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After these things the word of the Lord came to Abram in a vision... “Look toward heaven, and number the stars, if you are able to number them.” Then he said to him, “So shall your offspring be.” And he said to him, “I am the Lord who brought you out from Ur of the Chaldeans to give you this land to possess.” But he said, “O Lord God, how am I to know that I shall possess it?” He said to him, “Bring me a heifer three years old, a female goat three years old, a ram three years old, a turtledove, and a young pigeon.” And he brought him all these, cut them in half, and laid each half over against the other. But he did not cut the birds in half.'
Genesis 15
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In Kepler's fifth book, the astronomical part, he presents his great harmonic discovery: the realization of musical harmonies through the movements of the planets. After first musically examining the distances and orbital periods of the planets from various viewpoints, and obtaining no satisfying results, he then examines the angular velocities of the planets, as an observer on the sun would perceive them, and establishes that these velocities, at the perihelion and aphelion of each planet, when positioned on the monochord, yield the most beautiful musical harmonies-for each individual planet as well as for the various planets compared with one another. This result also applies to the outer planets discovered later, as calculated in modern times; it appears to be a universally valid principle of the structure of our solar system. If one is aware of this, and has pursued the many other typical harmonic analyses in Harmonice Mundi, then one will see the mathematical result of this work by Kepler, namely his famous Third Law, through entirely different eyes. This law states that the squares of the orbital periods are proportional to the cubes of the major axes. This means, in Kepler's harmonic mode of thought, that the temporal primal intervals of the orbital periods must be raised to the second intervallic power, and the spatial primal intervals of the major axes must be raised to the third intervallic power. This means a power ratio of 2 : 3, i.e. the fifth, the most important interval after the octave!'
-Hans Kayser
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Edward Dewey asserted that seemingly unrelated time series often had similar cycles/periods present and that when they did the phase of these cycles was mostly very similar (cycle synchrony). He also said that there were many cycles with periods that were related by powers or products of 2 and 3.'
-Wiki
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In 1923, Gann said markets move in threes and twos.'
-John Needham
As previously stated on this blog:
'29.7%, 44.5%, 59.3% and 89% are retracement levels per Mr. Needham's {thedanielcode.com} theories. Expressed in fractions, 59.3% and 89% are 16/27 and 8/9. These fractions can be seen on the picture of the 'Pythagoras guitar' above. The inverse ratios of 9/8 and 27/16 are the frequency ratios of D and A as they relate to the fundamental tone of C.
The major scale based on C (fundamental tone) obtained from Pythagorean tuning is based on a stack of perfect fifths each tuned in the ratio 3:2 the next simplest ratio after 2:1 which is the ratio of an octave.
The frequency ratios of D and A as you ascend by perfect fifths are 9/4 and 27/8 respectively. These two fractions are the inverse ratios of 4/9(44.44%) and 8/27(29.63%).'
AM here: The ancients' belief in the 'music of the spheres' was reintroduced to the modern age by Johannes Kepler. During his life man knew of only six planets and Kepler proposed that the distance relationships could be understood in terms of five Platonic solids. 'Kepler then discovered that when these solids are placed inside each other so that the outer sphere around one solid is also the inner sphere inside the next, the radii of the spheres accurately correspond to the distances between the planets' says Hans Kayser, described as a 20th century Phythagorean Master, who also has, for Gann students, a rather fascination description of Kepler's pursuits:
'Kepler's first approach to this subject was geometric. When one attempts to assemble regular three-dimensional solids from equilateral polygons, it becomes apparent that only five such solids are possible. From equilateral triangles, three solids can be built: the tetrahedron from four, the octahedron from eight, and the icosahedron from twenty triangles. From squares, only the cube can be built, and finally the pentagon-dodecahedron can be built from twelve pentagons. These five solids were first described by Plato, and are therefore called the “Platonic solids”. Now
each solid can be placed inside a sphere, so that all the corners of the solid touch the surface of the sphere on the inside; and another sphere can be placed inside each solid, so that the sphere's surface is tangent to the center of each surface of the solid from the inside.'
AM here: Focus on the bolded excerpt of that last sentence for a moment, consider that the corners of the simplest solid touching the surface of a circle would trace out a square, and compare this to Gann's most mysterious declaration : 'Within the circle forms the square, there is an inner circle and an inner square, as well as an outer square and an outer circle which prove the Fourth Dimension in working out price movements.'
As noted Gann expert Daniel Ferrera points out, the inner square is an exact musical octave of the larger outer square.
Now let's look at the second part of that last sentence from Kayser, 'the sphere's surface is tangent to the center of each surface of the solid from the inside.'
When considering a fourth dimensional view of the markets, agreement upon the first two dimensions being time and price is widely shared. Also the interchangeability of time and price, namely time and price being the same albeit on different axis, is commonly held. For those that peek into the esoteric the general consensus is that the third dimension is volume.
The fourth dimension? Well, one way to conceptualize it is to consider volume to be merely a cross-section of the fourth dimension.
For example, Mr. Needham states(and when reading the following please note that the retracement levels stated above, 29.7%, 44.5%, 59.3% and 89%, are what is being referred to with the term binomials):
'When we look at normal charts, they are representing 3 degrees on the linear plane. Price on the vertical axis, time on the horizontal axis and volume. These are the 3 degrees that most see.
Gann talked about a "4th Degree" and the 4th Degree is "An Angle". My Regression Channels are an angle and hence a derivative of the 4th Degree.
When we advance our knowledge of the Danielcode time and price ratios, we can conceptualise that rather than using these ratios on the linear plane, which gives us the blue line targets, red line retracements and DC time cycles, we can actually place them as an arc rather than a straight line. From this process we get the DC "Binomials" which I have written about occasionally. With the Binomials we are working in the 4th Degree, so the markets are coming "out" or going "in" to the linear charts. You can see the Binomials and the 4th Degree on a CAD-CAM program, but it is tedious as the software is not available to code sequential data points.
The fixed points in the Regression Channel are derived from the Binomials, so to some extent, the {long term charts I create} are just a 2 dimensional view of the Binomials. But they are a linear extrapolation as opposed to the tangents and arcs that express the DC Binomials.'
AM here: Now let's consider the works of Jerome Baumring author of, among other tomes: 'Gann Harmony, The Law of Vibration'.
As relayed by Brad Stewart of the Sacred Science Institute, 'Vertical = vector radius of price. Horizontal = vector radius of time. Diagonal angles tell you what stage of growth you are in. Tangent of curves show support levels. Gnomonic growth = harmonic composition. Waves are directional force fields(vectors). Slope of vector is its vibratory rate.'
AM here: Indulge me for one more moment and travel back to the dusty days of Trig and please recall that Tan θ = Opposite/Adjacent, Cos θ = Adj/Hyp, and Sin θ = Opp/Hyp (see right triangle above).
The second picture (above) is a unit circle. Cribbing from an old bbc.uk article:
The unit circle is simply a circle whose centre is on the Cartesian origin (0,0), and whose radius is 1.
The most interesting thing about the unit circle, as far as trigonometry is concerned, is that it gives us the values of sine and cosine for any angle.
Measure the angle θ between the x-axis of the Cartesian plane and a line that extends from the origin. Now, here's the really interesting thing; the sine of the angle is equal to the y-coordinate of the point on the unit circle where the line crosses, and the cosine of the angle is equal to the x-coordinate. This is true for any line extending from the origin.
Why is this? Well, the line segment from the origin to the point where it crosses the unit circle forms the hypotenuse of a right-angled triangle. Because the radius of the circle is 1, the length of the hypotenuse is likewise 1.
Sin θ = Opposite
Cos θ = Adjacent
Tan θ = Opposite/Adjacent
In other words:
Sin θ = y
Cos θ = x
Tan θ = y/x
AM here: So tying the strings together as it were, if x is time and y is price, and the tangent is support and resistance, as advocated by both Needham and Baumring, or in sacred geometry terms the form/volume, then the inverse tangent is the fourth dimension, an angle.
Circle smirking, taking the fifth, Kepler and Needham and Gann and Pyth.Ah, but there is a fly in the cosmic ointment, Kepler's assertion that the radii of the spheres accurately corresponds to the distances between the planets and his discovery of a 'congruence' between musical intervals and planetary relationships, the modern proof of Pythagorean tenets, has been dismissed in part due to the lack of a rigorous demonstration that such a relationship is not anything more than a random distribution.
Wouldn't it be nice if say there was a theory that offered to us that the formation of our planetary system was guided by the influence, or force, that led to the arrangement of orbital velocities in such a way that, with a 99%+ certainty, there is an explicit correspondence to the numerical relationships of musical/harmonic intervals?
Stay 'tuned' for my next posting.
Time and space/price and form.... oh my!
9 comments:
I was wondering how long it was going to take Mr. A. Monet to wend his way back down the windings of the historical labyrinth from Needham and Mr. Gann to the sublime celestial navigator Johannes Kepler and of course, the daddy of 'em all, the ineffable Pythagoras. The music of the spheres which Kepler traced the haunting echoes of, finds resonance on the pages of this humble blog. May it find an equal and pleasing reverberation in the minds of anyone who might have the good fortune to gather the gleanings which you so generously bestow upon so many unsuspecting wanderers in the blogosphere. You might have stumbled upon A. Koestler's "The Sleepwalkers" at some point ?
evidently the blog author is very restrictive in his choice of comments to be published here or might I say is possessed of a certain immoderate moderation. it is understandable that only opinions and views which reflect the tenor of this tidy and meticulously managed venue would be acceptable. Apparently the riff-raff, though they cannot be impeded from perusing its contents, must not be allowed to sully such a carefully erected and erudite framework with their uneducated and ill-informed persuasions. mea culpa.
Au contraire, mon frere.
Just getting around to it ...
Have not stumbled upon Koestler's book. It looks quite interesting though, will try to pick it up. Thanks for the reference..
Here is an brief description for WIKI : 'The book challenges the habitual idea of a progressive science working towards a definite goal. The suggestion of the title is that the scientific discoveries and the geniuses that come to them are like a game of sleepwalking. Not that they come by pure chance, but that often the genius doesn't really know that he has discovered, as it is evident for instance in the three Laws of Kepler.
A central theme of The Sleepwalkers is the changing relationship between faith and reason. Koestler explores how these seemingly contradictory threads existed harmoniously in many of the greatest intellectuals of the West. He illustrates that while the two are estranged today, in the past the most ground-breaking thinkers were often very spiritual.
Another recurrent theme of this book is the breaking of paradigms in order to create new ones. People - scientists included - hold onto cherished old beliefs with such love and attachment that they refuse to see the wrong in their ideas and the truth in the ideas that are to replace them.
"The conclusion he puts forward at the end of the book is that modern science is trying too hard to be rational. Scientists have been at their best when they allowed themselves to behave as "sleepwalkers," instead of trying too earnestly to ratiocinate.'
Ratiocinate was a new word to me! The definition is 'to reason methodically and logically.'
Needham has stated Mr Gann was a fraud...He also recently stated JCN (Webmaster) Mar 06, 2010 - 1:22am GMT
10 hours ago - Don't get hung up on Gann. It's mostly bunkum and the good stuff comes from Sepharial in any event.
But just to clarify. Gann worked on both stocks and commodities. His base was what he called the 1X1 line. Gann charts have some very particular properties, most notable of which is that time and price were measured on an equal scale. So if price went up 1 point (or $) in one day it would be holding the 1X1 line. He also used 1X3 (the angle on the triangle), 1X2; 1X4 and 1X8 lines.
The original meaning of "Time and Price" squared meant an equal move on both chart axis. So a market that moved 150 points in 150 days was said to "square" time and price.
Almost all charting programs have some form of Gann lines or Gann "fans" that create these lines, but as programmers and traders almost entirely fail to understand Gann's methodology; all but 1 of the Gann tools are wrong (including Genesis). Check out his website forum and view for yourself the hypocrite who looks to fool all.
Yes Anonymous,
Very familiar with John's analysis.
To expand upon your point using Mr. Needham's prescient observations:
'Gann's simplest teachings held that these angles would measure markets in a predetermined ratio such as 1X1 where price would move 1 'unit' for every 'unit' of time. Other popular Gann angles were 1X4 and 1X8 being angles on the square and the special 1X3 lines, angles on the triangles.
Gann's background in freemasonry and Sepharial's books 'The Silver Key' and 'Kabala of Numbers' are essential reading for a depper understanding of Gann's work.
Gann's opinion of market turns occurring when 'time and price are squared' is referring to the point on an angle where market price coincides with 1X1 or other angle.
This 'point on an angle' could be an important numerological sequence from Sepharial.
It could also be a time fractal from the astrological chart ruling the market in question.
Gann's discovery 'that markets move in fractals of 1/8th of the previous price range' should be a dominant plank of his claim to fame.
Markets still use 1/8th fractals of previous ranges as their boundaries (and 1/3rds).
For Gann these ratios were as far as he developed his price sequencing. For the Danielcode they are the base ratios.
The most common of Gann's time cycles were astrological cycles.
Gann's teachings hold that the high before the high and the low before the low were paramount chart points.
Danielcode market time can be measured from two points, the high and the high after the high. If we are seeking a high we usually measure from the low or the low after the low.
All markets have their own "vibration", what WD Gann called the "Law of Vibrations". So each market has an identifiable signature or vibration. Gann, who was much dependant on Sepharial for his market insights, thought that vibration came from each market's birth number ie its horoscope. In Sepharial's "Silver Key" he shows a horoscope of the “birth” date and time of the New York Stock Exchange and the first trade of a number of stocks on that exchange. He ascribes the NYSE signature vibration to those calculations.
Of course, most of that is nonsense and the true number or vibration for NYSE is the sum of its parts. If you run a best fit regression for every stock on NYSE and give them an exponential weighting, then take the mean of that rating, you will have the true vibration of NYSE.
Strangely it is not far from what Sepharial calculated 90 years ago with his birth charts!
Many have dedicated large parts of their life in the search for the twin Grails of trading: price and time. That they are the same thing juxtaposed on different axis is not a new concept. WD Gann, under the tutelage of his mentor, the British astrologer and numerologist “Sepharial” advanced this proposition in 1935. But Sepharial camouflaged his observations by claiming that they were related to astrological cycles. Indeed they are, but he scrupulously avoided saying that all of these cycles are of Biblical origin. What do you think the wise men, sages and prophets of Biblical time were looking at on those myriad of long nights as they sat outside their tents? They observed the stars and the heavens. And they wrote down, sometimes in code and sometimes openly, the great cycles of the heavenly orbs. Sepharial used that knowledge but fudged naming the source because it wasn’t cool'
Now Anonymous,
Pretty sure you know all of this given your familiarity with Needham however other readers might be curious enough to continue their exploration on this subject and I would urge them to do so...
To be mindful is a discontinuous process, our senses allow us a glimpse at the perfect form (truth) but that view can often be distorted by the flickering fire of perception that illuminates the shapes we perceive to believe...
Or to quote the venerable Gann expert and Swing trader Jeff Cooper, 'Is there a sacred geometry weaving through time and price or is the market a random walk? It seems to me if there is any threshold of geometry which runs through the market then all math leads to Rome. Number is as number does.'
As a last bit, continuing Jeff's ' Number is as number does' comment...
Gann did a Col. Jessup saying we couldn't handle the truth... and as such he never directly articulated his beliefs...in that sense, yes he was a fraud, albeit a clever one relying on the insight of some clever folks.
Hi and thank you very much for all the valuable posts on your blog, they help clarify & give extra insight Mr Needham's material as well as Gann's etc.
Out of interest, Sepharial’s NYSE birth chart was not in the Silver Key, it was actually in the Arcana or Stock and Share key.
Thank you for the kind words and the clarification :)
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