Metaphysical Nature of Price Movements

Mr Birkelbach does not offer investment advice, but merely his own personal opinion. This report has been prepared from original sources and data we believe reliable but make no representations as to the accuracy or completeness. Mr.Birkelbach , his affiliates and subsidiaries and/or their officers and employees may from time to time acquire, hold or sell a position in securities. Past performance is no guarantee of future success. Upon request, we will supply additional information.



Carl M. Birkelbach

The Metaphysical Search for the Ultimate Reality

The word physics is derived from the Greek word “physis,” which means the essential nature of things. The science of physics is the search for the ultimate truth above in the cosmos and below in quantum particles. Metaphysics is the spiritual search for the ultimate truth, above in heaven and below in the inner meaning of our soul. Presently, science is moving toward a Unified Theory that unites all the forces in nature into One. At the same time the spiritualists are unifying the God in heaven with the divine in our soul into the One. Science is also moving toward the metaphysical world with its Quantum Theory which reveals that space and time are only perceptions and that matter is no more than locked up energy and can only be expressed mathematically as a probability. Just as the metaphysical and Zen philosophers contemplated, the external world does not really exist. Hindu and Zen Buddhist tradition says that the ultimate truth is hidden by a “veil of maya.” In order to lift the veil of maya, there is a need to examine the repeating patterns of nature and its law abiding mathematical relationships for clues to reveal these hidden forces. Modern discoveries in the search for the ultimate reality of science can also help us understand our metaphysical truths. These hidden forces can influence our emotions and our lives.

Scientists tell us that at the time of “singularity” called the “Big Bang” all matter and energy were One. When the negatives separated from the positives, a process was begun through which the building blocks of our bodies and minds were formed. We are the conscious result of that process from the One. As we are part of this process from the One, we are part of nature and reflect these inherent force in our actions and in the marketplace. Price is the end result of all economic and psychological pressures and by examining the patterns of price movements, insights into the hidden forces can be explored. In the following, special attention is paid to the examination of these forces through the graphic presentation of price movements in the market as revealed through the Fibonacci Summation Series, the Dow Theory and the Elliott Wave Theory.

Historic Perspective

“What is below is like what is above, what is above is like what is below” is one of the oldest known quotations from antiquity. It is attributed to Hermes Tresmgistus, the Greek name for the Egyptian God Thoth, whose book Tabula Smaragdina(Emerald Tablet) has been preserved (the Romans called this God Mercury). Tradition has Thoth as the scribe of the Gods, the inventor of writing and the repository of all wisdom. Egypt is the source of much our ancient knowledge and has been the principal starting place for many a search for wisdom. There are occult beliefs that metaphysical truths of the ultimate reality of nature were revealed to Pythagoras and later to Plato (and maybe to Fibonacci) in their trips to Egypt. Myth has these secrets passed down to us from the past civilization of Atlantis.

The history of mathematics, as it is tied to metaphysical philosophy and science, goes back to Pythagoras(580BC-500BC). Pythagoras is known for his geometric theory, his divine musical harmony of the spheres and his doctrine that reality at its deepest level is mathematical in nature. Plato(421BC-347BC) carried on these traditions and believed that metaphysical truths are intuitive to the soul and can be seen in geometry. He reportedly said “God geometrizes” and inscribed over the entrance to his Academy “Let no man ignorant of geometry enter here.”

This philosophy that incorporates the divinity and the true nature of man into One continued in Spinoza (1632-1677) and in Teilhard de Chardin(1881- 1955). The Eastern civilizations seem more at home with these concepts as the sixth century B.C. Chinese Zen philosopher Lao Tzu said in his Tao Te Ching “the laws followed by the Tao were not laid down by any divine lawgiver, but were inherent in its nature.”

Fibonacci, Dow and Elliott

Following is a review of three individuals who saw the divine law of nature functioning in revealing ways: The works of Leonardo Fibonacci (1170-1240) and his Fibonacci Summation Series, Charles H Dow (1851-1902) and his Dow Theory and R.N.Elliott (1871-1948) and his Elliott Wave Theory reveal a mathematical symmetry inherent in nature which can be seen graphically in the price movements of the markets.

The Fibonacci Summation Series, Ratio and Spiral

Leonardo Fibonacci of Pisa, was an Italian mathematician who in 1202 after returning from Egypt wrote Liber Abaci (Book of the Abacus). The book introduced to the Western World the numeric system we now use (it replaced Roman numerals) where the position of a number determines if it is a 10 or 100 etc.

In addition to this great gift, Fibonacci in this book answers a problem about the creative reproduction function of rabbits in endless generations by introducing a mystical sequence of numbers to become known as the Fibonacci Summation Series. In the Fibonacci Summation Series (Figure 1) each new number is the sum of the previous two 1,1,2,3,5,8,13,34,55,89,144…and so on. This sequence repeatedly shows up in nature in the most surprising connections. In one instance, the botany law of phyllotaxis, has leaves growing from a plant stalk in the Fibonacci pattern. Sunflowers, daises, pineapples and pine cones also grow in swirls that obey the Fibonacci Series.


1+1=2; 2+1=3; 3+2=5; 5+3=8; 8+5=13; 13+8=21; 21+13=34;
34+21=55; 55+34=89; 89+55=144

The Fibonacci Series also tends asymptotically toward a constant ratio of 1.618 if we divide each number into the one immediately following it. The ratio had begun to gather special meaning even before the 15-century Italian mathematician Luca Pacioli gave it the name “Divine Proportion”. The Encyclopedia Britannica also calls this the Golden Ratio (Figure 2) and is algebraically designated by the Greek letter phi. While not as popular as pi (the Greek symbol used to represent the ratio of the circumference of a circle to the diameter, which is 3.1419265…) the ratio of phi also shows up in nature in a surprisingly variety of ways

1 2/1 =2.000
2 3/2 =1.500
3 5/3 =1.666
5 8/5 =1.600
8 13/8 =1.625
13 21/13 =1.615
21 34/21 =1.619
34 55/34 =1.617
55 89/55 =1.618
89 144/89 =1.618

The Golden Section (Figure 3) is found by dividing a line into two sections, so that the shorter is to the longer as the longer is to the whole. Thus one would find that this ratio is .618. The Golden Section is an important concept in both ancient and contemporary artistic and architectural design and is considered the most aesthetic proportion. Many of Leonardo Da Vinci’s artistic works are in these proportions.

A rectangle becomes a Golden Rectangle (Figure 4) when the sides of which are in the ratio of 3 to 5 (0.618) , which again is viewed as the most pleasant esthetically speaking. If a Golden Rectangle is subdivided and this process is continued and the circular arcs connected, a logarithmic Golden Spiral (Figure 5) is formed which is similar to the form of snails, animal horns and the spiral of our own Milky-Way galaxy. To check out other mathematical formulas see the Encyclopedia Britannica and other sources listed in the bibliography.

Figure 3: The Golden Section
Figure 4: The Golden Rectangle
Figure 5: The Golden Spiral

The Golden Ratio in the Great Pyramid, Euclid and the Quantum Theory

There have been attempts to associate The Great Pyramid of Cheops (2500 BC) with messages that its builders were trying to pass down to future generations. There is a myth that these messages were passed down to the Egyptians from a more advanced civilization, that Plato in his Timaeus called Atlantis. The largest of all the pyramids is The Great Pyramid, built by Khufu (Greek-Cheops), the second king of the fourth dynasty. Made of some 5,750,000 tons of stone blocks, it is the biggest building ever constructed. As a vehicle for communication it certainly was more reliable than the Great Alexandria Library which reportedly held the written knowledge of our far ancient past. Literature recorded its destruction by fire in Shakespeare’s Anthony and Cleopatra. The Greek historian Herodotus (484-425BC) was told by temple priests that The Great Pyramid was built in such a way that the area of each of its faces was equal to the square of it height. The shape of this construction yields some interesting properties. For instance, one half the base of The Great Pyramid divided into the apothem is equal to our old friend phi.

Measured in pyramid inches:
913 1/2 = 4565.5;
7387.15 / 4565.5 = 1.618

Figure 6: The Great Pyramid

Full View
Side View

The Kings Chamber in The Great Pyramid also reveals the Golden Ratio. If one were to split the two squares of the Kings chamber in half and swing the diagonal down to the base, the point where the diagonal touches the base is 1.618 in relation to the side of the square. It also appears that each flat face of The Great Pyramid was designed to represent one quarter of the Northern hemisphere. The height is to the perimeter at the base, as the radius of a circle is to its circumstance or the pole is to the earths circumstance. This happens only in The Great Pyramid. Also of interest is that the measurement around the base in pyramid inches equals 365.24 (if one divides by 10) which is the exact average of a solar and sidereal year. Maybe the builders were trying to tell us something. See the books in the bibliography for more revelations about The Great Pyramid.

Figure 7: Euclid’s Regular Partitioning Problem

Recently, it was reported by the Wall Street Journal (12/9/96) that two teen whizzes found the answers to Euclid’s “regular partitioning” problem presented 2,000 years ago. The problem states, given a line any length, devise a universal geometric method for subdividing it into any number of equal parts. The answer turned out to use the Fibonacci summation series. The graphic presentation of this solution has Golden Ratio angles that are same as a measuring tool used to predict future price movements. Even the sub atomic level incorporates the Golden Ratio. The April 1981 Scientific America displayed a graph of elementary particles of the Quantum world which showed a cubic symmetry that responded to the Golden Ratio. Some of these things can be explained away as coincidence. However, the evidence indicates a correlation between the Fibonacci Summation series and a deeper reality.

The Fundamental and Technical Schools of Price Forecasting

The fundamental approach forecasts price movements by logical cause and effect thinking. Consideration is give to all known facts such as financial statistics, earnings projections, management techniques and current news events. All this is difficult to interpret and is very subjective. While the fundamental approach is based on logic, price movements do not necessarily move based on logic, because people are affected by emotion. Price change reflects strength in supply or demand. The technical approach believes that all economic and psychological factors are reflected in price and that each investor’s fundamental knowledge and emotions are shown in price movements. By observing these price movements, the technical approach attempts to forecast future price movements by charting the price movements and interpreting their formations, cyclical patterns and trends, using an historic perspective. Particular attention has been given to stock prices because it is a social economic activity that represents a wide spread sample, there are long term statistics readily available and there has been a lot of information published about the subject.

The Dow Theory

Charles H. Dow is considered to be the first person to recognize that cycles occur in the stock market. To help prove his theory he formulated what is known today as the Dow Jones Industrial Averages which helped his Dow Jones Corporation and their fledgling publication The Wall Street Journal skyrocket to success. Today the theory he developed, and that which was later expanded on by William Hamilton and Robert Rhea, is known as the Dow Theory. Dow realized that stock prices did not drift aimlessly but seemed to rise and fall in patterns. He noticed that over the years stock prices moved in trends which had defined characteristics and that these patterns repeated themselves. By careful observation of these patterns he concluded that the stock market moved in three simultaneously movements. He compared these movements to the ocean where its primary dominating trend is the tide, its secondary trend are waves and the minor fluctuations being ripples. Dow saw the Primary Trend of the market lasting many years in either a rising ‘Bull Market’ or a declining ‘Bear Market’. The Secondary Movements against the Primary Trend lasts from days to months, while Dow believed Daily Movements to be of little significance.

Figure 8: The Dow Theory


Dow also observed that the primary trend went through phases. For a ‘Bull Market’ the Primary Trend went through three phases. Phase I would start from overly depressed perceptions about the future and see prices rise on the expectation that thing will get better. Phase II is a further rise in prices in response to things actually getting better. Phase III is when prices rise too far as investors become overly optimistic about the future. During a “Bear Market”, Phase I occurs as prices decline to more realistic levels on expectation about the future. Phase II would be further decline in prices reflecting reaction to negative news. Phase III would be the final decline in prices and would reflect an overly pessimistic view of the future. It is interesting to note that a contemporary view of individual biorhythms duplicate exactly the phases of the market movements. Observation of price movements is an excellent measurement of human activity and the hidden forces that drive emotional response.

The Publication of Elliott and His Disciples

R.N. Elliott believed that all of nature’s activities acted and reacted in a form that reflected a law-abiding mathematical relationship that repeated in cyclical rhythmic form. Elliott used the previously discussed Fibonacci Summation Series and its application for pattern and ratio to explain price movements. Elliott believed that this rhythmic regularity was central to and part of creation that could be observed in the price movement of the markets. Through Charles J. Collins, Elliott explained his theory in The Wave Principal published in 1938 and in 1939 Elliott published a series of articles in the Financial Word Magazine. In 1946 he publishedNatures Law. Reference to the works of Elliott after his death in 1947 were relatively obscure with the exception of A Critical Appraisal by A. Hamilton Bolton in May 1960 and references to the Theory in his Bank Credit Analysis.

In 1978 Robert R. Prector and A.J. Frost published the Elliot Wave Principal. In the early 1980’s Prector was the primary guru of Wall Street with his market letter The Elliott Wave Theorist having predicted the ‘Bull Market’ of the 1980’s. However, he predicted a ‘Tidal Wave’ collapse of the stock market for the 1990’s. The application of the Elliott Wave Theory to predict the future direction of price movements is obviously subject to varying interpretations. With this unfortunate and incorrect prediction, reference to the Elliott Wave Theory have once again become obscure. During the 1990’s investors didn’t need to pay attention to fluctuations, as it became a ‘no brainier’ to just buy General Electric type stocks or a mutual fund and to hold on.

The Elliott Wave Theory

Elliott observed that primary trends of bull cycles of price movements have five impulses (Fig. 1) with three moves up interrupted by two corrective moves down. He also observed that each primary trend of a bear cycle has three impulses, with two moves down and one interrupting corrective move up. It should be keep in mind that in counting waves, Elliot believed that wave three should be the longest except if there is what is called an unorthodox top (to be shown later). Elliott described cycles in great detail and how they could be broken down into smaller cycles. Each cycle works within the frame work of a larger cycle. As shown inFigure 9 – top, a major cycle consists of five major moves up with a correction of three moves down.

The five major moves up could be broken down further (see Figure 9 – middle) into five minor moves up and three minor moves down for a total of 21 waves and a correction of five minor moves down, three minor moves up, and five minor moves down for a total of 13 waves.

Breaking that cycle down into great detail (See Figure 9 – bottom) we would have a 21-13-21-13-21 wave cycle up for a total of 89 waves with a correction of 21-13-21 waves down for a total of 55 waves. Each wave can be broken down further into smaller waves. This method could be carried on infinitum. As a tip to simplify this process one should consider charts where every line represents a month when looking for the Primary Trend, weekly charts for Intermediate Trends and daily charts when examining minor trends. Sub Minute trends can only be seen in intra day activity. Charts below are from my Introduction to the Elliot Wave Principal.

Figure 9: Elliott Waves

Names and Designation of Elliott Cycles




PRIMARY ((I)) to ((V))



MINUTE 1 to 5




The largest cycles Elliott addressed were Grand Super Cycles that lasted several hundred years. Operating within the Grand Super Cycle are Super Cycles that last approximately 55 to 89 years. Within the Super Cycles are Cycles which last 21 to 34 years. Within the Cycles are Primary Cycles which last from 5 to 8 or 13 years. Within the Primary Cycles are Intermediate Cycles which last 2 to 3 years. Within the Intermediate Cycles are minor cycles that last about a year. Minor Cycles are completed about every month while Minute Cycles are as little as two days and as much as 13 days. Sub-Minute Cycles can be measured in hours.

Various Elliott Wave Formations

Elliott filled his publications with various formations and patterns such as what he called Zig Zag and Flat Corrections, Horizontal Triangles, Diagonal Triangles and the Extension of moves. These are outlined in my pamphlet Introduction to the Elliott Wave Theory. An explanation of these formations would not add much to this discussion and might be confusing. Below is one more Elliott formation for the end of a move and some basic trend line analysis from my Stock Market Profits Through Charting,

Figure 10: Another Elliott Wave and Trend Line Anaylsis

My Own Search for Interpreting the Elliott Wave Theory

My father took a ten-year hiatus from work after selling his business in 1951. He devoted all of his extra time to the study of the technical methods of predicting the future direction of stock prices. We took courses and did research on various technical methods for predicting the stock market. One such course in 1960, offered by a Detroit firm Swing Measurements Inc., was on the Elliot Wave Theory. Made available at this course was information on the theory and tools for measuring future price movements using the Fibonacci Ratio. In 1962, my father and I visited Charles Collins (mentioned above) in Detroit. This was the man who over the years vigorously corresponded with Elliott and helped him write his first book. He gave us many insights into predicting stock prices movements. Over time I have collected much information on the Elliott Theory. In 1975, I taught a $2,000 per person course on the Elliot Wave Theory and the Strategy Index.

I have consistently used the Elliott Wave methods in my own market letter The Investment Strategy Letter which began in January of 1975 with the Dow at 500 to herald in a new series of ‘Bull Markets’. I was quoted in 1979 and 1980 in Barron’s calling for a Dow of 2500 (the market went to 2600 in 1987 and then fell to 1600). In September of 1981 (with the Dow at 800) I wrote the now well known “Lone Bull Letter,” which predicted the oncoming ‘Bull Markets’ of the 1980’s and 1990’s. Because of the fall of communism and the new market driven economies throughout the world, in February of 1992 (with the Dow at 3000), I wrote the “Lone Bull Revisited Letter” in which I predicted (using the Elliott Wave Theory), a continuation of the ‘Bull Market’ to above a Dow of 8000. Below is a chart from the “Lone Bull Letter ” dated September 1981 in which I used the Elliott Wave to forecast the BIG UP MOVE!

Figure 11: Lone Bull Chart of 1981

The Da Vinci Code Addendum 2004

In writing the Metaphysical Nature of Price Movement I postulated that there are “hidden forces” within nature with repeating patterns and law abiding mathematical relationships. We humans, as part of nature, reflect these inherent forces in our actions and in the market place and therefore in price movement. I stated that there are “occult beliefs” that these metaphysical truths “were revealed to Pythagoras and later to Plato (and maybe to Fibonacci) in their trips to Egypt.” The burning of the Alexandria Library (so well dramatized in Shakespeare’s Anthony and Cleopatra) destroyed much of the written wisdom that should have passed down to us from antiquity. The recent best selling novel “The Da Vinci Code” uses as its theme the search for the “Holy Grail” of certain “truths” that were handed down to us from antiquity (through a secret society) from Pythagoras and Da Vinci and was suppressed by the early church. Earlier, in the synopsis, I point out in reference to the “Golden Section” and the “Golden Ratio” that “many of Leonardo Da Vinci’s artistic works are in these proportions.” The novel cleverly uses the Fibonacci coded messages in giving clues in the quest. Besides being entertaining reading, the novel offers the general public a palatable introduction into some of the theories presented here.
Additional help comes from Scientific American Magazine, which on page 44 of a February 2004 article entitled “The Cosmic Symphony” states: “New Observations of the cosmic microwave background radiation show that the early universe resounded with harmonic oscillations…Sound waves…reveal the age, composition and geometry of the cosmos.” So how far off was Pythagoras, who in 550 B.C. spoke of his divine “harmony of the spheres”?
Just as a scientist uses mathematical probability in interpreting the Heisenberg Uncertainty Principle, the technical analyst can use the Elliot Wave Principle in forecasting the probability of price movement. In this process the technician’s goal is not to tell the market what to do, but to obey and listen internally to the signals that the market is giving us. As Lao Tzu says in the Tao Te Ching (600 B.C.): “The laws followed by the Tao were not laid down by any divine lawgiver, but were inherent in its nature.” The fact that Tao and Dow are pronounced the same is merely a coincidence, or is it? All this is cause for deep and contemplative thinking and further research.
In the meantime, one must be internally “at peace” to listen to the market. Don’t forget to enjoy Beethoven’s “”Ode to Joy.” Beethoven was deaf at its first performance and never heard it as you can. However, I believe he could feel it internally. So, let your search for the “hidden forces” become internal. “The trend is your friend.” Listen to that internal inner voice within, until you can come in tune with the “harmony of the spheres.”

Estimating the Extent of Future Price Moves

Measuring the future price movement of a stock can be done by using variations of the Golden Ratio. Below is a representation of a measuring device which was improved upon by my father. This device can mechanically make the measurement given on the next page.

Figure 12: Measurement tool

Forecasting Future Price Movements

The below calculations are based on the process used in determining the Fibonacci Golden Ratio. The .618 phi ratio, has been rounded out to the nearest quarter of a point to .625, for easier calculations in predicting future stock price movements.

Figure 13: Forecasting Charts


1. Minimum AB(x) = BO x = 1.625 3 x 1.625 = 4.875
2. Maximum AB(x) = BN x = 2.000 2 x 2.00 = 6.000
3. Extension AB(x) = BM x = 2.625 3 x 2.625 = 7.875


1. Minimum AB(x) = BO x = 1.625 3 x 1.625 = 4.875
2. Maximum AB(x) = BN x = 2.000 3 x 2.00 = 6.000
3. Extension AB(x) = BM x = 2.625 3 x 2.625 = 7.875


D Minimum AB(x) = BD x = 0.500 12 x 0.5 = 6.000
C Maximum AB(x) = BC x = 0.625 12 x 0.625 = 7.500


D Minimum AB(x) = BD x = 0.500 12 x 0.5 = 6.000
C Maximum AB(x) = BC x = 0.625 12 x 0.625 = 7.500





NATURES LAW—————————————————————R. N. Elliott

THE WAVE PRINCIPAL—————————————————–R. N. Elliott

CHARLES H. DOW AND THE DOW THEORY————————–George W Bishop Jr.

THE ELLIOTT WAVE PRINCIPAL(an appraisal)————————-A. Hamilton Bolton

THE ELLIOTT WAVE PRINCIPAL—————————————–Frost and Prector


THE STORY OF PHILOSOPHY———————————————-Will Durant

THE TAO OF PHYSICS——————————————————–Fritjof Capra

BELONGING TO THE UNIVERSE——————————————Fritjof Capra

THE PHENOMENON OF MAN———————————————–Teilhard de Chardin

STOCKS WHEAT AND PHARAOHS—————————————-William O’ Connor

SECRETS OF THE GREAT PYRAMID—————————————Peter Tompkins


HORIZON MAGAZINE (Winter 1971)—————————————-Peter Tompkins

PERFECT SYMMETRY———————————————————Heinz R. Pagel

THE SPIRITUAL IN ART (Hidden Meaning in Abstract Art)—————Maurice Tuchman


Fibonacci, Leonardo ——————————————————- —-Book 7:279

numbers—————————————————————————Book 4:759

number games——————————————————————–Book 25:5

number systems——————————————————————Book 8:826

number theory——————————————————————–Book 25:22

cipher machine——————————————————————-Book 16:852

Da Vinci, Leonardo———————————————————– —-Book 25:361

Pythagoras———————————————————————— -Book 9:827

harmony of the spheres———————————————– ———-Book 19:92

philosophy————————————————————————Book 25:737

numbers as the real meaning————————————————– -Book 24:6

theorem—————————————————————————Book 19:901

number theory—————————————————————– –Book 25:23

Euclid——————————————————————————- Book19:899

Non Euclid Geometry———————————————————- —Book19:925

Plato————————————————————————— ——Book 25:893

pythagoreanism——————————————————————-Book 25:508


mysterious religion————————————————————- -Book6:469

mathematics———————————————————————–Book 23:565

Herodotus—————————————————————————Book 17:909

Hermes Trismeegistos————————————————————-Book 5:875

Hermetic writings—————————————————————-Book 24:711

Thoth——————————————————————————Book 11:731

The Great Pyramid—————————————————————–Book 5:288

measurements———————————————————————Book 23:687

construction———————————————————————–Book 18:111

k 18:111


1 thought on “Metaphysical Nature of Price Movements”

  1. Hi! Excellent article. Unfortunately all of the links to the pictures appear broken and I am unable to see the content of any of the pictures. Just the text. Do you have like say a pdf file as a back up you could send to my email?

    Best wishes


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