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 circumstances.

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 Fibonacci 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 analyzing 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

inter-connectedness 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 been 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.

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