Introduction to Fractals in a Time Space Continuum
by Michel Peragine
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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, 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, numerical, 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 minority
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.
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.
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
(electromagnetism, 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 constrain 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 a 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 it's 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 particularly the Greeks
told complex tales to satisfy the unknowns of nature. Today, nature is
understood partially or in full 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.
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 it's 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 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 microcosms 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 scientifically. 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.
The
idea of the atom was first introduced to science by Democritus and
Epicurus, more than 2,000 years ago. In humanities, artistic expression
of reality and his 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 mainframe 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 do
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.)
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 central data
banks 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 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. It's
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
12/21/2010
http://www.amazon.com/Fractals-Time-Space-Continuum-ebook/dp/B0072SN3AM/ref=sr_1_2?s=digital-text&ie=UTF8&qid=1328078458&sr=1-2
