Saturday, February 18, 2017

The Depiction of Time and Space out of Scipio's Dream

It is common to think of statistical graphics and data visualization as relatively modern developments in statistics. In fact, the graphic representation of quantitative information has deep roots, reaching into the histories of the earliest map making and visual depiction of astronomy, and later into thematic cartography and many other fields. The idea of coordinates was used by ancient Egyptian surveyors in laying out towns, earthly and heavenly positions were located by something akin to latitude and longitude by at least 200 B.C., and the map projection of a spherical Earth into latitude and longitude by Claudius Ptolemy (85–165) in Alexandria would serve as reference standards until the 14th century. 

Planetary movements shown as cyclic inclinations over time, by an unknown astronomer, appearing in a
10th-century appendix to commentaries by Macrobius on Cicero’s Somnium Sciponis. This is the earliest
known 2-dimensional charts (plotting time vs. celestial latitude; an apparent anomaly is that it appears to
show the celestial latitude of the Sun varying with time); the scribe used horizontal and vertical lines as
aids, resulting in a picture strikingly similar to modern graph paper as it did not become commonly used
before the mid 19th century, some 700 years later. This picture is a notable anomaly, as the earliest
comparable "graph" diagram do not emerge prior to the late medieval period, some 250 years after
this drawing was made. Source: Wikimedia.

Among the earliest graphical depictions of quantitative information is the above anonymous 10th-century multiple time-series graph of the changing position of the seven most prominent heavenly bodies over space and time. The vertical axis represents the inclination of the planetary orbits; the horizontal axis shows time, divided into 30 intervals. The sinusoidal variation with different periods is notable, as is the use of a grid,suggesting both an implicit notion of a coordinate system and something akin to graph paper, ideas that would not be fully developed until the 1600-1700s. In the 14th century, the idea of plotting a theoretical function (as a proto bar graph) and the logical relation between tabulating values and plotting them appeared in a work by Nicole Oresme (1323-1382), Bishop of Liseus, followed somewhat later by the idea of a theoretical graph of distance vs. speed by Nicolas of Cusa.

Sunspots and the Price of Corn and Wheat | William Stanley Jevons

William Stanley Jevons (1835–1882)
William Stanley Jevons (1835–1882) was a British economist and philosopher who foreshadowed several developments of the 20th century. He is one of the main contributors to the ‘marginal revolution’, which revolutionized economic theory and shifted classical to neoclassical economics. He was the first economist to construct index numbers, and he had a tremendous influence on the development of empirical methods and the use of statistics and econometrics in the social sciences. Jevons also analyzed business cycles, proposing that crises in the economy might not be random events, but might be based on discernible prior causes. To clarify the concept, he presented a statistical study relating business cycles with sunspots.

Daniel Kuester & Charles R. Britton (2000) - William Stanley Jevons summarized his thoughts on the effects of weather on economic activity in three chapters of his book Investigations in Currency and Finance (1909). An in-depth examination of these essays reveals some very interesting conclusions. In the first essay entitled “The Solar Period and the Price of Corn” (1875) he first investigates the striking similarity between the length of many historical business cycles and the length of the average length of the sunspot cycle. Jevons finds that the prices of most agricultural products vary dramatically over an eleven year cycle. He cites English agricultural price data from the years 1259-1400. The prices of wheat, barley, oats, beans, peas, and rye reach a relative minimum in the second year of the cycle, an absolute maximum in the fourth year of the cycle and an absolute minimum in the tenth year of the cycle before recovering in the final year of the cycle and the first year of the new cycle. There does appear to be a rather obvious and consistent trend in prices over these eleven year periods. Jevons discovers that the data (English wheat prices from 1595-1761) available to him in the Adam Smith’s The Wealth of Nations (1776) confirm similar although less marked trends in agricultural prices.

Jevons does not discount other significant factors that might cause the rather predictable nature of these business cycles. Technological advancements, wars, and other factors independent of agricultural and weather cycles can and do exhibit great influence over the economic well being of a nation. Also consumer confidence or a lack thereof could cause significant variations in spending and employment. However, Jevons believes that these consumer attitudes may also be related to the sunspot theory and the corresponding droughts and bumper crops which may result. “If, then the English money market is naturally fitted to swing or roll in periods of ten or eleven years, comparatively slight variations in the goodness of harvests repeated at like intervals would suffice to produce those alterations of depression, activity, excitement and collapse which undoubtedly recur in well- marked succession.” Jevons believes that if it were possible to accurately predict the sunspot cycle and the corresponding bumper crops and droughts then it would also be possible to predict impending economic crises.

In the second essay “The Periodicity of Commercial Crisis and Its Physical Explanation” (1878) with “Postscript” (1882) W.S. Jevons continues his study. In this essay he attempts to find empirical evidence to support his claim that business cycles follow predictable patterns which can be tied to the length of the sunspot cycles. Jevons claims that the relationship between weather patterns and business activity display a stronger relationship in primarily agrarian societies such as India and Africa. This claim makes this subject more meaningful in studying the relationship between weather patterns and economic activity in arid and semi- arid lands.

One piece of empirical evidence which W.S. Jevons believed would strengthen his sunspot business cycle theory actually has weakened this theory somewhat in retrospect. “There is more or less evidence that trade reached a maximum of activity in or about the years 1701, 1711, 1721, 1732, 1742, 1753, 1763, 1772, 1783, 1793, 1805, 1815, 1825, 1837, 1847, 1857, 1866. These years marked by the bursting of a commercial panic or not, are as nearly as I can judge, corresponding years, and the intervals, vary only form nine to twelve years. There being in all an interval of one hundred and sixty five years, broken into sixteen periods, the average length of the period is about 10.3 years.” Jevons points out that it is reasonable for the business cycles to vary somewhat in duration as it is reasonable to expect that there will be different lags between droughts and economic downturns based on inventories available and on the variations in trade patterns and ability to obtain imports quickly.

Potentially the most troubling conclusion that Jevons reached was that a sunspot cycle and the corresponding changes in agricultural yield and national productivity would follow a predictable pattern of approximately 10.3 years. Most astronomers now believe that the sunspot cycle does indeed last approximately 11.11 years which is somewhat troubling and is something that Jevons’ son attempts to address. This potential difference in sunspot duration is a primary reason this subject has not been studied as much as might be expected. However the findings of García-Mata and Shaffner provide some credence to Jevons’ theory. “Summing up, we can say that from a statistical point of view there appears to be a clear correlation between the major cycles of non-agricultural business activity in the United States and the solar cycle of 11+ years.” These authors also claim that it is reasonable that there could be some variation in the duration between sunspot cycles and that there is evidence that these cycles do correspond with business activity.

Christopher Scheiner's 1626 representation of the changes in sunspots over time (1630, recordings
from 1611). Scheiner, a Jesuit astronomer, eventually published the definitive work of the 17th
century on sunspots, in which he accepted Galileo’s argument that sunspots "move like ships" on
the surface of the Sun. Scheiner and Galileo agreed that sunspots counted against the Aristotelian
doctrine of celestial incorruptibility. Earlier Jesuits had been open on this point. Clavius argued
for the corruptibility of the heavens after the nova of 1572. Scheiner here publicized the fact that
the Jesuit theologian Robert Bellarmine had argued for the igneous nature of the stars and the
corruptibility of the heavens even before 1572 on the basis of biblical exegesis and the tradition
of the Church Fathers. Cardinal Orsini paid for the printing of this lavish work (Rosa Ursina - The
Rose of Orsini
, 1630).

The third essay on sunspots and the business cycle was entitled “Commercial Crisis and Sun-Spots Part I” (1878) and “Part II” (1879) completed W. S. Jevons thoughts on the relationship of weather and business activity. In this essay he continues to discuss the existence of a solar cycle of 10.45 years as being wholly consistent with his findings and being a better predictor of economic variables than the now widely used duration of 11.11 years. Despite this potentially unfortunate conclusion Jevons elaborates on the potential relationship between solar and weather cycles and economic activity. He concludes that solar patterns should be studied to determine if a causal relationship does indeed exist between solar patterns and economic activity. If so, then policies should be enacted to reduce the magnitude of the contraction/recession parts of the business cycle. Jevons further elaborates on the importance of the solar cycle on consumer confidence and spending. “From that sun which is truly ‘of this great world both eye and soul’ we derive our strength and our weakness, our success and our failure, our elation in commercial mania, and our despondency and ruin in commercial collapse.” Jevons also finds more empirical evidence that corn prices in Delhi reach maximum and minimum in a similar eleven year pattern which has been exhibited in Europe. Once more this theory seems much more applicably to arid and semi-arid regions such as India.

Sunspot illustration from Scheiner's Rosa Ursina, 1630.
William Stanley Jevons’ son H. Stanley Jevons continued his work on sunspots and published “Changes at the Sun’s Heat as the Cause of Fluctuations of the Activity of Trade and of Unemployment” in Contemporary Review in 1909. He reissued it in a monograph entitled The Sun’s Heat and Trade Activity (1910) in which he further examined and elaborated on the subject. H. S. Jevons believed that his father had some excellent ideas in relating the sunspot theory to the length of business cycles although he does acknowledge some of the criticisms which have been leveled at the work W.S. Jevons did. He states that the sun’s activity has some effect on economic outcomes and while it is not the only variable which should be considered when formulating economic policy it is worth considering when formulating economic policy.

H.S. Jevons acknowledges that his father was in error when he claimed that he solar cycle would only last approximately 10.45 years. He claims that W.S. Jevons attempted to oversimplify his findings and he ignored some events which created economic booms and busts which had nothing to do with arid land’s agricultural productivity. This is what led him to the false 10.45 year business cycle predictor. However he found that wheat production in the United States displayed significant variation during the nineteenth century and reached its peak approximately every 11.11 years. He found a direct relationship between solar activity and wheat production in the United States. H.S. Jevons believes that the eleven year sunspot cycle is actually a combination of three shorter sunspot cycles which were just over three years in duration. There would be a period of drought approximately every 3.5 years and a period of cold damp weather approximately every 3.5 years. This great harvest would precipitate a trade boom according to Jevons. He finds data that suggest the production of pig iron and agricultural produce in the United States were closely related and followed the sunspot cycle closely. He also states that on occasion the business cycle will only correspond with two of these shorter sunspot cycles explaining the variation in business cycles between seven and eleven years. This can explain the error that W.S. Jevons did not understand about the variation in the length of business cycles. H.S. Jevons provides several suggestions as to how this information about solar activity can be useful. He believes that if output and therefore trade can be expected to decline in the near future that there should be wage cuts to attempt to ensure full employment. This suggestion is not reasonable today but if we are going to engage in interventionary fiscal and monetary policy the potential to predict shortfalls in productivity and potentially consumer confidence can have meaningful implications for expansionary monetary policies being enacted. This is particularly useful if there are actual psychological ties between solar activity and consumer’s attitudes which sounds far fetched but may occur. Jevons also recommends less domestic reliance on crops would reduce the variation in economic prosperity. While crop production is still important in many arid and semi-arid lands, this is not as meaningful to the economy as it was when Jevons wrote.

Friday, February 17, 2017

Equal to the Ears and to One-Third of the Face | Da Vinci's Vitruvian Man

A palm is four fingers, a foot is four palms, a cubit is six palms, four cubits make a man,
a pace is four cubits, a man is 24 palms.
The length of the outspread arms is equal to the height of a man.
From the hairline to the bottom of the chin is one-tenth of the height of a man.
From below the chin to the top of the head is one-eighth of the height of a man.
From above the chest to the top of the head is one-sixth of the height of a man.
From above the chest to the hairline is one-seventh of the height of a man.
The maximum width of the shoulders is a quarter of the height of a man.
From the breasts to the top of the head is a quarter of the height of a man.
The distance from the elbow to the tip of the hand is a quarter of the height of a man.
The distance from the elbow to the armpit is one-eighth of the height of a man.
The length of the hand is one-tenth of the height of a man.
The root of the penis is at half the height of a man.
The foot is one-seventh of the height of a man.
From below the foot to below the knee is a quarter of the height of a man.
From below the knee to the root of the penis is a quarter of the height of a man.
The distances from below the chin to the nose and the eyebrows and the hairline are equal
to the ears and to one-third of the face

The Harmony of Being | Geometry in Man, Nature, and Cosmos

Proportional roots: (a) the √2 proportion, (b) the √3 proportion,
and (c) the golden mean (Phi) proportion.

Loai M. Dabbour (2012) - Geometry describes the assertions of a mathematical order of the intrinsic nature of the universe. Geometry is the very basis of our reality, and we live in a coherent world governed by underlying laws. Johannes Kepler stated that geometry is underpinning the cosmos, which was based on Plato’s ideas that God created the universe according to a geometric plan. The structure of the universe is determined by and revealed as certain mathematical and geometric constants which represent a confirmation that proportions are the underlying fabric of nature. This can be seen in man, nature, and cosmos.

Root proportions based on the square.

By contemplating geometric proportions, an understanding towards the sacred truth can be obtained since geometric proportions are one of the definitive geometric qualities of life itself. The Holy Quran tells us that man has within himself all what is reflected in the universe - the best proportions. Man is the core of God’s creatures; he possesses the most harmonious proportions, reflecting of the Divine harmony of being. "We have indeed created man in best of forms" – proportions (Surah At-Tin, 95:4). Leonardo da Vinci illustrated the mathematical proportions of the human body, showing that human being exhibits clearly golden mean proportions in his body based on ratios of 1.618.The Vitruvian Man drawn by Leonardo Da Vinci is based on Vitruvius, who believed that if human proportions could be incorporated into buildings, they would become perfect in their geometry. According to Vitruvius, the distance from fingertip to fingertip should be the same as that from head to toe. The sacred mean rules can be seen in the ratios of body parts throughout the human body. The human body contains in its proportions all the important geometric geodesic measures and functions. The proportions of ideal man are at the center of a circle of invariant cosmic relationships.

Proportions of Venus’ and Earth’s mean orbits.
The mathematical harmony of the universe can be seen from the proportions of the planets in our solar system. For example, the ratio of the sacred mean can be seen in the rotations of Venus and Earth around the Sun in that for each five years that the Earth rotates around the Sun, Venus rotates around it eight times. The connection between 5 and 8, both of which are Fibonacci numbers, is the golden mean proportion (8/5 = 1.6). The result of this motion is that Venus draws a pentagon around the Sun every eight years (Figure A). Figure B shows that a circle is drawn, which represents Venus’ mean orbit. A pentagon is constructed inside it and a small circle placed through the arm-crossing points. The radius of this small circle divides the radius of the large one into golden sections and can be used to space Venus’ orbit from Earth’s orbit. It can be seen from the agreement between eightfold and fivefold geometries that eight touching circles are drawn from Venus’ mean orbit. In turn, the circumference circle is enclosing these eight circles, defining Earth’s mean orbit. The ratio of the mean orbits of Venus’s to Earth is the √2 proportion. The geometric representation of these orbits creates the golden mean proportion.

Monday, February 13, 2017

Sunspots - The Real Cause of Higher Grain Prices | Tom McClellan

Tom McClellan (Jul 27, 2012) - Sunspots are a big driver for wheat prices. Various pundits are putting out stories blaming the drought in the plains states on global warming [...] A better explanation for the drought, and the ensuing spike in grain prices, is that this is all part of the normal 11-year sunspot cycle. But to find that relationship in the data is what the story is about. The first point to understand is that sunspot activity has now been scientifically linked to changes in cloud formation. When the sun is more active, the charge particles streaming out from sunspot activity help to sweep away cosmic rays that might otherwise hit earth's atmosphere, where they play a role in cloud formation [... | HERE + HERE] Once you get past that more difficult scientific hurdle of understanding that cosmic rays and clouds are related, it is pretty easy to understand that less cloud formation is related to less precipitation, and thus poorer growing conditions for rain-irrigated crops. That is what we are seeing with this year's drought, and it has been pushing up grain prices accordingly. Looking across the last hundred years of price data on wheat, it can be difficult to see the relationship between the sunspot number and wheat prices. Part of this comes from the fact that there are other factors which sometimes act upon crop yields and thus grain pricing. But a big factor is that the units we use to measure wheat prices, i.e. US dollars, can vary themselves, causing the relationship with sunspots to sometimes be disguised by what the dollar itself is doing. 

If we look at the history of these two sets of data before the modern era of floating currency exchange rates, we can better see how they were correlated. This chart shows raw wheat prices, un-adjusted for the value of the dollar. The sunspot number data is shifted forward by 2 years to reveal that bottoms and tops in the sunspot number tend to be followed a couple of years later by bottoms and tops in wheat prices. This relationship got into some trouble in the middle part of the chart, when President Roosevelt's New Deal price fixing artificially inflated wheat prices. The intention in the 1930s was to benefit farmers by keeping wheat prices up. That effort switched during WWII to the government putting a cap on all prices, including wheat, to support the war effort. Rationing of food, fuel, and other items took over for market forces. Additional trouble came in the 1970s, when the Arab Oil Embargo pushed up oil prices in 1973-74, reducing acreage under cultivation. Then later in that decade, the rising value in the dollar pushed down the dollar price of most commodities compared to prices in other currencies. So using dollars to see the normal cyclical relationship in price data became problematic.

All of this explanation brings us (finally!) back to the lead chart above. In [the above] chart, I have adjusted the dollar price of wheat, multiplying it by the US Dollar Index, which was created back in 1971. This mathematical step produces a unit-less measure of the value of wheat by factoring out the dollar's movements. Doing this allows us to better see how the peaks and troughs in wheat prices have been related to the sunspot cycle. I want to emphasize again that the sunspot number is shifted forward in that chart by 2 years, to reveal its leading indication for how wheat prices will behave. The conclusion from this is that the upward move in the value of wheat right now is just following the swoop upward in the sunspot number that began in 2009. We should expect to see generally rising prices for wheat and other grains until about 2 years after the sunspot cycle has peaked, a peak which has not even happened yet.

On the Insignificance of Herschel’s Sunspot Correlation | Jeffrey J. Love

William Herschel started to examine the correlation of solar variation and solar cycle and climate. Over a period of 40 years (1779–1818), Herschel had regularly observed sunspots and their variations in number, form and size. Most of his observations took place in a period of low solar activity, the Dalton minimum, when sunspots were relatively few in number. This was one of the reasons why Herschel was not able to identify the standard 11-year period in solar activity. Herschel compared his observations with the series of wheat prices published by Adam Smith in The Wealth of Nations.In 1801, Herschel reported his findings to the Royal Society and indicated five prolonged periods of few sunspots correlated with the price of wheat. Herschel's study was ridiculed by some of his contemporaries but did initiate further attempts to find a correlation. Later in the 19th century, William Stanley Jevons proposed the 11-year cycle with Herschel's basic idea of a correlation between the low amount of sunspots and lower yields explaining recurring booms and slumps in the economy. Herschel's speculation on a connection between sunspots and regional climate, using the market price of wheat as a proxy, continues to be cited. However, according to a study of Jeffrey J. Love of the USGS the evaluation is controversial and the significance of the correlation is doubted:

Jeffrey J. Love (Aug 27, 2013) - Our finding is that Herschel’s hypothesis is statistically insignificant [...] All of the data Herschel discussed in his 1801 paper were collected prior to 1717, during the Maunder Minimum and long before his paper was published. His identification of five durations of time with few sunspots and inflated wheat prices and five other durations that might have had sunspots and which had deflated prices [Herschel, 1801, pp. 313-316] would be an unlikely realization of binary statistics, but it is not clear whether or not Herschel was inspired to state his hypothesis after inspection of these data. Having said this, Herschel acknowledged that predictions based on his hypothesis “ought not be relied on by any one, with more confidence than the arguments ... may appear to deserve” [Herschel, 1801, p. 318]. Today, we have considerably more data than were available to Herschel; these were collected both before and after he stated his hypothesis, and they can be used for both retrospective and prospective testing.  For  London wheat  prices  both before 1801 and, separately, after 1802, binary significance probabilities and Pearson correlations and their effective probabilities are [...] indicative of statistical significance. While solar irradiance may affect global climate, from our analysis of data of the type considered by Herschel, we conclude that historical wheat prices are not demonstrably useful for inferring past sunspot numbers, and, conversely, sunspot numbers are not demonstrably useful for predicting future wheat prices.

Sunday, February 12, 2017

Ancient Alphabets | The History of Writing

Wilhelm Gesenius (1851) - Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Enlarge

The history of the alphabet started in ancient Egypt. By 2700 BCE Egyptian writing had a set of some 22 hieroglyphs to represent syllables that begin with a single consonant of their language, plus a vowel (or no vowel) to be supplied by the native speaker. These glyphs were used as pronunciation guides for logograms, to write grammatical inflections, and, later, to transcribe loan words and foreign names. However, although seemingly alphabetic in nature, the original Egyptian uniliterals were not a system and were never used by themselves to encode Egyptian speech. In the Middle Bronze Age an apparently "alphabetic" system known as the Proto-Sinaitic script is thought by some to have been developed in central Egypt around 1700 BCE for or by Semitic workers, but only one of these early writings has been deciphered and their exact nature remains open to interpretation. Based on letter appearances and names, it is believed to be based on Egyptian hieroglyphs. This script eventually developed into the Proto-Canaanite alphabet, which in turn was refined into the Phoenician alphabet. It also developed into the South Arabian alphabet, from which the Ge'ez alphabet (an abugida) is descended. Note that the scripts mentioned above are not considered proper alphabets, as they all lack characters representing vowels. These early vowelless alphabets are called abjads, and still exist in scripts such as Arabic, Hebrew and Syriac.

Phoenician was the first major phonemic script. In contrast to two other widely used writing systems at the time, Cuneiform and Egyptian hieroglyphs, it contained only about two dozen distinct letters, making it a script simple enough for common traders to learn. Another advantage of Phoenician was that it could be used to write down many different languages, since it recorded words phonemically. The script was spread by the Phoenicians, whose Thalassocracy allowed the script to be spread across the Mediterranean. In Greece, the script was modified to add the vowels, giving rise to the first true alphabet. The Greeks took letters which did not represent sounds that existed in Greek, and changed them to represent the vowels. This marks the creation of a "true" alphabet, with both vowels and consonants as explicit symbols in a single script. In its early years, there were many variants of the Greek alphabet, a situation which caused many different alphabets to evolve from it. The Cumae form of the Greek alphabet was carried over by Greek colonists from Euboea to the Italian peninsula, where it gave rise to a variety of alphabets used to inscribe the Italic languages. One of these became the Latin alphabet, which was spread across Europe as the Romans expanded their empire. Even after the fall of the Roman state, the alphabet survived in intellectual and religious works. It eventually became used for the descendant languages of Latin (the Romance languages) and then for the other languages of Europe (more HERE)

The Effect of Sunspot Activity on the Stock Market | Charles J. Collins

Charles J. Collins (1965) - Solar phenomena have been a source of scientific interest and investigation since Sir William Herschel, in 1801,found a correlation between sunspot activity and terrestrial phenomena [...] Modern science is giving considerable attention to solar phenomena in relation to disruption of the earth's magnetic field, to human health, and to weather, including rainfall, temperature, and cyclone frequency. The security analyst's interest is more directly concerned with the directly concerned with the effect of solar phenomena on business, and on speculation as evidenced by the ebb and flow of prices over our stock exchanges [This paper points] out one simple correlation of solar-stock market movements that will, fortunately, come to another test within the two or three years ahead. This is an apparent relationship between a recurrent phase of each sunspot cycle and an important stock market peak. The matter is of interest at this time for the reason that considerable attention is being given by students of the stock market as to when the broad advance that has been under way for a number of years is to reach a terminal point. This sunspot correlation, as discussed below, may throw some light on the subject. Briefly stated: It appears that an important market peak has been witnessed or directly anticipated when, in the course of each new sunspot cycle, the yearly mean of observed sunspot numbers has climbed above 50.

[...] Over the 94-year period under review, there were seven completed sunspot cycles, and it appears that an eighth was completed and a new cycle was started in 1964.During these eight cycles, not onlywas an important stock market peak concurrently witnessed (1881, 1892, 1916, 1936,1946, 1956)or directly anticipated (1906, 1929) by the above-50 count in sunspots, but, in four instances (1881, 1916, 1929, 1936), the designated peaks also marked the extreme or secular peaks for the entire sunspot cycle. The year 1890 seems an exception. In May of that year, the stock index reached its high of 5.62. In August 1892, the 5.62 level was again attained and, as concerns the yearly mean of the monthly stock indexes, the year 1892 peaked at 5.55, as compared with 5.27 for the year 1890 [...] In other words, in six instances, important stock market peaks and the sunspot climb above 50 came the same year, the two exceptions being 1906 and 1929. As to the 1906 exception, it will be noted, from the monthly range stock market chart, that the market peaked in January of that year, with December 1905 not far behind the January 1906 peak.

From a study of stock market history in relation to solar phenomena, a second theorem may be adduced: In each solar cycle, the largest stock market decline, in terms of percentage drop, comes after the sunspot number, on an annual basis, has climbed above 50. In the light of the foregoing observation, the 94 years of sunspot activity under review seems to occupy a rather narrow latitude for dogmatism. Thus, the preceding remarks should not betaken as a definitive prognosis of pending stock market behavior. Instead, they present a rather interesting correlation that has existed for a period of years between sunspot activity and major market peaks. Ergo, since the solar cycle is now at a point germane to this correlation, it seems worthwhile to present the previous relationship and await events, not without interest, of course, but mostly in the spirit of an enquiring attitude.

Originally printed in Financial Analysts Journal, November-December 1965; reprinted in Cycles Magazine in March 1966, and again in Cycles Magazine, Vol. 40, No. 3, September/October 1989]; editor's postscript of the 1989 reprint: "It is interesting to note the relation between above-50 crossingsand the stock market since 1965. In July 1966, the mean sunspot number moved above 50. The stock market shortly thereafter plunged in a major correction. In January 1978, the mean sunspot number again went above 50. The stock market, which had been in a downtrend, continued into a bottom after this date. In October 1987, the mean sunspot number went well above 50 to 60.~ and the 1987 crash followed. The mean sunspot number will next rise above 50 in about 1998."

Saturday, February 11, 2017

The Best Seasonal Time of the Year | Feb 15 - May 10

Feb 15 - May 10 (Source: Nautilus Research)
First Quarter 2017 | Presidential Cycle + Seasonal Pattern + Decennial Cycle of the DJIA (HERE)

The Sunspot Cycle and Stocks | Robert R. Prechter, Jr. and Peter Kendall

Robert R. Prechter, Jr. and Peter Kendall (2000) - Some effects from solar radiation are well documented. Sunspots disrupt satellite systems, radio transmissions and electric power grids. In the realm of mass human activity, the sun’s role has been a source of speculation since the dawn of civilization. In 1926, Professor A. C. Tchijevsky traced the sunspot activity back through 500 B.C. and found that it produced nine waves of human excitability per century. “As sunspot activity approaches maximum,” Tchijevsky found, “the number of mass historical events taken as whole increases.[...] the Wave Principle and unconscious human herding behavior as a function of the human limbic system, which is the gatekeeper of emotion within the human brain. However, the limbic system is not necessarily independent of outside forces. As the radiating center of our solar system and the wellspring of practically all the energy on the planet, the sun is certainly an intriguing contender for some degree of external mass mental influence.

Why does the stock market typically peak before sunspots do? One very plausible explanation is that the collective tendency to speculate peaks out along with the rate of change in sunspot activity. If sunspots affect humans’ positive-mood excitability, that appears to be the point of maximum effect. When we explored this possible explanation, we found something additionally interesting. 

The figure above shows that as the solar radiation thrown off by the sun increases to a maximum rate (shown by our optimized 39-month rate of change in sunspot numbers), the human urge to speculate in general hits a fever pitch. Two months after the rate-of-change peak in 1916, the stock market established an all-time high that was not materially exceeded until the sunspot count was accelerating again in the mid-1920s. The next rate-of-change peak in October 1926 preceded the final stock market high by a full three years, but the speculative fever that accompanied the Florida land boom ended almost coincidentally, about two months earlier. The next peak was a double top that finished in February 1937, one month before a major stock market high. In 1947 and 1967, the rate of change peaked within 13 months of major stock peaks. In 1957, the peak coincided with with the all-time high in the advance-decline line, which stands to this day. The September 1979 peak was four months before a century-long high in precious metals prices. The August 1989 peak accompanied the all-time high in the Nikkei and the end of a big real estate boom in California and Japan. Since scientists’ grasp of the sunspot cycle is based on empirical observation rather than an understanding of what causes it, there is no way to verify that a rising rate of sunspot activity is behind these outbreaks. However, the speculative fall-off in the wake of every peak since 1916 is itself strong evidence of an effect. The latest peak rate of change came in December 1999, and that sets up a test. Will this peak in sunspots mark the end of the greatest mania in the history of the stock market? 

"Lower sunspot cycle maximums portend the largest bear markets."
"Shortly before a sunspot cycle hits bottom, stocks turn up." [Chart HERE]