Math for Mystics | # 1

The Pythagorean Definition of God

St. Bernard of Clairvaux: "God is breadth and length, height and depth."

SPX vs JUP-SAT Cycle

Expected CITs: Sep 29 (Tue), Oct 09 (Fri), Oct 15 (Thu), Oct 23 (Fri), Nov 01 (Sun), Nov 04 (Wed), Nov 08 (Sun)

SPX vs AstroMetric Indicator

SPX vs MER-VEN Cycle

SPX vs Declination of MER + VEN

SPX vs MER-MAR Speed Differential

SPX vs MER Speed

SPX vs Sunspots

SPX vs True Lunar Node's Speed + Eclipse Crash Window

Expected CITs: Oct 05 (Mon), Oct 08 (Thu), Oct 11 (Sun), Oct 17 (Sat), Oct 21 (Wed), Oct 23 (Fri), Oct 25 (Sun), Oct 30 (Fri), Nov 04 (Wed)

Contrarian Riddle

The one sentiment reading that is NOT contrarian just turned bearish
(above 50 = bullish, below = bearish) ...
Source: Market Vane via ‏@Not_Jim_Cramer

... while FT covers like this one reliably show up
when market bottoms are close-by or already in.

The US Economy Is Doing Great!

Credits: FRED

Yesterday Sunspots Increased = Today Market Should Decline

However, the daily sunspot number reached a 2 year high (154) while the SoLunar Map signals an upturn in the stock market (see also HERE)

Cosmic Cluster Days in October - November 2015

Upcoming Cosmic Cluster Days (CCDs) are:
Sep 30 (Wed), Oct 02 (Fri), Oct 07 (Wed), Oct 11 (Sun), Oct 24 (Sat), Oct 26 (Mon), Nov 01 (Sun),
Nov 03 (Tue), Nov 04 (Wed), Nov 19 (Thu), Nov 21 (Sat), Nov 26 (Thu), Nov 28 (Sat), Dec 02 (Wed).
Previous CCDs are HERE

HERE

SoLunar Map for October - November 2015

A Low in the SoLunar Map frequently is a High in the Stock Market and vice versa. Inversions occur. Upcoming turn-days are:
Sep 28 (Mon), Oct 01 (Thu), Oct 05 (Mon), Oct 09 (Fri), Oct 13 (Tue), Oct 16 (Fri), Oct 20 (Tue), Oct 24 (Sat), Oct 28 (Wed), Oct 31 (Sat),
Nov 03 (Tue), Nov 07 (Sat), Nov 11 (Wed), Nov 15 (Sun), Nov 18 (Wed), Nov 22 (Sun), Nov 26 (Thu), Nov 30 (Mon), Dec 03 (Thu).
Previous SoLunar Maps HERE

HERE

SoLunar Intraday Maps - October 2015

The charts show the hourly solunar forces over Wall Street. Intraday movements of financial markets are strongly influenced 
by daily and intraday solunar forces. They usually closely follow their direction - either directly or inverted. Turning points can
be fine-tuned using the previously described planetary hours as well as the times of rising, culminating and setting planets.
Please note: The times calculated refer to EST (not EDT).

Gold Prices 1257 - 2011 (Historical Chart)

Stock Prices 1509 - 2014 (Historical Charts)

Commodity Prices 1170 - 2011 (Historical Chart)

Interest Rates 1150 - 2014 (Historical Charts)

See also HERE

Ranking Sovereign Debt - Three Ways To Look At Keynesian Insanity

Credits: Visual Capitalist

Jeff Hirsch: October’s Typical Performance

Jeff Hirsch (Sep 26, 2015) - October’s typical performance appears in the chart at left over the recent 21-year span 1994 to 2014. On average, early month weakness has proven to be an excellent buying opportunity, especially for NASDAQ (purple line) as early losses were quickly recouped leading to an average gain of over 3% from early month lows to the close.
Since 1991, October, the first month of the fourth quarter has improved substantially, climbing to fourth best DJIA month with an average gain of 1.6%. It’s the third best S&P 500 month (+1.6%) and second best for NASDAQ (+2.3%). Russell 2000 has not seen as much improvement with October climbing to just #8.

Highest Daily Sunspot Number since April 2014

Source: NOAA

Bund Spread Gives Permission for Bear Market | Tom McClellan

Tom McClellan (Sep 24, 2015) - [...] German government bonds are known in the industry as “Bunds”, a contraction of the prefix “bundes” which is German for “federal”.  At the major stock market tops in 2000 and 2007, we saw the peak in the 10-year Bund-Treasury spread appear well in advance of the final price tops for stocks.  So because that spread was still rising in April 2014, my supposition then was that the uptrend had more months to live. Now we see a different condition.

Credits: Tom McClellan HERE + HERE

The Bund-Treasury spread peaked at 1.81 percentage points back in March 2015, and has since been contracting. Meanwhile, the DJIA and SP500 kept on rising to incrementally higher price highs as the summer wore on, eventually breaking down with the August 2015 minicrash. 

[...] With a divergence now in place between the DJIA and the Bund-Treasury spread, we can have a reasonable expectation that a bear market for stock prices should ensue.  If it plays out like the last two, the bear market should last until the Bund-Treasury spread gets back down at least to parity, or preferably even lower. That could take a while; in the 2000 and 2007 examples, it took a couple of years. The eurodollar COT leading indication already tells us to expect a downward trend until April 2016, so that gives us at least several months to see how the Bund-Treasury spread behaves.

SPX 2015 vs SPX 1987

Calculated and charted with Timing Solution.

SPX 2015 vs SPX 2011

Calculated and charted with Timing Solution.

SPX vs Sunspots

Sunspots shifted +49 days

The Ap index measures geomagnetic activity and the 10.7 cm Flux is considered a sunspot-proxy.
Source: NOAA

Martin Armstrong on the DJIA

Martin Armstrong (Sep 23, 2015) - [...] Yes, if this week simply closes on the Dow below 16280, then we can be looking at that slingshot move I have warned about where in one year, we have a crash and a swing to the upside to new highs (see also HERE + HERE).

[...] Remember, if the stocks decline into 2015.75, that should push more and more capital into government bonds completing the BUBBLE. This is by no means a BUBBLE in stocks, commodities, or the dollar. This is a peak in GOVERNMENT. This is not even a Kondratieff Wave based upon commodities. This is the 309.6 year cycle in government and unfortunately, the other side of 2015.75 is not looking very pretty. This not about just the collapse of Europe. This is the collapse of Western forms of government that aids the shift in the financial capital of world to China by 2032 (how to read the above Forecast Array = HERE + HERE).

SPX vs Lunar Node's Speed

Market CITs are likely when the Lunar Node's Speed (degrees longitude/day) is at MIN/MAX and at 0.
The Eclipse Crash Window opens and closes around 21 days before and 21 days after the Solar- and Lunar Eclipses.
The table at left shows the nodal speed at MIN/MAX and at 0 during the next 30 days.
The Sun will conjunct the Lunar Node (North Node) on Sep 24 (Thu).
See also HERE + HERE

Volkswagen "totally screwed up" - Value Down EUR 20 Billion (so far)

HERE

BBC (Sep 22, 2015) - Volkswagen shares plunged nearly 20% on Monday and another -19% on Tuesday (so far) after the US Environmental Protection Agency (EPA) found that software in several diesel cars could deceive regulators. Michael Horn, the boss of Volkswagen's US business, has admitted the firm was dishonest in using software to rig emissions tests. He said the firm was dishonest with US regulators, adding: "We have totally screwed up." Last Friday, the regulators said VW diesel cars had much higher emissions than tests had suggested. Volkswagen was ordered to recall half a million cars in the US on Friday. Up to 11 million cars worldwide might be affected by the diesel deception. In addition to paying for the recall, VW faces fines that could add up to billions of dollars. Volkswagen could be fined $25 billion for US emissions scam. There may also be criminal charges for VW executives.

If your work is affected by geomagnetic disturbances ...

... then it is wise to avoid the equinox months ... [HERE + HERE]

HERE

HERE

By That Pure, Holy, Four Lettered Name On High | Pythagoras

The Pythagorean Oath mentions the Tetractys:
"By that pure, holy, four lettered name on high,
nature's eternal fountain and supply,
the parent of all souls that living be,
by him, with faith find oath, I swear to thee."
Credits: Michæl Paukner

Albert Mackey (1873) - "The Greek word 'Tetractys' signifies, literally, the number four, and is synonymous with the quaternion; but it has been peculiarly applied to a symbol of the Pythagoreans, which is composed of ten dots arranged in a triangular form of four rows."   

The first four numbers symbolize the harmony of the spheres and the Cosmos as: (1) Unity (Monad); (2) Dyad - Power - Limit/Unlimited; (3) Harmony (Triad); (4) Kosmos (Tetrad) - The four rows add up to ten, which was unity of a higher order (The Dekad).  The Tetractys symbolizes the four elements — fire, air, water, and earth. The Tetractys represented the organization of space: the first row represented zero dimensions (a point). The second row represented one dimension (a line of two points). The third row represented two dimensions (a plane defined by a triangle of three points). The fourth row represented three dimensions (a tetrahedron defined by four points). 

The Pythagorean musical system is based on the Tetractys as the rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison 1:1 and the octave 2:1. The diapason, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to the tetractys of the decad. The diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.

Squaring the Circle with the Earth and the Moon

The perimeter of a square around the Earth equals the perimeter of a
circle drawn through the center of the Moon.
Credits: Michæl Paukner

Common Wisdom (2015) - Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.

In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for some decades before then that the construction would be impossible if pi were transcendental, but pi was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π.

SPX vs Declination of MER + VEN

Stock Markets change direction when the direction of the declinations of Mercury
and Venus is changing (MIN + MAX), and when the declinations are parallel (crossings in the chart).

Sell in May - Buy in October

Credits: Jeff Hirsch

Jeff Hirsch (Sep 16, 2015) - Prior to about 1950, farming was a major portion of the U.S. economy and from 1901-1950, August was the best performing month of the year, up 36 times in 49 years (market closed in August 1914 due to World War I) with an average gain of 2.3%. July was the second best month, up 31 of 50 with an average gain of 1.5%. June was fourth best, averaging 0.9%. Why, you may ask. In a single word, harvesting. As crops were brought to market and sold, cash began to move and so did the stock market.

Agriculture’s share of GDP began to shrink post World War II as industrialization created a growing middle class that moved to the suburbs where hard-earned salaries would be spent filling new homes with all the modern conveniences we all take for granted now. Farming became more efficient and fewer and fewer people worked on the farm. Suddenly, summer was less about the hard work of harvesting crops and more about vacations and relaxing. As the economy evolved and peoples’ lives changed, the market evolved. June and August went from being top performing months to bottom performing months. August went from #1 to #10 in 1950-2014 with an average loss of 0.1%. June went from #4 to #11 (–0.3% average loss). The shift in DJIA’s seasonal pattern is clear in the [above] chart. “Sell in May” is a post WWII pattern, prior to then it would have been “Buy in May”.

China's Raw Materials Consumption

Visual Capitalist (Sep 11, 2015) - Over the last 20 years, the world economy has relied on the Chinese economic growth engine more than it would like to admit. The 1.4 billion people living in the world’s most populous country account for 13% of global GDP, which is significant no matter how it is interpreted. However, in the commodity sector, China has another magnitude of importance. The fact is that China consumes mind-bending amounts of materials, energy, and food. That’s why the prospect of slowing Chinese growth is likely to continue as a source of nightmares for investors focused on the commodity sector.

China consumes a big proportion of the world’s materials used in infrastructure. It consumes 54% of aluminum, 48% of copper, 50% of nickel, 45% of all steel, and 60% of concrete. In fact, China has consumed more concrete in the last three years than the United States did in all of the 20th century. China is also prolific in accumulating precious metals – the country buys or mines 23% of gold and 15% of the world’s silver supply. With many mouths to feed, China also needs large amounts of food. About 30% of rice, 22% of corn, and 17% of wheat gets eaten by the Chinese. Lastly, the country is no hack in terms of burning fuel either. Notably, China uses 49% of coal for power generation as well as metallurgical processes in making steel. It also uses 13% of the world’s uranium and 12% of all oil.

China’s Middle Class Growing Explosively

While the Long Noses are converting good parts of the world - including most of their home countries - into disaster zones and failed states, half a billion Chinese are ascending into the middle class: In 2010 mainstream consumers—those with enough money to buy cars, fridges and phones but not Rolls-Royces—made up less than a tenth of urban Chinese households. McKinsey predicts that only by 2020 the income-middle class will grow by 1,000% to make up well over half of the Chinese population while the percentage of the very poor will be cut in half. Credits: McKinsey + The Economist

Most Commodities Historically Cheap

Many of the commodities seem to have had a consistently decreasing real price prior to the last 100 years. Commodities that look particularly cheap are generally agricultural ones while the more industrial based commodities seem to be at the more expensive end of history, in part fueled by significant demand from China over the past decade. This is particularly true when looking at data over the past 100 years. Precious metals also look expensive from a historical stand-point, which probably reflects the post-1971 fiat currency regime we currently operate in. One of the problems with this analysis is that the importance of these commodities changes over time as does the cost of mining them. Source: Deutsche Bank (2015)  - Long-Term Asset Return Study.