Imitations, Falsifications and some Truths
[Exert from an introduction note as backwards analysis to The fake, the future
and the finite (a commemoration of the absolute in the 21st century)]
A regular pentagon is a five-sided polygon, where all sides are equal and all angles are equal
to 108 degrees. The interior of a pentagon is its body. In the construction of a pentagon the
golden ratio is to be found, this proportion is believed by some to be aesthetically pleasing.
In the book On learned ignorance from 1440, Nicholas of Cusa makes the comparison
between a non-circle that cannot measure a circle to what ever is not truth and therefore
cannot measure truth precisely. He describes it as “the intellect, which is not truth, never
comprehends truth so precisely that truth cannot be comprehended infinitely more precisely.
For the intellect is to truth as [an inscribed] polygon is to [the inscribing] circle. The more
angles the inscribed polygon has the more similar it is to the circle. However, even if the
number of its angles is increased ad infinitum, the polygon never becomes equal [to the
circle] unless it is resolved into an identity with the circle.” 1
triangle
hexagon
quadrilateral
heptagon
pentagon
octagon
enneagon
decagon
no name
chiliagon
A Henagon is a polygon with one side and one angle. In Euclidean geometry, it is considered
to be an impossible object, because its single side will extend to infinity. I imagine though
that when drawing a henagon on earth, earth’s circular boundary is to force the line to close
into a circle, or cause it to end just were it begins.
A Googolgon is the polygon with (1 followed by one-hundred zeros) sides, I have no tool to
draw one, and I must use a circle to represent it. If I were to draw one as big as necessary to
reveal each and every one of its sides, it would result in an enormous drawing. The distance
needed to view it in its entirety would be so great that it would again resemble a circle, or
else only fragments of it could be seen at a time.
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000
‘Descartes uses a (Polygon with a very large number of very small sides) as an example […]
to demonstrate the difference between pure intellection and imagination. He says that, on
imagining a (Polygon with a very large number of very small sides), the image produced is
not as clear and distinct as that which occurs on imagining a triangle, for example. It is also
no different from (one of a larger number of sides). However, he does understand what (this
polygon) is, just as he understands what a triangle is. Therefore the imagination must be in
some way different from the intellect’. 2
We know that understanding truth is a so-called ‘imaginary understanding’. My intellect is
not capable of imagining a googolgon as a clear and distinct form, though I know what a
googolgon will look like. I can approach few angles at a time and study them closely; I can
even join two separate angles of opposite sides and try to interpret them. But even when
doing so, each angle is too obtuse to tell if it is accurate or imprecise, it is its context that
suggests its accuracy, and its context–its absolute being– is a googolgon. This complex form,
which can be identified only by its name, resembles a truth, but by being so well defined it
remains as abstract and indistinct as a Henagon.
In the book Flatland from 1884, Edwin A. Abbott describes a two-dimensional Flatland
where Men are represented by polygons whose social status is determined by the number of
their sides. A triangle having only three sides is at the lowest social order and is considered
an unintelligent being. At the top of the social hierarchy are the priests who are polygons
with a very large number of very small sides and that approximates to a circle. So the more
generations to a shape the higher it is within the social structure. Women are a single line,
front wards they resemble a point, while from the side they can be mistaken for a priest.
The regular pentagon is a polygon with the least amount of sides of a dubious complex form.
I assume that the aesthetically pleasing regular pentagon in Flatland is similar to a
bourgeoisie, and in On learned ignorance it is some low intellect with no resemblance to
truth. To some extent the regular pentagon is a complex form, but in fact, it is simply a
square with an extra side, just a common form that suggests complexity.
This is another pentagon
And this is the pentagon within its inscribing circle
These are the parts a pentagon lacks in order to be a circle
This other circle it incorporates within could be regarded as its internally inscribed truth
When talking of a pentagon it can hardly be separated from the image of The Pentagon, this
perfect symmetry of fives is a symbol for ‘the goodness of truth and knowledge’ for some,
and ‘the evils of lies and manipulation’ for others. It is claimed that damage from its attack in
2001 was minimized due to the pentagonal form being physically a perfect shape that can
bear external powers and thus, minimize damage to the object. And so, the pentagon’s
monumentality is resolved into an identity with the perfection of a circle, for some a symbol
of the powerful protective shield while for others the house of evil.
The Torah refers to the first five books of the Hebrew Bible, also known as the Pentateuch, a
reference to the cases containing the five scrolls of the laws of Moses. The Pentateuch is
another form of a powerful and protective shield, not a visual one, but one of the word and of
narrative. The first of the five books, Genesis, is the story of a Creation and the first laws of
order, its Hebrew name literally means ‘in the beginning’.
In the beginning a reference to the enemy of order to the Creation is the Leviathan. The word
has become a metaphor for a great power opposing the power of God and is often represented
by a large aquatic monster or creature.
Destruction of Leviathan, 1865 engraving by Gustave Doré
The Satanist symbol –a pentagram with one point down inscribed by a circle, is encircled by
five Hebrew letters positioned in an anticlockwise order (in accordance with the five points of
the pentagram) reading Leviathan. In ancient times, a pentagram represented the symbol of
destruction. These two symbols of chaos and destruction are the absolute representation of evil,
though formally the construction of a pentagram is based on the Golden ratio. It is formed by
the extension of all sides of the pentagon, and therefore it possesses a pentagon in its centre.
In religion and philosophy the phrase good and evil is a reference to the appraisal of objects,
desires, and behaviours within the dualistic range –on the one side the essentially positive
and on the other the essentially negative attributes. This bipolar system is the equivalent to a
navigation device determining Man’s directions in a highly contrasted reality; it encompasses
an elaborate set of symbols and signs that are guarded by narratives and myths. Good is
assumed to be the absolute truth and is represented by white while evil is ultimately the
ignorance of truth and thus represented by black.
a
b
(a) An old style dualistic range with a gradient
(b) A contemporary dualistic range with only two poles
Good can only be identified within evil surroundings, it needs a contrasting background or
else it blends and becomes one with its surroundings. Evil’s identity cannot be mistaken
either when being a pole only, or when existing as the entire whole.
white = light
black = darkness
light = day
darkness = night
In Genesis, on the first day God creates the light, he separates the light from the darkness and
calls the light Good. Though the source of light is not mentioned it is attributed to the sun.
Our first understanding of the sun is of a glowing circle in the skies; whose presence above
the horizon creates day and absence causes night. It has been worshiped since early human
history and monuments were constructed with the sun represented as a symbol or as
metaphor for Good in the heavens.
Crop circles are geometric formations of flattened crops. It is disputed weather these are a
man-made formations, paranormal, alien or unknown creations, just as Stonehenge in the
back of this Fractal is disputed over. Stonehenge is a prehistoric monument formed by a
group of standing stones arranged in four series within a circular trench. It is believed that it
was used as an ancient scientific tool for observing the motions of the moon and the sun.
The Stonehenge Fractal, 1996
The sun in Dürer’s Melancholia I from 1514 is setting down. Man’s attempt of inventing
something new by the use of scientific tools and human reasoning has failed and led him to
frustration. All he achieved is a complex polygonal shape and a sphere. At the background of
the geometrical reasoned forms is a rainbow. A beautiful and at the time still difficult to
explain natural phenomenal, the artist’s attempt is not more than a reinvention of the
reasoned and the known.
Melancholia I, Albrecht Dürer, 1514
It is only in 1637 that Descartes gives a complete reasoning to the appearance of the
rainbow.
Until then, in religion and mythology the rainbow due to its beauty and the difficulty in
explaining it, was considered to be a path made by a messenger between Earth and Heaven or
an agreement between God and man.
The arch is a man made superstructure, in its form resembling a rainbow but requiring all its
elements to hold it together. Its configuration eliminates tensile stresses in spanning an open
space, and it can support significant distances. Triumphal arches dating back to ancient Rome
were erected to commemorate triumphs. The Euro notes depict arches of different periods
and styles in its history, though they do not represent any actual existing monument, all are
imaginary arches. These symbolize ‘the close cooperation and communication between
Europe and the rest of the world’ as has been declared by the European bank. But they
simply are a daily celebration and commemoration of forms meaning absolutely nothing.
There is a clear hierarchy of value with the representation of the oldest structure being on the
five Euro note and the newest structure on the five hundred Euro note. The five Euro note is
the common daily value that can be found in every ones pockets representing the old
classical Roman arch and aqueduct. Were as the five hundred Euro note –the ‘higher value’–
is a representation or is using the representation of modern and advanced technology that we
seek to attain. Some studies were conducted on the arches and bridges on the notes so as to
analyse their potential physicality if they were ever to be built. Studies concluded that these
structures would not be able to support themselves and consequently would collapse. Their
monumentality can therefore only be obtained in their imaginary representation.