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Fractals in a Time-Space Continuum
Second
Edition
By
Xiphias Press
Copyright ©
2015
All Rights
Reserved.
Xiphias Press
San Diego, CA 92107
Copyright © 2015 by Xiphias
Press.
All Rights Reserved.
Copyright © 2010 by Xiphias Press
Cover Design Copyright © 2015
Published in the United States of
America
First Electronic Printing:
December 2010
In Memory of
Benoit B. Mandelbrot
(1924-2010)
Contents:
Introduction - 7
Cymatics
Cymatics -
21
Ernst
Chladni - 24
Rosslyn
Chapel - 28
Math
Alan Turing
- 33
Sacred
Geometry - 39
Vitruvian
Man - 43
Platonic
Solid - 47
Rule 30 - 62
Venn Diagram
- 66
Golden Ratio
- 73
Fibonacci
Numbers - 97
String
Searching Algorithms - 107
Integral
Test for Convergence - 111
Great
Pyramid of Giza - 116
Fractals
Benoit B.
Mandelbrot - 128
Fractals - 133
Mandelbrot Set
- 141
Julia Sets
in Fractal Art - 159
Fractal
Analysis - 162
Fractal
Cosmology - 164
Diamond-square
Algorithm - 170
Banach Fixed
Point Theorem - 173
Fractal
Compression - 178
Fractal
Antenna - 183
Physics
Harmonices
Mundi - 188
Time - 191
Non-mathematical
notion of Unified Spacetime - 213
Planck
Constant - 237
Inverse-square
law - 253
Chaos Theory
- 260
Atomic
Theory - 274
Freeman
Dyson - 282
Quantum
Mechanics - 288
Electromagnetic
Radiation - 304
String
Theory - 317
Polarization
- 327
Holography -
343
Holographic
Paradigm - 359
Holographic
Principle - 363
Unified
Field Theory - 370
Theory of
Everything - 374
Biology
Evolution -
382
Human
Evolution - 406
Mathematical
and Theoretical Biology - 424
AI + DNA
Hans Moravec
- 431
Cellular
Automata - 435
Richard
Dawkins - 455
DNA - 460
Genetic
Engineering - 479
Bioinformatics
- 488
Lev Manovich
- 496
Network
Mapping - 501
Intelligence
Amplification - 505
Psychology
Brainwave
Entertainment - 510
Psychology
of Religion - 514
Experimental
Psychology - 530
DMT - 543
Parietal Eye
- 551
Magic - 553
Astonishing
Hypothesis - 576
Sacred Geometry
Vesica
Pisces - 579
Tree of Life
- 584
Flower of
Life - 591
Sri Chakra -
596
Golden
Spiral - 601
Eye of Horus
- 605
References - 610-727
Introduction
To
Fractals in a Time-Space Continuum
Second Edition
A
"Fractal" is a rough or fragmented geometric shape that can be split
into parts, each of which is a reduced-size copy of the whole, a property
called self-similarity. The origins of fractals can be traced back to geometric
functions by Karl Weierstrass, Georg Cantor and Felix Hausdorff in studying
functions that were continuous but not differentiable. The term ''fractal'' was
coined by Benoit Mandelbrot in 1975 and was derived
from the Latin ''fractus'' meaning "broken" or "fractured."
A mathematical fractal is based on an equation that undergoes iteration, a form
of feedback based on recursion.
The
mathematics behind fractals began to take shape in the 17th century when
mathematician and philosopher Gottfried Leibniz considered recursive
self-similarity. Approximate
fractals are easily found in nature. These objects display self-similar
structure over an extended, but finite, scale range. Thus, examples include
clouds, snow flakes, crystals, mountain ranges, lightning, river deltas,
cauliflower or broccoli, neural networks, systems of blood and pulmonary
vessels, sea shells, pine cones, leaves of a fern, branches of a tree and
galaxies can all be considered fractal in nature.
The
Mandelbrot set has become popular outside mathematics both for its aesthetic
appeal and for being a complicated structure arising from a simple definition,
and is one of the best-known examples of mathematical visualization. Many
mathematicians, including Mandelbrot, communicated this area of mathematics to
the public.
Fractals of
all kinds have been used as the basis for digital art and animation. Starting
with 2-dimensional details of fractals, such as the Mandelbrot Set, fractals
have found artistic application in fields as varied as film and video graphics,
medical imaging, plant growth simulation and landscape generation. In 1999,
certain self similar fractal shapes were shown to have a property of
"frequency invariance"; the same electromagnetic properties no matter
what the frequency; from Maxwell's equations.
Fractal
Analysis is the modeling of data by fractals. It consists of methods to assign
a fractal dimension and other fractal characteristics to a signal, dataset or
object which may be sound, images, atomic structure, molecules, networks,
statistics, or other data. Fractal analysis has been introduced to financial
market analysis, medicine, construction methods, engineering, and is now widely
used in all areas of science.
In physical
cosmology, "Fractal Cosmology" is a set of cosmological theories
which state that the distribution of matter in the Universe, or the structure
of the universe itself, is fractal. More generally, it relates to the usage or
appearance of fractals in the study of the universe and matter. A central issue
in this field is the fractal dimension of the Universe or of matter
distribution within it, when measured at very large or very small scales.
Fractals can
be demonstrated in observational cosmology. The first attempt to model the
distribution of galaxies with a fractal pattern was made by Luciano Pietronero
and his team in 1987, and a more detailed view of the universe’s large-scale
structure emerged over the following decade, as the number of cataloged
galaxies grew larger. Pietronero argues that the universe shows a definite
fractal aspect, over a fairly wide range of scale, with a fractal dimension of
about 2. The ultimate significance of this result is not immediately apparent,
but it seems to indicate that both randomness and hierarchal structuring are at
work, on the scale of galaxy clusters and larger galaxy superclusters.
The use of
fractals to answer questions in cosmology has been employed by a growing number
of serious scholars close to the mainstream, but the metaphor has also been
adopted by others outside the mainstream of science, so some varieties of fractal
cosmology are solidly in the realm of scientific theories and observations, and
others are considered Fringe science, or perhaps metaphysical cosmology. These
various formulations enjoy a range of acceptance and legitimacy.
In Classical
Mechanics, Newton's concept of "relative, apparent, and common time"
can be used in the formulation of a prescription for the synchronization of
clocks. Events seen by two different observers in motion relative to each other
produce a mathematical concept of time that works pretty well for describing
the everyday phenomena of most people's experience. "Time" has been
defined as the continuum in which events occur in succession from the past to
the present and on to the future. The title of this book uses Time-Space rather
than the accepted Space-Time usage to place an emphasis on the time factor in
the fractal equation but otherwise accepts the conventional term in physics.
Einstein
''The Meaning of Relativity'': "Two spacetime events taking place at the
points A and B of a system K are simultaneous if they appear at the same
instant when observed from the middle point, M, of the interval AB. Time is
then defined as the ensemble of the indications of similar clocks, at rest
relatively to K, which register the same simultaneously." Einstein wrote
in his book, ''Relativity'', that simultaneity is also relative, i.e., two
events that appear simultaneous to an observer in a particular inertial
reference frame need not be judged as simultaneous by a second observer in a
different inertial frame of reference.
Graphic
timeline animations visualize the different treatments of time in the Newtonian
and the relativistic descriptions. At heart of these differences are the
Galilean and Lorentz transformations applicable in the Newtonian and
relativistic theories, respectively. The vertical direction indicates time. The
horizontal direction indicates distance, and the curve is the spacetime
trajectory "world line" of the observer. Small dots indicate specific
past and future events in spacetime. The slope of the world line (deviation
from being vertical) gives the relative velocity to the observer.
"The
magical power of the subconscious mind". To believers who think that they
need to convince their subconscious mind to make the changes that they desire,
all spirits and energies are projections and symbols that make sense to the
subconscious. A variant of this belief is that the subconscious is capable of
contacting spirits, who in turn can work magic. "The Oneness of All."
Based on the fundamental concepts of monism and Non-duality, this philosophy
holds that magic is the application of one's own inherent unity with the
universe. That personal realization, or illumination, is that the self is
limitless, one may live in unison with nature, seeking and preserving balance
in all things.
Time has
historically been closely related with space, the two together comprising
spacetime in Albert Einstein's special relativity and general relativity.
According to these theories, the concept of time depends on the inertial
spatial reference frame of the observer, and the human perception as well as
the measurement by instruments such as clocks are different for observers in
relative motion. The past is the set of events that can send light signals to
the observer, the future is the set of events to which the observer can send
light signals. The brain's judgement of time is known to be a highly
distributed system, including at least the cerebral cortex, cerebellum and
basal ganglia as its components. One particular component, the suprachiasmatic
nuclei, is responsible for the circadian (or daily) rhythm, while other cell
clusters appear to be capable of shorter-range (ultradian) timekeeping.
From the age
of Isaac Newton to Albert Einstein's profound reinterpretation of the physical
concepts associated with time and space, time was considered to be
"absolute" and to flow "equably" (to use the words of
Newton) for all observers. The science of classical mechanics is based on this Newtonian
idea of time.
Einstein, in
his special theory of relativity, postulated the constancy and finiteness of
the speed of light for all observers. He showed that this postulate, together
with a reasonable definition for what it means for two events to be
simultaneous, requires that distances appear compressed and time intervals
appear lengthened for events associated with objects in motion relative to an
inertial observer. Einstein showed that if time and space is measured using
electromagnetic phenomena (like light bouncing between mirrors) then due to the
constancy of the speed of light, time and space become mathematically entangled
together in a certain way (called Minkowski space) which in turn results in
Lorentz transformation and in entanglement of all other important derivative
physical quantities (like energy, momentum, mass, force, etc.) in a certain
4-vectorial way.
A
"Theory of Everything" is closely related to unified field theory,
but differs by not requiring the basis of nature to be fields, and also
attempts to explain all physical constants of nature. String theories and
supergravity (both believed to be limiting cases of the yet-to-be-defined
M-theory) suppose that the universe actually has more dimensions than the
easily observed three of space and one of time. The motivation behind this
approach began with the Kaluza-Klein theory in which it was noted that applying
general relativity to a five dimensional universe (with the usual four
dimensions plus one small curled-up dimension) yields the equivalent of the
usual general relativity in four dimensions together with Maxwell's equations. Fractal
waveforms of electromagnetism are also in four dimensions. This has led to
efforts to work with theories with large number of dimensions in the hopes that
this would produce equations that are similar to known laws of physics. The
notion of extra dimensions also helps to resolve the hierarchy problem, which
is the question of why gravity is so much weaker than any other force. The
common answer involves gravity leaking into the extra dimensions in ways that
the other forces do not.
In the late
1990s, it was noted that one problem with several of the candidates for
theories of everything (but particularly string theory) was that they did not
limit the characteristics of the predicted universe. Fractal cosmology is
essentially a visualization technique to diagram the universe in multiple
dimensions as well as cosmological constants simultaneously. Even the
"standard" ten-dimensional string theory allows the "curled
up" dimensions to be compacted in an enormous number of different ways
(one estimate is
each
of which corresponds to a different collection of fundamental particles and
low-energy forces. This array of theories is known as the string theory
landscape.
A modal phenomena of an oscillating cymatic system is
a pattern of motion in which all parts of the system move with the same
frequency and in phase. The frequencies of the normal modes of a system are
known as natural frequencies or resonant frequencies. A physical object, such
as an architectural structure, a transmitting antenna or molecule, has a set of
normal modes that depend on its structure, materials and boundary conditions.
When relating to music, normal modes of vibrating instruments such as strings,
pipe organs, or drums, produce what are known as "harmonics" or
"overtones". The most general motion of a system is a superposition
of its normal modes. The modes are normal in the sense that they can move
independently, that is to say that an excitation of one mode will never cause
motion of a different mode. The concept of normal modes also finds application in wave
theory, optics, quantum mechanics, and molecular dynamics.
Fractals are
identified not as separate from the heavens but rather a force that acts and
permeates throughout the Universe. Fractals demonstrate an indisputable
connection between the invisible God and the visible heavens. Such a conception
would, to the Western Scientist, be known as electromagnetic activity
manifesting endless waves of probability. "Deus sive Natura", is the
universal metaphysic. Perception of external objects are the result of both
mental activities and external conditions. All the ultimate objects of
knowledge, nature, thought, and deity, are known by us in the same way. Keeping
our minds open to receive the necessary impressions can alone convey to us the
causes of phenomena, the psychology of interpretation and their origin.
The
"Holographic Principle" is a property of quantum gravity and string
theories which states that the description of a volume of space can be thought
of as encoded on a boundary to the region, preferably a light-like boundary
like an apparent gravitational horizon. Digital holograms can be numerically
multiplexed and demultiplexed for efficient storage and transmission. Amplitude
and phase can be correctly recovered. The numerical access to the optical wave
characteristics (amplitude, phase, polarization) made digital holography a very
powerful method. Numerical optics can be applied to increase the depth of focus
(numerical focalization) and compensate for aberration. Wavelength multiplexing
of holograms is also possible in digital holography as in classical holography.
It is possible to record on the same digital hologram interferograms obtained
for different wavelengths.
Human
History
For hundreds
of thousands of years, man's evolution must be measured by his stone tools.
Then about 120,000 years ago, a different type of man appeared in different
parts of the world. This was the Neanderthal man, named after the German valley
where the first remains were discovered. At this time, earth was in its final
glacial period so Neanderthal men took to living in caves. He hunted animals
such as reindeer, musk ox, woolly mammoth, and bear which lived at the edge of
the glaciers.
Prehistory
carried great stories with colorful parables to teach the young and entertain
the elderly. Early man (40,000 B.C.), created legends of man-like beings that
controlled nature. The sun always seems to be deified. The Sumerians, Egyptians,
Mayan, and the Greeks told complex tales to satisfy the unknowns of nature.
Today, nature is understood partially or as complete systems by science.
Scientific methods using logic and reason developed into specialized branches
that can accurately define, measure and analyze complete systems. The sun is a
star, the earth evolves around the sun, and the moon effects tides, lightning
and thunder are caused by electrically charged particles and so on.
In Sumer,
Babylon, and ancient Egypt, the priests, astronomers, mathematicians, were
often the same person, or employed by the ruling class. Mesopotamian people
merged magic, science and religion. The myth reveals history, magic is applied
to science and technology, and mystery becomes knowledge and reason. It is true
the sun is not a god but it's real. We now know that the sun is simply a star
of billions of stars in our galaxy. Consider the fact that all life of earth is
the result of light and heat radiating from the sun. Without it there would be
no life at all.
The
'''Flower of Life''' is the modern name given to a geometrical figure composed
of multiple evenly-spaced, overlapping circles. The five Platonic Solids are
found within the symbol of Metatron's Cube, which may be derived from the
Flower of Life pattern. They are arranged to form a flower-like pattern with a
sixfold symmetry, similar to a hexagon. The center of each circle is on the
circumference of six surrounding circles of the same diameter. It is considered
by some to be a symbol of sacred geometry, said to contain ancient, religious
value depicting the fundamental forms of space and time. In this sense, it is a
visual expression of the connections life weaves through all sentient beings,
and it is believed to contain a type of Akashic Record of basic information of
all living things.
There are
many spiritual beliefs associated with the Flower of Life, as with the symbols
of the Vesica Piscis, an ancient religious symbol, and Borromean rings, which
represents the Holy Trinity. These platonic solids are geometrical forms which
are said to act as a template from which all life springs. They called it the
Flower of Life because it looks like a flower and because it represents the
laws and proportions for everything alive and even not alive; everything that's
manifested. This is a significant example on how geometry allows us to
understand how the mind and body are a unitary physical and causal system. The
dreams of the human mind should be made a conscious activity tending towards
the good of the human species and all life on earth.
When a
person moves from believing to thinking, they move from the visible world to
the intelligible world, from the realm of opinion to the world of knowledge.
The state of mind that Plato calls thinking is characteristic of the scientist.
The scientist works with visible things but not simply with his vision of them.
Plato's theory of ideas have been refined and modified since they were
originally written. Nevertheless, it represents an important advance in
philosophy. "The Allegory of the Cave" is the first theory to
seriously examine the problem of universals. Practical knowledge can be applied
to daily routines to improve our quality of life. Although opinions are not as
reliable as knowledge they exist as a motivational factor generating attraction
and repulsion in biological organisms. Opinion is concerned with beautiful
things, but knowledge is concerned with beauty in itself. People who are without
a sense of spirituality can be compared to prisoners in a cave. Most people,
according to Plato, are ignorant of the external world around them, and are
preoccupied with belief, opinion, and sensory experience. Geometry is the
transformation of appearance to the world to an understanding its inherent and
underlying ultimate reality.
Quantum
Mechanics
Quantum Mechanics
challenges a simple materialistic view of the universe with the Uncertainty
Principle, the Principle of Complementary and question, "is the electron a
particle or wave?" Epicurus was generally correct in stating that atoms
fall and recoil and some lock into each other and that motions have no observed
beginnings because atoms and the void are the cause themselves. All our
thoughts and sensations conscious or unconscious are caused by atomic and
molecular relationships. Today we can trace thought to neurons and
electrochemical impulses. The mind or soul is corporeal as far as quantum waves
exist. The mind or soul exists within temporal-spatial limits and man lives
within a spectrum of reality. Only a small band of visible light can be seen
compared with the entire electromagnetic spectrum. As with our other senses,
hearing, taste, smell and touch, scientific instruments act as tools to expand
our senses, our reality, to find the answers to life, the universe and any
supreme reality beyond that if it exists.
Picture a
wave spreading out through space as though it were an ever-expanding sphere. It
describes the probability that a certain event will occur. Physicists call this
the quantum wave function. Any observer along the wave, anywhere in the
universe, could discover its secrets; but only one will. The first to look at
it is the first to collapse it into a single real event. For example, the wave
function for a particular photon from a star will fold into a spot of light
only on the retina of the first observer. Once seen, this event cannot occur
anywhere else. Everyone within the reach of the wave, regardless of the
distance from one another, is affected by this invisible quantum wave
connection. Man discovers the big bang.
Human Nature
Inherent in
man is his "Human Nature", a nature found in every man. Each man is
an example of the universal conception of man. Whether he be a primitive native
or part of the cultured bourgeois, they all have the same fundamental physical
and emotional qualities. All men posses the same essence and their essence
precedes their historic existence, which is learned through experience. The
answer is their scientific and historical discoveries. Similar events have
occurred to many great men in history. Aristotle (father of analytics and logic
in the physical sciences), Spinoza (pantheistic philosopher), Darwin
(discoverer of evolution), Gregor Mendel (father of genetics), Sigmund Freud
(founder of modern psychology), Max Plank, Albert Einstein, Niels Bohr, Werner
Heisenburg (the fathers of quantum physics).
People are
inherently different. They are pluralistic in nature, with different
economic opportunities, abilities and
geographical differences as well. Politics on a local level is as important as
global issues, however, what all people do have in common are the
Universal
truths. These universal truths tend to follow natural laws, a social political
animal forming a physical matrix of man-made laws and public architecture. How
do we live a simple natural lifestyle in such an increasingly complex world?
One solution is creating network maps of data using fractal geometry. And
applying metadata to index content and model web browsers and search engines to
quickly organize and retrieve results. With these network mapping tools we can
solve social problems with business, medical and engineering solutions based on
fractal forms.
Human
consciousness exists because of the division of hemispheres in our brain, the
physical microcosm’s manifestation of reason and emotions. The Cortex acts as a
bridge, an interface of the two halves, separate identities or modes of logic,
perception, memory and recall. Synthesized, we emerge from a primitive ocean of
pure skepticism and dogmatic solutions. The four major questions of men on our
planet are: the creation of life, creation of the universe, the purpose of
life, and finally, what happens after death.
Nature
exists independently of what man thinks of it until we decide to change it.
There are, however, an infinite amount of ways to interpret it. The differences
of how we interpret nature, life, is what ultimately divide us, as we often
work toward self interest. This is what causes differences in opinion;
politically, socially, theological, but interesting enough, not the scientific
process. And law, of course, is there a "natural law" enshrined in
the social contract of men? What do all people desire? How do we achieve the
feeling of happiness? By our ability to provide the necessary things to sustain
life: air, water, food, shelter, and peace with other people and communities
through friendship, love and understanding. Yet he can be challenged enough to
satisfy man's insatiable scientific curiosity and ability for artistic
expression. At first, scientists disagree on how this or that happens. Once the
path is observed, upon discovering the cause and nature of a particular
phenomena, it is generally accepted as fact. Sometimes man understands nature,
sometimes he does not. That is not to say science is perfect or infallible.
Science is a process. In searching for common ground of all cultures, the
answer is twofold: nature and man's will. Science and mathematically expressed
art forms allow us to assimilate experience to be creative and solve problems.
The idea of
the atom was first introduced to science by Democritus and Epicurus, more than
2,000 years ago. In humanities, an artistic expression of reality and in the
emotional response to mystery, there is not one path to follow, there are many.
Nature exists independently of what people think of it. There is only one
reality but there is potentially an infinite amount of directions to interpret
nature. This interpretation manifests as mathematics and may be used as a
universal language. The language of physics provides substance, quality and regulation
to organisms of all kind. The human animal part of an electromagnetic,
biomechanic and electrochemical matrix. Consciousness in the form of memory,
cognitive faculties, and emotions all originate from encoded cryptic seeds.
Biological tides of a sea of electricity ripple as logarithms of opposing
forces. Animate or inanimate, existence and reality are corporal,
temporal-spatial cause and effect relationships. Existence precedes essence, in
an existential world where people are self-governing and assume responsibility
for their own actions. The theory of gravity, laws of thermodynamics, particles
physics, genetic engineering, psychology, all form an impression, a signature
of nature and life. Man's architecture is comparable to the electronic slaves
he designs in anthropomorphic manifestations. Achievements of automation and computers
can reconstruct time, space, financing, manufacturing and art, all digitized
into a temporal world similar to Leibniz's monads. Digitized into reality.
Evolutionary
Logic in Analysis and Design
Evolution is
a fact. It still remains, however, a valid question to ask how things evolve.
The evolution of life, humankind, and of the universe, to the formation of
amino acids, proteins, and DNA. These questions are answered by science and
history. The first cell division, plant life, fish, birds, and mammals all
follow fractal patterns. Man is not the final product of design. Darwin's
metaphysic has continued to be the most influential scientific principle of the
century. The original thesis of Darwin's theory was to confirm a biological
natural selection in nature. As a general principle, evolutionary logic has a
profound significance in all areas of scientific analysis and design. Cellular
Automata, or the patterns of growth, are studied at Princeton. Evolution is a
method of understanding everything that occurs in nature; the growth of cities,
population densities, the history of human psychology, the cause of disease,
computer graphics for video animation, the history of architecture or even the
evolution of religion. Man emerged from the jungle and plains of Africa. He
migrated north along the Nile River. Upon reaching the fertile delta at the
mouth of the Nile, decisions were made that determined the future of the world.
Some people stayed and founded Egypt, many others traveled further along the Fertile
Crescent and divided. One group followed the sunrise to the East, while still
others choose the sunset in the West. This migration is symbolic of the left
and right hemispheres of the brain, Eastern and Western philosophy, reason and
emotions. In the brain the Corpus Callosum acts as a bridge between the two
hemispheres. The Sinai is the Corpus Callosum of the old world the internet the
social neural network of the new world.
Self
actualized, transcending ethics and morality in an amoral universe. Judgment
and value are also the logic of semantics. To educate is to facilitate
understanding of language; whether that of a general medium, (Latin, English,
BASIC, etc.) or specialized as in computer sciences, medicine, engineering,
business, or law. Fractal logic traces causality as one of the forms of general
interdependence of phenomena in the objective world. In essence, cause and
effect are only moments of interdependence in universal relation of the
evolutionary connection of events; that are present in the chain of development
of matter. There can be no phenomena without causes. All natural phenomena have
natural and material causes.
Human
Technology
Human
technology can be defined a number of ways. It is a devotion to the humanities,
that is education, music, art, poetry, philosophy, or it can be a lifestyle
centered on human interests or values. Technology is a practical systematic
treatment of applied science or art. It is what we are and why we do it.
Imagine a computer planed society not without individual initiative, but rather
one that grows like a unified biological organism, simultaneously creating a
cellular "entity", a self-actualized being with expanding artistic
value. Science and religion are concerned with different dimensions of life.
Ancient religions thought of natural and social phenomena as manifestations of
a god's will and wisdom. As science advanced some theological doctrines were
proven unreasonable in their approach to nature and human affairs, and they
were discarded as they became increasingly insufficient to explain the real
phenomena of the universe. Each individual ought to find his or her own purpose
in life. People are inherently different. They are pluralistic in nature, with
different jobs, education, mental and physical abilities and geographical
differences as well. Politics on a local level is as important as global
issues, however, what all people have in common are the universal truths. These
universal truths tend to follow natural laws, a social political animal forming
a physical matrix of man-made laws and public architecture. People will mostly
live in urbane complexes, surrounded by numerous machines (Automata). In
particular the World Wide Web has linked databases and electronic libraries
with fully automated access. A credit card economy in which cash will be
virtually eliminated. Cell phones, MP3 players and other personal and mobile
devices facilitate communications with persons everywhere.
Economic
power is more important than military power in determining a nation's
influence. The movement to worldwide free trade economic considerations
transcending political consideration, developing telecommunications and an
advancement of democracy and the spread of free enterprise. In Benoit
Mandelbrot's 2004 book “The (Mis)behaviour of Markets”, fractal mathematics are
used for modeling many aspects of the financial markets and changes the way we
should consider risk. Fractal art is a direct way to correlate everything one
has ever learned. By understanding how artistic styles modified the
environment, one can achieve a better comprehension of past civilizations and
emulate patterns in our present culture. Picasso, possibly the most important single
figure in modern art, has constantly changed his personal style and has
introduced intellectual and subjective elements of modern art into his work. He
thus maintained his position as a creative and active force. To experience the
initial illusion and the overcoming of illusion, the mind's self awareness is
the achievement and return to the nature of reality. Weltgeist, the world mind
of Hegel, the German idealist philosopher, extends beyond the confines of human
experience. Human technology has dreams, purpose, function and form.
The
Animation of Spirit
The kind of
spirituality needed to relate man to the new technologically created
environment is a spirit of synthesis and design. The animation of spirit lies
within us, our desires scan the heavens, our collective memory, the seed of the
new world. The essence
of spirit is without mystery. Traditionally defined as the soul, it is now
generally accepted by scholars and scientist to mean the part of human beings
associated with the feelings and mind. The word spirit, originates from the
Latin spirare, which means to breathe. The concept however, of soul and spirit
has been the subject of theological debate for millennia, until the founding of
modern psychology and medicine. George Hegel (1770-1831), the German idealist
philosopher, translated "spirit" as "mind". Mental activity
differs from nature in that the mind is an "I". Spirit or mind exist
for itself. This consciousness recognizes three types of spirit: subjective, objective,
and absolute. The philosophy of subjective spirit studies the individual in
relation to his social relations and discusses such topics as consciousness,
memory, thought and free will. The objective spirit deals with man's rights
towards his fellow men. These rights suppose a legal sense founded in the study
of ethics and political theory. The highest stage of spirit is the
"absolute spirit", whose three parts are art, religion, and
philosophy. According to Hegel, the study of absolute spirit has to do with
spirit as "infinite", not spirit as something boundless, but as
having returned to itself from self-alienation. That is to say that, at this
stage of thought, one recognizes that subjective and objective are one. This
absolute spirit can be experienced in the highest profundity level of the
psychedelic experience, as noted by R.E.L. Masters and Jean Houston, two
leading investigators in this area. Images journey the general history of human
beings, animal evolution and rituals of passage. The most profound level,
seldom reached is called the Integral level. Experience at this level are
religious and mystical, often dealing with a confrontation with God. The
individual may experience a union with nature. The feeling is profoundly
religious and cannot be easily defined in verbal terms.
Our mind,
thoughts and consciousness are electrochemically activated in the brain,
specifically located in nerve cells or "neurons." There are neurons,
a synapse (the gap between the neurons) and molecules that cross from one
neuron to another. These molecules are called neuro-transmitters. Our memory,
emotional characteristics and cognitive functions are encoded in a neuron or
string or matrix of neurons in the brain.
The research
of neuroscientist Efrain Azmitia of New York University demonstrates that the
brain is an active, dynamic, ever changing structure, that, in fact, can be
neurotronically engineered. Scientists speculate that alien civilizations may
have already initiated the process of breeding a race of beings whose brains are
perfectly adapted to the computer. Hans Moravec, a computer scientist at
Carnegie-Mellon University, believes that by the early part of the twenty-first
century, it will be possible to dump the data from each neuron in our brains
into a computer program, creating electronic clones that can merge with other
forms of artificial consciousness. DNA can be digitized in binary form and
reconstructed chemically in physical space.
Once in a
very great while scientists' minds discover principles and put them to rigorous
physical tests before accepting them as principle. "Acknowledging the
mathematically elegant intellectual integrity of eternally regenerative
Universe is one way of identifying God." R. Buckminster Fuller. Fractal
geometry opens a window to all the knowledge of the universe. Microcosmic and
macrocosmic worlds formed by cymatic waves unified by a single event, perhaps.
Fractals by definition are infinite time and space, absolute, pure, all
knowledge: past, present and future.
The
Mandelbrot set is a keystone in the study of the cosmos. Its cosmology requires
all current scientific knowledge in the natural sciences. To know is to
understand or be aware and recognize a truth or fact. Doing so by experience,
directly through perception of our senses or indirectly with scientific
instruments, or logic and reason. The universe is infinite. Numbers and
knowledge are potentially infinite. The known universe is and probably always
will be finite, from man's point of view. What mankind collectively knows is
finite.
All rational
men seek to understand nature or the universe, even if it is a small portion of
the whole. In this sense all men, even the Atheist, seek to know God. The
universe is constantly changing. Atoms, life and stars go through an
evolutionary process. This definition has a great unifying force that can be
shared by all people regardless of their political ideology. Arthur C. Clarke
said, “The origin of the universe might be forever unknown, but all that had
happened since obeyed the laws of physics”. Fractals unify laws and forces of
nature as one and simplify the complex world so we can understand the beauty of
it all.
Michael
Peragine
