positive, +, is right and up) – there perhaps begins to emerge some vague and simplified idea of how the construction and operation of the Circles#* might begin to be mathematically described.

The prospect of linking this in some way with actual experiment in Probability (i.e. Random) and Chaotic states makes this particularly interesting, as these are the two areas of mathematics which seem to have the most success in describing the World we actually experience every day.

*[See two last previous entries]

**NB Distributive Law separates! <880724>#

The obvious relationships are:

(1) Difference of:

2(x²+y²) – (x+y)² = (x-y)²

= 2x² + 2y² -x² -2xy -y²

= x² -2xy +y²

= (x-y)²

– which was arrived at by experiment;

i.e. 2 X (Circle Formula) less (Pascal#** Line 3 (Circle)) = ((Vertical Dimension) less (Horizontal Dimension))^squared

(or vice-versa, presumably, & no matter which is greater of x & y)

&

(2) If x = y (as they would in a circle),

(x+y)² = 2(x²+y²)

i.e. (Pascal#** Line 3#*** formula) = Twice (Circle Formula)

<880724>

***[where r = radius – see [Redbook5:206][19880703:0145]{A Mathematical Experience}[3rd July 1988]]

****[In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c: “a² + b² = c²”, where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. (Adapted from Wikipedia)]

#Murphy, Additional Mathematics Made Simple, p67.

#*(or ‘Circle’ – can be viewed (per Pascal’s#** Δ [Triangle]) as simply one circle rotating 2 ways.)

#**[See last previous entry but one, [Redbook5:218-239][19880722:2307]{The Sphere}[22nd July 1988]]

#***[ms has Pascal Line 2 but this must be a mistake for Pascal Line 3]

[continues]

[PostedBlogger13092018]