A Little Diatribe on the Most Basic Perception of Dimension

8/9/2019 A Little Diatribe on the Most Basic Perception of Dimension

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A little Diatribe on the Most Basic Perception of Dimensions.

Ok people, Im going to have a little bit of fun here; and once youve realised the blocks

of what Im passing along in your own minds; so will you if you have an artistic bias.

This lesson actually owes a big debt of thanks to the late Dr. Israel Regardie, who

unveiled the teachings, rites and mysteries of the Golden Dawn (Im guessing the term only

actually makes a reference to what they of the Quabbalistic Arts consider to be the ability to

perceive the Prima Materia which is the Astral Realm. But it takes a slice of numerological

knowledge to explain something with very visual foundations inside its beating heart.

There are three or four concepts that all artists should begin to fully understand the

implications of:

Pi (equations for finding the volume of a sphere by taking measurements of its 3 radial

circumferences),

Phi (the pyramid builders calculation; involving , two thirds the base equals the height),

the Golden Mean (also called Fibonaccis measurement; and basically equates to the fact

that if the Earth and the Moon were combined, they would equal 1 unit; but as separates, the

Earth is three-fifths, and the Moon is two-fifths; so the Golden Mean ratio is 0.6:1.0, which

means that give a number of people a straight line as a straw-poll and they will usually pick a

point closer to being six-tenths of the way along the line, whereas before these experiments,

predicted ideas wouldve indicated they thought people would choose to bisect a line half-way

along; not two-thirds or 66% of the way along. Many people dont know why this ration looks

better on the eye, but it is the foundation of the Imperial system; rather than the metric

imperial is about the hexadecimal (units of sixty), whereas metric is about the dodecimal (units

of one hundred). Interestingly, if you plotted a line between Earth and the Sun, the Moon occurs

one-third of the distance, in a direct line; which is partly why an eclipse can hide all o f the sun

but the corona).

The last concept is one Im not all that familiar with myself; its called the Sacred Cut. I

think I may be aware of it, but not by name as much as by having figured a few spatial

relationships out on my own.

The first part of this little exercise focuses on a cube and its relative planes of symmetry

and both bisection and dissection; since the two things are not entirely the same, in relative

nature. Other interesting subjects include; the Lost Cubit, and proves that geometry seems a

much more interesting sphere of mathematics than simple arithmetic or anything else metric.

First, we will look at the simple construction of the cube as an isometric drawing; which

is pretty interesting on its own. You have to excuse any crudeness I may present in rendering

images; but I do it all freehand. I believe Leonardo da Vinci helped to devise rulers, compasses,

set squares, etc. to help artists express their ideas if they didnt have senses as honed as his to be

able to use predictive thought the essential confidence that you are powerful enough to do it

on your own without relying on such pieces of mechanical actuation. Well lords and ladies, that

isnt me.


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First, well describe the cube as it should be easiest to perceive and recreate. The mode

is isometric; across the flat and [any appropriate vagary of] diagonal plane [which is

appropriate to get the image across in a way that is easily perceived and understood by others].

Two parallelograms located directly one above the other and then four lines beginning at the

one point of the above square and linking to the corresponding point it lies directly above on the

lower.

This is an interesting theorem in itself, since my mind free-associates, and equates the

top parallelogram to the Astral Realm, the linking lines to the Realms of Mentation or thought

, and the lower parallelogram as the Physical Realm; just as in Hindu beliefs the eggs shell

equates to the body, the yolk equates to the mind, and the white equates to the soul. But enough

of that stuff for now.

As I have indicated on the drawing itself; there are twelve primary sides, eight

secondary sides, eight corners, six faces, three planes of dimension. One object; many meanings.

But this is only the ideology behind the cubit; the cubit block encl oses a pyramid six times if the

pyramid has four tri-corner sides and a square base and the centre of the points converge

within the centre point.

The next part of this which will be explored in a moment or so, after the diagrams are

applied; is the bisection and dissection along with what is known as The Sacred Cut. Or, to be a

little less ambiguous since this manages to fuse at least two concepts together; the Diagonal Cut

in application across the cube to demonstrate the relationship of spaces. I suppose, to be any

more ambiguous, the point where things converge and diverge could also be called The Book Of

Crossroads; although that concept is Greek and rather Bacchanalian in nature and ideology.


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Now, we have to start to bisect and dissect the cube as seen; in order to be able to start

to understand some of the overlying and underlying spatial relationships in the simple act of

partition.

Now this small sketch deserves another shown in orthographic (a mode of drawing

showing all sides on one sketch to be able to describe it from the sides, plan, and end elevations)

view, to help show the mirrored facets and indicate what I mean, when I say the opposing

factions equal across four sides to describe two shapes in quintet or eight configurations (four

with three sides, four with five sides).


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Okay, this small diagram tends to look like a bifurcated roofing eave (A frame). But it

starts from the first point visible on the diagram above it and then also turns around counter-

clockwise to show the mirrored perceptive forms that are flipped in reverse from square tosquare after the first bisection line is given.

Next, its time for us to explore a little more and add a second bisection line, to show the

forms evolution; Ill probably have to start going into colour pretty soon, to be able to describe

things a little better on subsequent sketches.

Now, we can start adding more planes of dimension by adding other cuts and examining

the structure as it changes. I was going to turn the cuts at right angles to each other; but then I

remembered a little of my blacksmithing training, and was advised that if you dont forge

parallel sides as the metal is shaped i.e.: 180 degree turns from one side having been worked

on to the next side; and if you dont then you can manage to turn the outer surface around a


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spiral against the central core of the molecular structure, which is divisive to the overall

structural integrity of the finish component, which explains why I turned to the corner 180

degrees away from the first cut to add the second one. Although the amount of labelling is now

the most divisive element, and needing a quick remodelling of the sub-diagram to show the

relationships as the form changes through the dissection and bisection process.

As I say, it shows the mirroring principle across the adjacent sides well enough; but now,

it begins to take on the more confusing aspect, as the pieces that are mirrored start to share the

dual numbers on a single shape; and in fact, b and d represent the Palindrome concept across

two cuts, so the label reverses, as the shape also mirrors in the opposition (i.e. the figure marked

a is a small perpendicular triangle elongated right angle; whereas the figure marked b is

now the truncated pentagram; whereas c is the mirroring small perpendicular triangle

elongated right angle; and the figure marked d is the mirroring truncated pentagram of the

figure labelled b; the same but opposed and overlapping.) And the worse news is that next, its

to get a bit more complicated still.


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Now the figure has the second to last cut added. Im not going to try to draw any

conclusions from this little project Ive set myself (especially since there are still another three

diagrams to go before Im finished and the top of my head might explode in the process; since

Im only using memory, eye, mind, and hand to render the images). I think the thing I perceived

that interested me the most happened in the mental analysis of the form, when I applied one cut

to it and then looked at the inter-relationship between the spaces left, and saw them mirroring

each other from adjacent face to adjacent face, because the cogs in my mind also put my

thinking along the lines of positive and negative polarities and the meeting points, and Ill do

some more drawings based on the phi concept to illustrate what I thought I figured out about

this (Although its hypothetical, so I could be wrong; but on with the next orthographic synthesis

of the three-cut sketch):

Now, we start to see something even more interesting emerging from the figure, as the

progression unfolds. It now has three diagonal cuts (Sacred Cuts which, I suppose means to

make the opposing slice across the furthest distance which truly centralises it in a cube, to

equally oppose the forces of good and evil; speaking more of the philosophical implications. Im

a big fan of walking the line.) After the next two sketches, well see something more interesting

emerge from out of the form which is now not just related to the actual spaces and how they

interrelate; but also in how the diagonal lines visible across the orthographic view interrelate toone another as well. Ill say nothing for now, and let it unfold itself as I produce it.


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Now I start to give a clue to what the last drawing actually is. The clue is that as the first

lines were diagonals playing against one another on the first two drawings; so a second

mirroring effect comes into play, and the first clue came from the paralleling of the one line, and

the next clue before I actually provide the sketch itself, is the fact that to complete the form, the

other line must have its mirroring partner; in order to give us the final part of the puzzle.

Im glad I set it out this way; in terms of the ordering of the drawings and the positioningof them upon subsequent pages (e.g.: a little piece at a time but on cambered page layouts).

There are a lot more parts to unravel in the riddles posed by the relationships of pi, phi, the

sacred cut, the golden mean; but now, Ill provide th e last piece of this puzzle and draw it all into

a much more easily recognisable form upon which we can all be focusing. As I said, there is a

form to be found in the arrangement of lines; and its another piece of an ancient puzzle that

uses the cube, the arrangement of the four cuts located at ninety degree angles, and the

positioning and centralisation procedure on the opened out model, which shows the final object

in this set, IN ADDITION to showing the interrelatedness of forms adjacent to one another.

And there we go. Weve just perused the construction of the Celtic Knot four-strand

straight braid (dissemination of knowledge across four mental worlds, perhaps?) anddiscovered, in the series of cuts itself within the divisions in the cube, the eight -pointed star; and

shown the symmetry of the form. Who would normally expect to find such intricate artistic

forms hidden within the deconstruction of a standard cube? Thats part of the convergence of

forces which form the basis of geometry and how it affects the worlds of art, science,

mathematics, construction, and music.

Those in the Quabbalistic Orders would say that this essence is the serpent which was

used to reverse the damage the original did in the Garden of Eden, at the time when Moses was

allowed to create a serpent which he wound around a staff to help free the Canaanites from the

scourge of the fire serpents in the desert; the re-unifier; which is put in the centre of the form

known as the Radix. This point is called sphere7

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D Tree of Life: Tiphareth or Beauty, orthe Sun, or Gold; to state its original Hebraic name and original number within the system, the

Sphere of the Solar System it corresponds to, and the Alchemical Metal Element that is also

equated to it. The essence of benign Fire. More will follow later; but this little lesson is enough

Light to ponder for now.

This has explained more about phi; and golden mean and sacred cut together, if pi has

been a little excluded. But even so, it is one of an ongoing list of lectures. Enjoy for now.

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A Little Diatribe on the Most Basic Perception of Dimension