The Gann Pyramid, Square of Nine Essentials. By Daniel T. Ferrera. A groundbreaking course on the Square Of Nine, Gann's most mysterious calculator.
This course explains the essence of this fascinating tool and its useful principles, with detailed expositions of key applications to the market. Gann's most secret and powerful trading tool!
George Bayer's Works
Complete Works Of George Bayer. 2 Vols. Vol 1. - George Wollsten: Expert Stock and Grain Trader - Turning 400 Years of Astrology to Practical Use Vol 2 - The Egg Of Columbus - Traders' Hand-Book of Trend Determination - "Money" or Time Factors In The Market - A Course In Astrology - Bible Interpretation - Preview of Markets - Gold Nuggets For Traders.
Ferrera Gann Textbook
The Path of Least Resistance, The Underlying Wisdom & Philosophy of W. D. Gann Elegantly Encoded in the Master Charts, by Daniel T. Ferrera.
A detailed comprehensive elaboration of W.D. Gann's most powerful trading tools. Gann's core mathematical and important geometrical techniques in his master calculators, angles and spiral charts.
A fundamental principle of Cosmological Economics is the interconnection between galaxies, solar systems, stars, and planets, along with their interactive influences.
For example, the rotation of our galaxy is responsible for temperature fluctuations on Earth as a result of cosmic ray variations as we rotate through the spiral arms.
Esoteric and Pythagorean sciences love to play with the value and meaning of numbers, from the complex mathematical theories of the Platonists, via Fibonacci’s ideas, to number progressions, ratios, proportions, sequences, and chaos theory.
We specialize in the overlap of numerical and esoteric systems positing a more integrated cosmology.
The Sun is the most dominant influence in our lives, and a primary source of influences from the cosmos transmitted to the Earth.
Ancient and esoteric traditions had advanced theories of solar influence.
We cover theories concerning all kinds of solar effects.
Dr. Jerome Baumring
Dr. Baumring is the only known person to have fully cracked W. D. Gann’s full Cosmological System! He reproduced Gann's results, forecasting markets within 3 minutes of turning points.
He extended Gann's Law of Vibration into DNA Coding, Chaos Theory, and Topology, creating multi-dimensional, mathematical models of the markets.
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.
Dr. Jerome Baumring
The work of Dr. Baumring is the core inspiration upon which this entire website is based. Baumring is the only known modern person to have cracked the code behind WD Gann’s system of trading and market order.
Baumring found and elaborated the system of scientific cosmology at the root of Gann’s Law of Vibration.
There is no other Gann teaching that gets close to the depth of Baumring’s 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.
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.
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:
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
1/3 · 3/1
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:
therefore, the quadrilateral’s area:
1/4 · 4/1 = 1
1/2 · 2/1 = 1
3/4 · 4/3 = 1
1 · 1 = 1
4/3 · 3/4 = 1
2/1 · 1/2 = 1
4/1 · 1/4 = 1
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.
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.
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.
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.
Thimus: Harmonikale Symbolik des Alterthums, 4th part. H. Kayser: Hörende Mensch, 65, 66, 126, and familiar geometry textbooks.
Bradley's Stock Market Prediction. 100 Years of Siderograph Charts and Software. The Siderograph Indicator is a market model used by many analysts to give current turning points and trend indications for the markets.
This book includes the original text and charts for 100 years from 1950 to 2050, along with the software to produce the charts.
Sepharial's Kaleidoscope. A Monthly Column from the British Astrology Journal. Walter Gorn Old, 1111 pages.
This was a centerpiece of the British Journal of Astrology, 6 pages of each 16 page issue. Sepharial wrote the column for 22 years, and it represents the bulk of Sepharial's work including some of his best and most revealing writings.
Law of Vibration
The Law of Vibration 4 Volume Series by Dr. Lorrie Bennett on Gann analysis explains the scientific foundations behind W.D. Gann's forecasting system, the Law of Vibration. Dr. Bennett is the first person since Dr. Baumring to solve much of the puzzle left behind by Gann! V1-Patterns, V2-Numbers, V3-Planets, V4-Geometry.
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.
Gann Analysis goes deeply into fields of history, economics, science, metaphysics, ancient civilizations, occultism, astrology, numerology, astronomy and time cycles.
Gann's Recommended Reading List of 90 titles laid a foundation extended by Baumring to over 500 titles,
We provide comprehensive resources on the deep principles of Gann's work.
Biographies of market masters, traders and historical figures in our field.
Gann Science, The Periodic Table and The Law of Vibration. By Eric Penicka. The solution to Gann's Law of Vibration from the 1909 Ticker Interview correlates Gann's words with the cutting edge science of the Periodic Table of Elements to create a system of order based upon atomic structure and harmonic principles.
Systems of numerology date back to ancient Egypt, India and Israel. Hebrew number science, Gematria, was woven through the sacred texts of Semitic religion.
Plato used numerical codes in his works, and Thomas Taylor elaborated the advanced systems of Pythagoras in his "Theoretic Arithemetic of the Pythagoreans".
The Canon refers primarily to an ancient esoteric system of knowledge and cosmology encoded into temples, artifacts, art and monuments.
The Egyptians had a specific Canon to lay out the grids upon which they designed their art, and there are also canons of proportion used in the Renaissance, as well as by later artists, geometers and musicians.
We may be indebted to Ancient Greece, but Greek knowledge derived from Ancient Egypt, and Hermes Trismegistus, the Thrice Great Hermes is the Greek name of Thoth, the Egyptian God of Knowledge.
Hermetic teachings were first translated into Western languages by Ficino at the dawn of the Renaissance, forming the inspiration for modern esotericism.
We have a selected collection of unusual books presenting alternative metaphysical concepts and mathematics, including conceptual approaches useful for financial forecasting or more esoteric cosmological theory.
Both WD Gann and Dr. Baumring used methods of calculating universal ordering processes focused upon methods of prediction.
Natural Order has from ancient times looked deeply into principles of order behind nature and the universe, like phyllotaxis which governs the placement of leaves on plants, the harmonic ratios between the placement of the planets in the solar system, or the spirilic mathematics of galaxies.
Natural order reveals magical relationships in the natural world.