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.