The universe exhibits a mysterious underlying order. It is
interconnected at levels that are hidden from the most powerful
scientific minds in existence today. Nothing is as it first
appears. One of the prime examples of this is the Fibonacci
numbers – a sequence that is built into all levels of creation.
They crop up in many places and circùmstances.



The Fibonacci numbers were discovered by the 13th century Italian
mathematician Leonardo Fibonacci and written about in his great
work Liber Abaci. It is more accurate to say that he
re-discovered them, because they were definitely known to the
Ancient Greeks and Egyptians. The Greeks based most of their Art
and Architecture upon the Fibonnaci ratio, and Egyptians
incorporated this ratio into the Pyramids.

Fibonacci derived the number series to solve a mathematical
problem related to the breeding speed of rabbits. The series
itself is very easy to generate. These are the first few terms:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…..

Basically, the next term in the series is generated by adding the
two preceding terms, e.g. 144 = 55+89.

The Fibonacci ratio itself is also easily derived. Take any two
adjacent terms of the series and divide the earlier term by the
later. For example 2/3 = 0.666, 3/5 = 0.600, 5/8, 0.625, 8/13 =
0.615, 13/21 = 0.619, 21/34 = 0.617, 34/55 = 0.6182, 55/89 =
0.6180…..

You will find that these ratios eventually converge to the
"magic" Fibonacci ratio of 0.618. This is also known as the
Golden Ratio. It is prevalent throughout Nature, as well as
in man-made creations. For example, the width of all standard
picture frames are 0.618 of their length. Notes in music are
related to each other by Fibonacci ratios.

The ratio itself has some weird mathematical properties. If you
square 0.618, i.e. multiply it by itself, you get 0.382:

0.618*0.618 = 0.382.

However, this is the SAME number you get by subtracting the
Fibonacci ratio 0.618 from unity, i.e. 1 – 0.618 = 0.382

 If you take any term in the Fibonacci series and divide it by
the
term two places later, you again converge to 0.382 as you proceed
up the series. For instance, 21/55 = 0.3818, 34/89 = 0.3820,
55/144 = 0.3819, 89/144 = 0.382. Conversely, divide the same two
terms the other way round and you get 55/21 = 2.619, 89/34 =
2.6180, 144/55 = 2.6181, 233/89 = 2.6180. In other words, you get
2 + 0.618. The same Fibonacci ratio of 0.618 crops up yet again!

In truth, there are even more relationships than the ones pointed
out so far. However, these examples should demonstrate to even
the non-mathematical reader that this is a VERY strange number
series indeed! Suffice it to say that there is a Fibonacci
Association, complete with Fibonacci Quarterly Journal, dedicated
to analysing all the strange relationships of these intriguing
numbers!

The numbers themselves crop up throughout Nature. For instance,
it is said that the number of seeds and petals on a sunflower are
both Fibonacci numbers. Many other examples of the discrete
numbers abound in Nature. However, a particularly common and
interesting manifestation is the Golden Spiral.

The Fibonacci Spiral – Its Presence Throughout Nature.

As we have said, this ratio of 0.618 occurs widely throughout
Nature. The most famous example is the Golden Spiral, which is
the basis of all spirals witnessed in Nature; from the spirals on
the shells of marine creatures right out to the vast shapes of
spiral galaxies. Again, the Golden Spiral is very simply derived
mathematically.

Here are some examples:

(a) The classic example of the Golden Spiral is the shells of
shellfish like the Nautilus.

(b) The spiral can also be found in the vastness of galactic
space, in the form of some spiral galaxies a hundred thousand
lights years or more in diameter.

(c) On more earthly levels, skilled surfers moving through the
eye of a wave are covered by a partial Fibonacci spiral.

(d) The epeira spider spins its web in a Fibonacci spiral.

(e) Bacteria grow at an accelerating rate that can be plotted
along a Fibonacci spiral.

In fact, virtually everywhere that you see spirals in nature,
they are described by Fibonacci numbers.

The Fibonacci Ratio In the Financial Markets

Examples of Fibonacci phenomena abound in the stock, commodity,
bond and currency markets too. In fact, this is so much the case
that Fibonacci calculation methods are included as standard in
all software programs used to plot price charts. Currency
dealers, despite being a hard-boiled lot, do know their Fibonacci
levels extremely well for purposes of trading the markets.

The common appearance of Fibonacci is in the relationships
between highs and lows on a price chart. For example, if you
calculate the price difference between a market top and its
subsequent bottom, you will very often find that the next peak or
trough is formed at a Fibonacci relationship to this distance. In
other words, the market may retrace exactly 38.2% or 61.8% of the
previous move. This happens often enough, and exactly enough, for
it to be a law of the markets, and not merely wishful thinking.

The higher ratios work too. If a market made a top, followed by a
bottom, and then trades ùp to make even higher highs, you will
often find that a new top forms at a 1.382 or 1.618 multiple of
the distance between the previous top and bottom.

These relationships work to some extent in time too. Thus, a
third top or bottom may be found to have formed at a time
multiple of 1.382 or 1.618 of the time interval between two
previous two peaks. Also, the actual Fibonacci numbers themselves
work quite well in time, so analysts look for tops 7, 13,21,
34,55… weeks, months, or even years, after previous major tops
of bottoms!

It should also be mentioned that these Fibonacci relationships
exist at all time scales. Thus, you can observe them on a price
chart where the minimum time increment is only 5 minutes, as well
as on very long-term charts where the minimum time increment is
one month.

Metaphysical Significance of Fibonacci Structures

The existence of Fibonacci number structures throughout the
universe, at every level, has tremendous implications. it is
important to understand THAT THERE IS NO SCIENTIFIC EXPLANATION
WHATSOEVER for their existence. That they do exist, no scientist
would ever dispute. However, WHY they exist is a complete and
utter mystery.

Thus, with Fibonacci numbers, as well as other numerical
sequences that are present in nature, we have direct evidence for
an underlying structure to the universe; a shaping principle that
defies our rational intelligence to explain. If these numbers
were isolated in one instance, such as ONLY on the shells of
snails, we might think no more of it. It is a local phenomenon,
peculiar to the specific situation. However, the fact that they
occur almost everywhere you look, and in a breathtaking diversity
of forms, gives any open-minded observer serious pause for
thought.

Thus, there are certain engineering principles built into the
universe, and Fibonacci numbers are an outward evidence of this
secret order. Although we do not understand the mechanism, the
presence of this constant structure of numbers across a wide
range of nàtural phenomena is proof of a hidden order to
creation. At present, this hidden order remains within the realm
of mysticism.

Fibonacci numbers also point to a powerful interconnection
between all things. For we have seen that living beings, like
snails and insects, inanimate objects like spiral galaxies, and
even abstract phenomena like stock price charts, all exhibit the
same underlying number sequence. This implies an
interconnectedness between all things that is at present
unexplained. Science is coming to a realization of the extent to
which the universe exhibits this holistic structure. However, as
it has bèen for countless ages past, the mystery of Fibonacci
numbers, and the underlying unity of Creation with Consciousness
itself, remains within the realms of mystical exploration.

Copyright 2001, Asoka Selvarajah. All Rights Reserved.

_______________________________________________________________

Asoka Selvarajah is a writer on personal growth and spirituality, and the author of "The 7 Golden Secrets To Knowing Your Higher Self". His work helps people achieve their full potential, deepen their understanding of mystical truth, and discover their soul's purpose. You can subscribe to his FREE ezine, and get his FREE ebook "Inner Light Outer Wealth" at:
http://www.aksworld.com/AspireToWisdom.htm?imk=Blog _______________________________________________________________

You have permission to reproduce this article in your ezine, website or offline publication as long as you do so in its entirety, and include both the copyright notice and the resource box at the bottom.

In the midst of our busy, frantic, high-tech lives, it is vital
to keep hold of the real reasons why we are here; the things that
really matter. 



It's far too easy to get entrapped by high-tech society and
its toys, or by career and its nèver-ending promises. Should we
get the latest DVD system? Or satellite TV? How's the car doing?
Perhaps a new one wouldn't be a bad idea. And don't forget the
computer, plus related software! Oh, and then there's the mobile
phone. Do you have the one that sings and dances yet?……

The point is that none of this is what life is really all about
at the deepest level. Certainly, these trinkets are fun to have
at times. Often, they can be most useful. However, all too often,
we are in danger of letting our minds get bogged down in this
stuff; paying the bills, bùying gadgets, and other peripheral
preoccupations. Yes, you do have to budget time for some of this.
However, let's not budget away all the time that there is!

If you fall prey to doing so, a certain hardening of the
spiritual arteries occurs imperceptibly. What you focus your mind
upon always expands. Thus, if your focus is primarily external,
concerned with gadgets and getting ahead in life, then this is
what will inevitably grow in your awareness. At the same time,
you can gradually become spiritually desensitized; less aware of
your essential humanity and your basic capacity to relate to
others and to Nature in an authentic manner.

People tend to compartmentalize their lives in an attempt to
retain some sanity. For instance, many talk about spending
"quality time" with their family. In other words, with little
time to spare in a busy life, such people are determined that
whatever time they do spend is the highest "quality time".
However, this kind of thinking is a product of a modern
high-speed society, and betrays a fundamental misunderstanding of
how human nature really works. Children don't want "quality
time". They don't even understand the notion of it. They want ALL
the time and love that you can possibly give them! Most parents
who preoccupy themselves with "quality time", whilst indulging in
their real obsession – their careers – wake up one morning to
discover that they have missed watching their kids grow up.

We can also live for the future whilst failing to live in the
present. It's so easy to make ambitious plans involving jobs,
assets, and money in the bank. These plans pròmise you happiness
at some indefinite time in the future. In the meantime, you fail
to be happy right here and now! We should indeed remember to stop
and smell the roses. Instead, we motor right on by; eyes fixed
firmly on the shimmering mirage dancing on the horizon, which we
nèver ever quite seem to reach, no matter how fast we drive.

The point of all this is that what really matters in life usually
lies in the immediacy of the moment. It lies in relationships
with loved ones, intimate moments of communion with Nature,
dwelling in silent meditation upon your inner core, giving of
your time frèely to others without harboring resentment or
regret, experiencing the journey RIGHT NOW instead of at some
indefinite point in the future.

The in-tray will always be full. That will be as true on the day
you die as it is today. On the deathbed, nòbody has ever wished
that they could have spent more time at the office. The time for
living and being happy, and for sharing your life with others, is
right now. If you await some future date, when everything is
"just right", you will wait forever.

None of this implies that you should throw away goals and
strategic planning for the future. These are essential tools for
shaping the life you desire. However, it is vital to find the
right balance. This is all too often missing. The secret of
happiness is to realize that it is a moment by moment choice. To
be happy, choose to be happy wherever you are in life, and
regardless of external circùmstances. Most people miss this. They
think that being happy is some rare elusive state, attained only
as a result of achieving external material, or status, targets.
In truth, you achieve happiness by consciously choosing happiness
NOW, and living in the moment.

Precious experiences only emerge when you make time for them.
They do not always show themselves during periods of "quality
time". They cannot be summoned to order. They unfold gently as a
result of an attitude to life. Moreover, they are different for
each person. These experiences can warm your heart and perform
deep inner transformation. They may be very simple; so much so
that to describe them to another might evoke a "so what?"
response. Yet, they remain infinitely precious to you.

For one person, it might be finding a baby bird that has fallen
from a nest, and having the unique learning experience of
nurturing that tiny creature for a while. For another, it might
be watching a son or daughter grow up, and giving love
unconditionally to that child. It may be the thoughts that come
to you gently, as you stroll alone in the countryside, or in the
company of your beloved.

Are you now going to "allocate" some time for these activities?
If so, you are missing the whole point. It is a matter of
lifestyle and life purpose – what you are really here for – and
not of time management. If our schedules are too long, and our
minds too filled with out own self-serving needs, such moments
will be extremely rare. Then life may "jolt us awake" with some
unexpected happening or deep tragedy. 

First-hand experience of things that really matter and touch us
deeply only come if we allow plenty of untroubled time for them.
We need to always conduct our lives in a spirit of gentleness and
inner searching. Then, we shall reap the true riches within our
lives; riches that cannot be bought with money. We will live
authentically and in happiness. This is our true purpose in life.

Copyright 2001, Asoka Selvarajah. All Rights Reserved.

_______________________________________________________________

Asoka Selvarajah is a writer on personal growth and spirituality, and the author of "The 7 Golden Secrets To Knowing Your Higher Self". His work helps people achieve their full potential, deepen their understanding of mystical truth, and discover their soul's purpose. You can subscribe to his FREE ezine, and get his FREE ebook "Inner Light Outer Wealth" at:
http://www.aksworld.com/AspireToWisdom.htm?imk=Blog _______________________________________________________________

You have permission to reproduce this article in your ezine, website or offline publication as long as you do so in its entirety, and include both the copyright notice and the resource box at the bottom.

It's an interesting fact that the concept of zero had to be
invented. In fact, it was invented around 500BC by the
Babylonians for largely mathematical purposes. Prior to that,
there was no such concept.

In fact, it's not too hard to realize why it took so long for
this concept to come to us. The concept of "nothing" or "zero" is
an abstraction; a mathematical concept that we need to juggle
numbers, but which does not really exist as such in Nature.

Does that seem absurd? Think about it for a moment. Everywhere we
look around us, we see a fullness of something. If a person
leaves a room, you don's see "nothing", but rather, you see a
room. It may have a lot of other things in it, but at that
precise moment, there is no person there. That is not "nothing"
or zero.

The vacuum of outer space is not zero either. It is filled with
particles and energy. Indeed, it is particles and anti-particles
are continually popping into existence and disappearing again
through the vacuum of space. There is no zero there. 

Zero is a mathematical tool that we are so used to that we think
it is in Nature. However, for the most part, it is not. You can
readily see the numbers in Nature, e.g. two (arms), six (legs on
an insect), and so on. Where do you see zero, apart from in your
own mind? 

We continually conceive of things in Nature emerging from zero or
going back to it. Science tells us that the universe came into
being from nothing. Many believe that after death, there is
extinction. However, if zero is really the abstraction we have
been discussing, then it might be better to think of it, not as
extinction and non-existence in a negative sense, but rather as
an invisible fullness, a field of latent possibilities from which
all things emerge.

Not only is this more representative of reality, it is also a lot
less unnerving. Throughout Nature, we see transformation from one
form to another. We see growth and decay. But we do not see a
move to "nothing". Perhaps you fear extinction when you die? Yet,
this "extinction" is no different to the mode of non-existence
you experienced before you were born. At that time, you were
awaiting manifestation out of the fullness of the zero from which
all things emerge. Upon death, you simply transform back into
that state. 

Behind the universe moves the unnamable mystery of nothingness.
However, it is a nothing that is really a something that can only
be described in negative terms by human language. It is a
pregnant darkness of thought and intelligence, ready to
continually give birth to new forms and absorb old and wasted
ones in order to give them rebirth in new forms.

This zero is the mystery behind the Kabbalistic Tree of Life. It
is the Brahman of the Hindus. It is the Nirvana of the Buddhists.
In modern scientific terms, it is the quantum flux underlying the
matter and energy that manifests in our visible universe. 

Hence, Zero has a POSITIVE quality about it. It is not the
depressing void of extinction and emptiness that our habitual
mental association with mathematical conceptions has led us to
believe. Perhaps we can even say that the zero better resembles
infinity, i.e. infinite possibility, than it does nothing. 

This has tremendous practical applications. One of the most
important is in facing Death. With this new understanding, it is
possible to understand that your life energy GOES somewhere on
death. It does not fade out to non-existence. If we think
otherwise, it is because we associate too much with the false
"permanence" of the body, and this physical life we have created
for ourselves, and not enough with the processes of change
transformation and rebirth that are the very fabric of the
universe.

You can meditate upon this. Contemplate zero, the infinite mother
of all manifested reality, and the home to which it all returns,
only to emerge once more in new and interesting forms. As you do
so, it will be a comfort to your life, and a source of spiritual
insight and depth for you.

Copyright 2004. Asoka Selvarajah. All Rights Reserved.

_______________________________________________________________

Asoka Selvarajah is a writer on personal growth and spirituality, and the author of "The 7 Golden Secrets To Knowing Your Higher Self". His work helps people achieve their full potential, deepen their understanding of mystical truth, and discover their soul's purpose. You can subscribe to his FREE ezine, and get his FREE ebook "Inner Light Outer Wealth" at:
http://www.aksworld.com/AspireToWisdom.htm?imk=Blog

You have permission to reproduce this article in your ezine, website or offline publication as long as you do so in its entirety, and include both the copyright notice and the resource box at the bottom.