In the 1940’s Gann published a 2-page list of about 90 Books that he stocked and sold to his students, known as "W. D. Gann’s Recommended Reading List".
Each book contains some component of Gann’s system of knowledge essential for piecing together his system.
Any one book may have one simple idea critical to Gann's perspective.
Weather Forecasting
Weather has a strong influence on the potential prices of crops, so Astrological weather forecasting was of great interest to market analysts.
We publish George McCormack's Long Range Astro-weather Forecasting which is considered one of the better classics.
A.J. Pearce also wrote some sections on weather forecasting which are classics.
Magick
Magick in the Western Esoteric tradition represents a Western equivalent to the internal training systems that are found in Eastern traditions, but is focused on the development of human powers and abilities.
These include mastery of physical, emotional and mental bodies, control over the elements and development of psychic perception and influence.
Prophecy
A generalized term for any kind of metaphysical methodology for predicting future events. Examples would be psychic phenomena, reading crystal balls, scrying mirrors, numerology, astrology, and many more such divinatory techniques.
These systems are popular amongst esoteric traders and forecasters seeking insight into future events.
Spiritual
Books exploring the human spirit, its state and development and relationship to higher planes and beings. General works on spirituality that are otherwise hard to categorize.
Cosmogenesis
Cosmogenesis explores the basis of Cosmic origins via intelligent universal creation, rather than materialistic random forces.
Consciousness or intelligent energy serves as the true plenum of creation, not random ordering of unintelligent matter.
Intelligent Cosmogenesis has dominated all scientific, metaphysical and spiritual ideas from ancient times.
Memory Systems
Providing systems to train the mind in the retention of concepts, lists, ideas and the like, Memory Systems can simplify much modern school study involving memory.
We explore systems used by ancients and moderns to memorize entire books, lists of items, and concepts, as a sub-section of our accelerated and advanced systems of learning.
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.
Ferrera's Collected Outlooks 2008 - 2019 are like instructional manuals in the Art of Financial Forecasting, providing educational studies on market theory and technique by a highly respected forecaster.
They expand the toolbox of even seasoned traders, providing new tools and deep insights into cycles, technical analysis and Gann forecasting.
W. D. Gann's Courses
Collected Courses of William D. Gann, by W. D. Gann. 1920 - 1954. This is the most complete and best organized collection of Gann's Master Courses, his most important writings.
Without these, Gann is impossible to understand! We've collected all the missing pieces and reorganized them back into Gann's original order.
Market Software
Technical analysis requires sophisticated measurements and calculations, so good software tools save time and allow wider scope.
We have carefully selected software for market analysis, geared towards Gann, geometric, astronomical, cycles or other related topics that we most use, including pre-programmed Gann and Astro tools.
Speculation
Speculation is the trading of market positions for the sole purpose to make money.
It is a secondary industry from general investing in stocks or trading in commodities where individuals buy and sell with no fundamental interest in the underlying market.
We publish many works using this term, like Gann’s "Speculation a Profitable Profession".
Technical Analysis
Technical Analysis involves using technical tools and mathematical measurements in order to determine expected directional movements, reverses or changes in the market.
Advanced forms of this technique use mathematical and scientific or geometric tools to project market action or forecast future movement, looking at elements of price, time and trend.
Baumring Metaphysical List
Dr. Baumring compiled long reading lists much more comprehensive than Gann's, covering all areas of the markets, science and metaphysics.
Baumring read 1800 words a minute and had a photographic memory, so he was able to collect a vast set of source works in his 10,000 volume library.
Around 500 are highly relevant to Gann’s work.
Theosophy
Theosophy, a school of esoteric thought developed my Helena Blavatsky in the late 1800’s presented a revival of many lost esoteric traditions.
Many of Gann’s contemporaries were closely involved with Theosophy, and it influenced the Anthroposophy of Rudolf Steiner, the Arcane School and work of Alice Bailey and the teacher Krishnamurti.
Physics
We don't cover all theories of modern or academic physics, but specializes in unusual books relating to applications connected with such topics as financial forecasting, and alternative or ancient cosmology.
We cover theories like electromagnetism, energy grids, vortex systems, wave theory, vibration, relativity, power laws and hyper-dimensions.
