Like W D Gann, Bayer understood the Secret Cosmology behind the financial markets discovered within Ancient teachings.
His 9 books cover deep esoteric finance, including topics like Squaring of the Circle, the Ellipse, and the 5 Fold Horoscope. We do a quality hardcover reprint of each of his works and offer a 2 Volume Suede Edition of his Complete Works.
Egypt
Ancient Egyptian culture can be traced back 72000 years via Egyptian and Greek records, and encompassed the worlds greatest architectural achievements.
What we know of Egypt seems to indicate a legacy from a still older civilization lost in the annals of time.
Our collection seeks to uncover the lost wisdom and mysteries of this great civilization.
Glass Bead Game
This derives from a book by Hermann Hesse, representing an underlying symbolic cosmology that is the basis of all science, philosophy, spirituality and thought.
Hesse imagines a game created using universal symbols to represent flows of thought or information.
This is a metaphor for systems of esoteric symbolism underlying all knowledge.
Mysticism
Most mystical systems tend to come from Eastern Traditions, dominated by Hindu Vedanta and Buddhism, followed by the Sufi tradition.
Judaism has the mystical tradition of Kaballah, and Christianity has great figures like Meister Eckhart, St. Teresa of Avilla, Hildegard von Bingen and Thomas Merton.
Learning Systems
Special Learning Systems use maximally efficient techniques to accelerate learning, enhancing memory, rapid mathematical calculation techniques, artistic systems, physical, and mental or spiritual training programs.
Ancient and modern intellectual technologies combine to create new fruitful approaches to learning and understanding.
Philosophy
In ancient times science and philosophy were interwoven, such as in the ideas of Pythagoras, Plato, Aristotle, the Alchemists.
Philosophy is at the root of human knowledge, and we specialise in systems of thought and ideology, particularly concentrated upon alternative and classical works.
Time
Time is a primary consideration in science, philosophy or financial market theory.
Our collection of titles on Time in all of its elements covers subjects which range from Hyperdimensional Time Cycles to Relativity and Spacetime.
Books selected by Dr. Baumring and W.D.Gann provide deep insights into market analysis and scientific or esoteric cosmology.
W.D. Gann Works
We stock the complete collection of the works of W.D. Gann.
His private courses represent the most important of his writings, going into much greater detail than the public book series. Our 6 Volume set of Gann's Collected Writings includes supplementary rare source materials, and is the most reliable compliation of Gann's unadulterated vital work.
Hans Kayser's Textbook of Harmonics - Excerpts §27. Parabola, Hyperbola, Ellipse
By Hans Kayser
Kayser’s harmonic research provides profound insights into W. D. Gann’s Law of Vibration and the function of parabolic and hyperbolic growth in space as described by Dr. Jerome Baumring.
Introduction
Hans Kayser’s work presents a masterful elaboration of the system of harmonics and vibration, looking at it from the standpoint of a universal system on order which applies from mathematics to geometry to astronomy and even to subjects such as the financial markets. Our clientele is deeply involved in the theory of the Law of Vibration developed by W. D. Gann, and this section will demonstrate to traders the valuable applications to Gann theory and analysis which Kayser’s work brings. Subjects like the parabolic and hyperbolic and elliptical growth in the markets and the use of ellipses and harmonic relationships between impulse waves and reactions through key lines, like the angles on Gann’s geometrical market charts can be seen in the Gann like diagrams below.
Let us imagine two tone-generating points surrounded by circles of equidistant waves. At some point, depending on the distance between the points, these circles of waves will intersect. In reality, of course, they will always be spheres, but projection on a plane is sufficient to discover the laws by which these intersection points occur. One must then simply imagine the relevant figures transposed into the spatial realm, turning an ellipse into an ellipsoid, a parabola into a paraboloid, and a hyperbola into a hyperboloid.
If we connect the intersection points of the two groups of concentric circles, we will trace out ellipses or hyperbolas (Fig. 167), depending in which direction we proceed. Since Fig. 167 is very easy to draw, the reader can derive the formula of the ellipse (Fig. 167a) and the hyperbola (Fig. 167b) by counting off the radii that generate the respective intersection points. This shows that the ellipse traces all the points for which the sum of their distance from A and their distance from B is equal, while the hyperbola traces all the points for which the distance from A minus the distance from B is equal.
Figure 167a
Figure 167b
Figure 168
We have thus achieved the derivation of the ellipse and the hyperbola through the intersection of two fundamental phenomena of general vibration theory: the two wave-spheres.
We can read off the parabola directly from our diagram (Fig. 168). Its ratios are:
Major
0/2
1/1
(0/0)
0/3
2/2
2/1
(0/0)
0/4
3/3
4/2
3/1
(0/0)
0/5
4/4
6/3
6/2
4/1
(0/0)
0/6
5/5
8/4
9/3
8/2
5/1
(0/0)
c
c′
g′
c′′
e′′
etc.
Minor
2/0
1/1
(0/0)
3/0
2/2
1/2
(0/0)
4/0
3/3
2/4
1/3
(0/0)
5/0
4/4
3/6
2/6
1/4
(0/0)
6/0
5/5
4/8
3/9
2/8
1/5
(0/0)
c
c,
f,,
c,,
as,,,
etc.
Figure 168
Here is the proof that they are parabolas: the familiar parabola equation x2 = 2px changes into y2 = x for a parabola whose parameter is 1/2, i.e. the y-coordinates (perpendicular lines) are equal to the square roots of the corresponding x-coordinates (parallel lines). For the parabola 0/65/58/49/38/25/10/0 in Fig. 168, 5/1 is the perpendicular line 2 units away from the point 5/3 on the x-axis, and the length of the x-line 9/3-5/3 contains 4 units. The y-value 2, then, is the square root of the x-value 4. The x-value 0/3-9/3 has 9 units as its axis, the corresponding y-value 9/0-9/3 = 3 units. √9 = 3, etc. The apexes of these parabolas generate further parabolas. We obtain a beautiful image of these parabolas (Fig. 170) from their fourfold combination, anticipating what will be further discussed in §32.
The hyperbola also has a simple and interesting harmonic derivation. If we draw the partial-tone-values of its string-length measures perpendicularly (Fig. 171) and turn them sideways, always using unity as a measure, then we get perfect rectangles, identical in area to the unit-square. Connecting the corners then produces a hyperbola, whose equation is a2 = xy, as is generally known. In our case, this means that
1/1 · 1/1
}
1/2 · 2/1
= 1
1/3 · 3/1
etc.
Figure 170
Figure 171
Figure 172
As we saw above, the hyperbola is the geometric location for all points for which the difference between the x- and y-coordinates is the same. Thus we can also explain their “harmonics,” as in Fig. 172.
The hyperbola, drawn in points, continuing endlessly in both the x- and y-directions, indicates that from any point placed on it, a rectangle of consistently equal area can be introduced between the curve and the axes A B C. If d – B = 1, then we have:
for:
length:
height:
therefore, the quadrilateral’s area:
a2
1/4
4/1
1/4 · 4/1 = 1
b2
1/2
2/1
1/2 · 2/1 = 1
c2
3/4
4/3
3/4 · 4/3 = 1
d2
1
1
1 · 1 = 1
e2
4/3
3/4
4/3 · 3/4 = 1
f2
2/1
1/2
2/1 · 1/2 = 1
g2
4/1
1/4
4/1 · 1/4 = 1
Figure 173
The law of hyperbola construction therefore shows us an increasing arithmetic series (1/n2/n3/n4/n ...) and a decreasing geometric series (harmonic n/1n/2n/3 ...)—a precise analogy to the intersecting major-minor series of our diagram.
And if we consider, moreover, that the ellipse is the geometric location for all points for which the sum of two distances has an unchanging value, then it is easy enough to construct the ellipse harmonically with reciprocal partial-tone logarithms, since their sum is always 1—for example, 585 g (3/2) + 415 f (2/3) = 1000. In Fig. 174, this tone-pair is drawn with a thick line and marked for clarification. We mark two focal points 8 cm apart (Fig. 174) for the construction of the ellipse, draw one circle around one focal point at radius 5.9 cm (585 g) and one around the other at radius 4.1 cm (415 f), then trace the intersection points of each pair of rays, up to the point where the two shorter f-rays intersect with the circumference of a small circle drawn around the center of the ellipse, and the two longer g-rays intersect with the circumference of a larger circle drawn around the center of the ellipse. These two outer circles, whose radii are of arbitrarily length, serve simply to intercept the vectors (directions) of the single tone-values and to distinguish them clearly from one another. All other points of the ellipse are constructed in the same way. The tone-logarithms here were simply chosen in order for the construction of the ellipse points to be as uniform as possible. If the reader has a good set of drawing instruments, then he can use all of index 16 for point-construction—a beautiful and extremely interesting project. In this case it would be best to use focal points 16 cm apart, and to double the logarithmic numbers.
Figure 174
Even if this construction of an ellipse from the equal sums of focal-point rays is nothing new and can be found in every elementary textbook, its construction from the reciprocal P-logarithms still gives us an important new realization. As one can see from the opposing direction of rays in the ratio progression of the outer and inner circles, the tones are arranged here in each pair of octave-reduced semicircles, and thus the directions of the ratios of the two circles are opposite to each other. From the viewpoint of akróasis, then, there are two polar directions of values concealed in the ellipse: a result that might alone justify harmonic analysis as a new addition to a deeper grasp of the nature of the ellipse.
Parabola, hyperbola, ellipse, and circle (in §33 we will discuss the harmonics of circular arrangements of the P) are of course conic sections, i.e. all these figures can be produced from certain sections of a cone, or of two cones tangent at their apexes. The above harmonic analyses, of which many more could be given, show that these conic sections are closely linked to the laws of tone-development, which supports the significance of the cone as a morphological prototype for our point of view. In pure mathematics, this significance has been known since Apollonius, renewed by Pascal, and discussed in De la Hire’s famous work Sectiones Conicae, 1585 (the reader should definitely seek out a copy of this beautiful volume at a library), right up to modern analytical and projective geometry. For those interested in geometric things and viewpoints, hardly anything is more wonderful than seeing the figures of these conic sections emerge from an almost arbitrary projection of points and lines, aided only by a ruler. For a practical introduction see also L. Locher-Ernst’s work, cited in §24c.
§27a. Ektypics
Mathematically speaking, ellipses, parabolas, and hyperbolas can be defined as the geometric location of all points for which the distance from a fixed point (the focal point) is in a constant relationship to the distance from a fixed straight line (the directrix). On this rest the projective qualities of conic sections and the possibility of constructing them by means of simple straight lines (the ruler).
In detail, as remarked above, these “curves of two straight lines” have many more specific harmonic attributes—for example, the octave relationship (1 : 2) of the areas of a rectangle divided by a parabola, the graphic representation of harmonic divisions in the form of hyperbolas, etc. One obtains the “natural logarithm” when one applies the surface-content enclosed by the hyperbola between the two coordinates (F. Klein: Elementarmathematik vom höheren Standpunkt aus, 1924, p. 161); thus, a close relationship also exists between the conic sections and the nature of the logarithm. The applications of the laws of the conic section are many, especially in the exact natural sciences. I will mention only the Boyle-Marriott Law, which connects the respective number-values of pressure and volume, and in which the hyperbola emerges as a graphic expression (and thus the pressure : volume ratio of the reciprocal partial-tone values 4 : 1/4, 2 : 1/2, 1 : 1, 1/2 : 2, etc. are expressed most beautifully). I am also reminded of the “parabolic” casting curves in mechanics, the properties of focal points, parabolas in optics, the countless “asymptotic” relationships, etc. Admittedly, these applications are mostly obscured by differential and integral calculus, though doubtless simplified mathematically—in other words, the morphological content of conic sections is outwardly diminished in favor of a practical calculation method, but remains the same in content.
Figure 175a
Figure 175b
Because of this, it is not astonishing when a figure such as a cone, from which all these laws flow as from the source of an almost inexhaustible spring of forms, is applied emblematically even in the most recent deliberations of natural philosophy, as a direct prototype for the “layers of the world” and for our “causal structure.” In Figures 175a and b I reproduce the diagrams from H. Weyl: Philosophie der Mathematik und Naturwissenschaft, 1927, pp. 65 and 71, which speak for themselves.
§27b. Bibliography
Thimus: Harmonikale Symbolik des Alterthums, 4th part. H. Kayser: Hörende Mensch, 65, 66, 126, and familiar geometry textbooks.
The Law of Cause and Effect, Creating a Planetary Price Time Map of Market Action, by Daniele Prandelli. This course presents the correct application of W. D. Gann's Planetary Longitude Lines, using a proprietary conversion factor to properly tune them by sympathetic resonance to any market!
One of Gann's most powerful trading techniques.
PFS Grain Forecast
2019 PFS Grain Forecast Bulletin by Daniele Prandelli. A Swing Trader's Forecast Based Upon Gann's Key Principles. The PFS Forecasting Model gives a model of the most expected highs, lows, turns and impulses and is then combined with Key Price Levels as determined by Gann's planetary longitude lines, creating a tradable forecast for the coming year.
Elliot Wave
Techniques, tools and systems particularly focused upon or the Elliot Wave pattern.
Spirals Growth & Decay
The Spirals of Growth and Decay, Exposing the Underlying Structure of the Markets. By Daniel T. Ferrera 2005.
Utilizing deep concepts from nonlinear mathematics to mechanically describe the structure of price waves in financial market data, linking the ideas of shock, balance, instability, static and dynamic form in all trading markets.
Hans Kayser
Kayser was a leading 20th century scientist who made a profound mathematical, geometric and philosophical study of Harmonic Science. Available in English though our Translation Society, Kayser's works explore deep principles of Pythagorean Harmony and Order.
His books give critical insights into Gann Theory and The Law of Vibration.
Celestial Mechanics
Celestial Mechanics deals particularly with the motion of celestial bodies, especially the solar system, but also wider regions of cosmic space.
The subject explores the relationships and processes of heavenly bodies, examining cycles of time, motions of celestial bodies, and the influences between cosmic and local forces.
Gann Science Reading List
In the 1940’s Gann published a Recommended Reading list of about 90 books, each containing an essential part his system, which he sold to his students.
n the 1980’s Dr. Baumring compiled about 70 of these titles, and we have collected the remainder, providing the only complete set available.
We strongly recommend these works to all Gann students.
Natural Philosophy
In the 1700-1800’s Natural Philosophers studied a wide range of scientific subjects, while not overly specializing in narrow and limited fields as scientists do today.
WD Gann espoused this more holistic system of science, where the different branches were more easily integrated and the grand vision of the scientific system was more interlinked.
