Julia Robinson and Hilbert’s 10th Problem


On Fibonacci Day, November 23rd, Science Magazine published a bio on a modern mathematician who utilized the Fibonacci series to uncover how to solve Formalist David Hilbert’s 10th problem. International Fibonacci day itself is a annual celebration that honors one of the most influential mathematicians of the Middle Ages – Leonardo Fibonacci of Pisa.

Fibonacci was a medieval Italian mathematician who wrote Liber abaci (1202; “Book of the Abacus”), the first European work on Indian and Arabian mathematics. He discovered an intrinsic and self-evident algorithm that appears throughout nature called in his honor the Fibonacci Series. We have no hard dates on Signore Fibonacci and so cannot do a chart but we know it would be spectacular.

For Fibonacci Day, an agave plant whose leaves exhibit a Fibo sequence. Count them and see.

Microsoft’s Bing search engine also celebrated Fibo Day with a shot of an agave and a quiz.

What a fibonacci number

A Fibonacci sequence starts with 1, 2, 3, 5, 8, 13, 21, 34, 55 (Fibonacci himself omitted the first term) and goes on with each number in the sequence being the sum of the two preceding numbers, (i.e. 1+2 =3, 3+2 =5 and so on). It is a recursive  number sequence because to go forward you must go back (sort of like back stitch in embroidery).

The Fibonacci numbers are also exemplified by the botanical phenomenon known as phyllotaxis where the whorls on a pinecone , pineapple, or petals on a sunflower follow a sequence of Fibonacci numbers or the series of fractions

Figure 4: Golden rectangles and the logarithmic spiral.
The Fibonacci whrol

Back to Julia

Julia Robinson wanted to know the answer to Hilbert’s 10th problem and though she did work on it, she did not find the answer. Just after her 50th birthday, the twenty two year old Soviet mathematician Yuri Matiyasevich announced that he had solved the problem and gave her the nod for helping in the solution. The key was in her early papers that showed how to algorithmically compute functions (also called the recursive functions) that map the natural numbers into themselves.

One of the initial functions is just the successor function S(x)= x+1. The other, which Robinson calls E, is defined as the difference between a given number and the largest perfect square that does not exceed it. (Thus E(19) = 19 – 16 = 3 and E(25) = 25 -25 = 0.)

The three operations are as follows:

(1) from given functions F and G obtain the function H(x)=F(G(x));

(2) from given functions F and G obtain the function H(x)=F(x) + G(x); and

 (3) from a given function F whose values include all natural numbers obtain the function H where H(x) is the least number t for which F(t)=x.

from her paper which uses not only the Fibo sequence but the Turing wheel for support.
A bucket with a Uranus handle. Her Ascendant is 28 Scorpio.

Julia was born on December 8 1919 in Saint Louis, Missouri to Ralph Bowers Bowman and Helen Bowman who died when Julia was two. Her father remarried and moved the family out to California where Julia got both rheumatic and scarlet fever. In 1936, Robinson entered San Diego State University at the age but transferred to UCal Berkeley in 1939 where she met Raphael M. Robinson, her mentor and later husband. Her specialty was game theory and she was the first female mathematician to be elected to the National Academy of Sciences.

Her Ascendant is 28 Scorpio, [HS] a book about memory techniques or the ability to bring into being a state of accord a system. Her Moon is incredibly fast at 15.07 and then while her Mercury is just 4 degrees away, it is in another sign at 03 Sagittarius 21, making it unfettered. Thankfully her Mercury is also retrograde giving Mrs. Robinson the ability to jump forward in her thought process and visualize what she was looking for, and then be able to trace that process back and write it in mathematical notation. We have not run into this configuration previously.

Footnotes:

  • I saw this article in Science News and was struck by her. I thought this was a chart was ought to do, so I did.
  • Julia’s sister, Constance Reid, wrote a biography on both Julia and German mathematician David Hilbert.

French Astrologer Andre Barbault reposes


French astrologer, Andre Barbault, reposed on the afternoon of 7 October 2019. Commencing his studies at seventeen years old,Monsieur Barbault gave the world eighty one years of profound study. His predictions of world events are well-known and his wisdom came from intense study of human psychology married to relentless research.

He was born at a solar eclipse on October 1, 1921, at 5:00 p.m. in Champignelles, France (about 4 hours away by Metro; 2 hours by voiture). He rectified his chart to 4:54:21 p.m. that of course we use for his chart. His website is AndreBarbault and he has many free papers both in French and English available for study. We recommend nabbing them now.


Updating Astrologer-Psychologist Liz Greene


In Ms. Greene’s book, The Outer Planets and their Cycles, section #5, Liz admits that her “Mercury is in Gemini”. Based on her birthday of September 4th that cannot be literally true Mercury is never that far away from the Sun (which in September is in Virgo), so she must mean is that it is in its the third house or Gemini.

Re-rectifying Liz

When we originally rectified her chart, we put her Mercury in the 9th, and Sagittarius. Now we have to switch it around 180 degrees and Mercury is in the 3rd house (vivification or the ability to make things come alive). Instead of a 28 Scorpio ascendant for 1 PM, she now has a 15 Cancer for 1 AM and the Hyperion Symbol of “candles in a shadowy room.” This highlights her ability to be attuned to opposite conditions with the fine skill which discerns each. Gavin McClung gives this symbol, the keyword of “Sensitivity.”

Change in Type

Greene was a deviated bowl; now she is a bucket with a Uranus handle at 12.33 Gemini [HS] “antique seals and sigils” commenting on her conscious sense for dealing with the unknown and forgotten pasts. As this is in the 12th house or the hidden world of the psyche, her focal determinator Uranus allows her contribute Jungian archetypes and myths in self-awareness.

Opposite her Uranus handle is a preponderance of planets in Sagittarius (Administration) in the 6th house where her daily work as a psychologist cum astrologist encourages her to travel both physically and metaphorically to expound her theories and techniques. Her South Node (SN) there is a mutable (cadent) house that always deal with realization.

With two planets and a node there, we see that Ms Greene employs understanding to find an untapped market to which she acts like a guru because coming right after the preponderance of in Leo (assurance) she makes her students (audience) feel that she not only has an “instinctive response” (the 4th) to the problems but also can express the answer both creativity and personally.” (the 5th). Such an ability has led to her unparalleled financial success (she and Robert Hand own Astro.com and now Astrotheme.com).

Greene’s Yod

Using again her idea of Pluto and Neptune for the yod points, as they a sextile away, her original yod is still at 8 Virgo but now in 3rd house. Here we see that Liz has a strong philosophical nature (she has Ph.D. in philosophy) with an abundance of ideals and concepts that do not always translate into practical terms. While she is a glib conversationalist, it’s hard to fully grasp her meanings, as talks on an abstract plane. This was apparent in the Outer Body book with her insistence Pluto is a female planet akin to the Furies, where elsewhere it is associated with Mars. Those who have read her other books can discern that same thread. Her discussion with her audience keeps her grounded, they can point out inconsistencies (and they do!) and jumps in logic that are perplexing. This is like to the conversation she has with her clients who probably do the same.

If you found this or any other of our essays helpful, please give us a like, we appreciate it.

Treaty of Versailles, twice


April 7, 2019, marks the hundredth anniversary of Article 231 of the Treaty of Versailles — the infamous war-guilt clause. Although the treaty was not signed until June 28, the Supreme Council approved the notorious article on April 7, 1919. The authors were John Maynard Keynes, & John Foster Dulles.

The Allied and Associated Governments affirm and Germany accepts the responsibility of Germany and her allies for causing all the loss and damage to which the Allied and Associated Governments and their nationals have been subjected because of the war imposed upon them by the aggression of Germany and her allies.

Bucket with an Uranian Handle.

Points seven and eight stipulate, “Belgium, the whole world will agree, must be evacuated and restored,” and “All French territory should be freed and the invaded portions restored.” The term “restored” is significant, for it meant France and Belgium could seek compensation from Germany for the invasion.


The formal Date, June 28, 1919

The formal signing was 28 June 1919 at the Palace of Versailles, exactly five years after the assassination of Archduke Franz Ferdinand which directly led to World War I

Bucket with an Uranian Handle

Living long, Roslyn’s story


I happened to be going thru some old charts I have and noticed this one of my friend’s mother. I realized that Roz was now 93 years old and had never been sick a day in her life — literally. her pregnancies were a walk in the park, her deliveries effortless. She met her husband thru the posters on the new York Subway, she was June 195? Miss Subway and her future husband took one look at the luxuriant brown wavy hair and was entranced.

Roz is a Bucket with an Uranian handle at Pisces 23 in the Seventh House, perhaps that suggests what an odd way she met Mr. Right. The Symbol is an “inhabited island,” which in a way is what Brooklyn and the boroughs are — inhabited and heavily populated islands; only the Bronx is part of the mainland. For Roz this symbol suggest adequate resources to obtain all that she needs which was true.

Venus in the third conjunct Saturn struck me, as her husband is just a year older than she but i think instead of being about age, it is about that he was a Conservative Jew and that their life was bound by rigourous adherence to their faith and fidelity to one another. Her moon is in Capricorn. Many say that where the Moon lies is one’s mother, if so, Roz’s Mom, Ethel, lived to 96 and died at home with her family.  In her daughter’s chart, Roz shows up as Leo the lion, perhaps because Hattie saw her mother as a fierce protective lioness.

Our header image is of Flatbush, Kings Co. New York c. 1927

This week in Carson City, Nevada 10/10-14/2018


Carson City, the capitol of Nevada, is about 30 miles south of Reno.  It is a picturesque town filled with slot machines like every town and gas station in the state.  This week we have a bucket with an Uranian Handle so look for things to break, change and suddenly pop up that are either electronic or via electronic means.  In my case this meant my Samsung 6 got pushed out my head by my dog, Ruffian, while I was reading and smashed the front glass.  I found out that unlike Apples, Samsungs are not repairable, or at least not easily, hence why the newest ones are under warranty and the old ones, are cheap.

carson city.png

NEVADA  is a  Spanish word meaning ” snow-clad ” or ” snowy land,” originally applied to a snow-capped mountain range on the Pacific slope), and it is one of the far western states of the American Union, lying between 35° and 42° N. and 114° 1′ 34″ and 120° 1′ 34″ W. (370 and 430 W. of Washington).

It is bounded N. by Oregon and Idaho, E. by Utah and Arizona, the Colorado River separating it in part from the latter state, and S. and W. by California.

Nevada ranks sixth in size among the states of the Union and with the minor  exception of its N.E. and S.E. corners, the state lies wholly within the Great Basin, the floor of which is really a vast table-land between 4000 and 5000 ft. above the sea. This plateau, however, is not a plain, but contains many buttes and mesas and isolated mountain. ranges rising from loco to 8000 ft. above its surface.

In the N.E. an unnamed range of highlands, with an E. and W. trend, forms the water-parting between the streams tributary to the Humboldt river in Nevada and those that flow into the Snake river through Idaho and Oregon and to the Pacific Ocean.

This range is very broken and ill-defined, with peaks often reaching altitudes of from 9000 to 12,000 ft., and with numerous spurs diverging N. and S. from the main divide. Between this ridge and the valley of the Colorado river lies all that portion of the Great Basin included within the state. The surface of this table-land is very rugged, and frequently broken by mountain ranges running N. and S. and from 5 to 20 M. wide at their bases. Intersecting the mountains are numerous ravines and passes.


Carson City the capitol and county seat of Ormsby county, about 120 M. N.E. of Sacramento, California. Pop. (1890) 3950; (rgoo) 2100; (1910) 2466. It is served by the Virginia and Truckee railway, which has repair shops here, and by stage to Lake Tahoe, 12 M. W. of the city. It is picturesquely situated in Eagle valley, near the east base of the Sierra Nevada, at an elevation of 4720 ft. above the sea.

It was named in honour of Christopher Carson &  settled in 1851 as a trading post, was laid out as a town in 1858,  & made the capital of the state and the county seat of the newly erected county in 1861.  The city itself was chartered in 1875.


CHRISTOPHER [” KIT “] CARSON (1809-1868) was an American hunter and scout, born in Madison county, Kentucky, on the 24th of December 1809. When he was a year old his parents removed to Howard county, Missouri, then a frontier settlement, and the boy was early trained in the hardships and requirements of pioneer life. He served for a while as a saddler’s apprentice, and after 1826 devoted himself to the life of a professional guide and hunter.

He was hunter for the garrison at Bent’s Fort on the Arkansas river in what is now Bent county, Colorado, from 1832 to 1840, and accompanied John C. Fremont on his exploring expeditions of 1842 and 1843-1844, and on his California expedition in 1845-1846. Carson took part in the Mexican War, and, after the rush to the Pacific Coast began, engaged as a guide to convoy emigrants and drovers across the plains and mountains.

In 1854 he became Indian agent at Taos, New Mexico, in which position, through his knowledge of the Indian traits and language, he was able to exercise for many years a restraining influence over the warlike Apaches and other tribes.

During the Civil War he rendered invaluable services to the Federal cause in the south-west as chief scout in charge of the various bodies of irregular scouts and rangers participating in the constant border warfare that characterized the conflict in that part of the Union.

In March 1865 he was brevetted brigadier-general of volunteers for gallantry in the battle of Valverde (on the 21st of February 1862) and for distinguished services in New Mexico, and after the war resumed his position as Indian agent, which he held until his death at Fort Lyon, Colorado, on the 23rd of May 1868.

” Kit ” Carson occupies in the latter period of American pioneer history a position somewhat similar to that held by Daniel Boone and David Crockett at an earlier period, as the typical frontier hero and Indian fighter, and his hairbreadth escapes and personal prowess are the subject of innumerable stories.

To read more about this American hero see.

  1. Charles Burdett, Life of Kit Carson, the Great Western Hunter and Guide (New York, 1859; new ed., 1877) ;
  2. De Witt C. Peters, The Life and Adventures of Kit Carson, the Nestor of the Rocky Mountains, from Facts Narrated by Himself (New York, 1858).
  3. and most recently, Blood and Thunder: The Epic Story of Kit Carson and the Conquest of the American West by Hampton Sides (c. 2007).

Next week we head back east to Columbus, Ohio.

#329 Farida, Queen of Egypt.


Farouk in London King Farouk was 17 (see above)  when he met Safinaz Zulficar -her name in Turkish means the beautiful woman- on a trip to London.  She was part of the royal entourage for Queen Nazli’s voyage.   Her mother Kareema was the queen’s  lady in waiting, and also one of the daughters of Mohammed Said Pasha, an Egyptian prime minister of Turkish origin & sister of Mahmoud Said, an Egyptian painter and judge, who encouraged his niece in art.
A painting by autodidact Mohammed Sa’id.
They were married on January 20, 1938 at the Saraya el-Kubba Palace. Her wedding gown was a stunning affair designed by the House of Worth, see our header picture.  Pictures of the wedding are also available on the Royal Couturier’s site.  

After the marriage she changed her name to Farida as a fortune teller had told Farouk that “F’s” would bring him luck. She was Farouk’s first wife and bore him three girls that he found insulting to his manhood. After the third, Farouk divorced Farida  on 19 November 1948 though he had already an “official mistress” that he nightclubbed with (it was improper for a Muslim wife to carry about around town).

Her two youngest daughters, Fawzial and Fadia have since died.  Only her eldest Ferial b. 1938 is still alive. It was his second wife, Narriman, who gave him his only son, Ahmad Fouad on January 16, 1952.  Shortly afterward, he was deposed.  Farouk’s sister (see the lower photo of the trio below) Fawzia, married the Shah of Iran, Reza Pahlavi of Persia (1919-1980) on March 15, 1939.   That did not last either. Marc Jones has her birthday at 9-5-1921 at 5 pm based on her recollection, but does not cite a birth place. The Egypt Independent newspaper says that the Queen was born in Alexandria.  Her hobby thanks to Uncle Mohammed was painting but unlike his realistic portraits, hers tended towards abstracts. She died of leukemia on 17 October 1988 in Cairo. Her husband, King Farouk I died March 18 1965 in exile on the island of Capri, Italy. You can read more about Farouk on the Dutch MadMonarch’s site (there are two).
Farouk_I,_Narriman_&_Fuad_II_in_Capri.jpg
Queen Narriman, Prince Ahmad and King Farouk
So first up is the Jones chart as specified in the Sabian Symbols book, without a place but with a 5 pm time.  We put that to Alexandria.  This gives her a 16.44 Aquarius ascendant, with the symbol of a “watch dog standing guard.”  It also makes her temperament type a bucket with an Uranian handle, with Uranus as the focal determinator (as singleton) on the east side of the chart demonstrating her resourcefulness. queen farida.png

Then there is our rectification below.  We still have has a bucket with a Uranian handle, but this time Uranus is in Pisces 07.27 and gets the symbol of “a girl blowing a bugle” that highlights her participation in life’s events and success in handling them.  We feel that works better as she was a beloved queen, and in the twelfth house, shows how she seemed to manage things behind the scenes for her husband.  To what extent?  We cannot say, but we do know that about 5 years after the divorce, Farouk was dethroned.

Queen Farida and Daughters

We also threw in some asteroids on our lilac chart.  First is Child at 26 Libra, semisextile Pandora at 26 Scorpio suggesting the Pandora’s box of troubles she unwittingly unleashed by having daughters.  Then another semisextile away, now a square from Asteroid Child, is the asteroid Hygeia that shows her marriage to a germophobe.

We threw in some location asteroids too.  First is Alexandrinus for her birth place in Alexandria and highlighting her Egyptian Circassian heritage.  Circassians are natives of the northern Caucasus that were exiled from their homeland by the Russian Tsar’s in the 19th century and fled to the welcoming middle east.  While originally Eastern Orthodox some converted to Islam.

After the queen's death

The second Asteroid is Europa, for the continent of Europe, at 24 Aries and basically a semisextile away from Alexandrinus, but in her first house, showing how she returned to her ancestral home when she was divorced.

If you make a yod from Pandora in Scorpio to Jupiter in Virgo and then the apex at the ascendant 01 Aries, we see that the head of her yod ends up at Hygeia in the seventh, and that being the source of all her woes, Farouk.  As that asteroid is quicunx her Uranus, it puts a lot of stress on her being innovative to handle him and protect her interests.  In the end though, she could go do so much, particularly when Uranus was opposite her Sun and transforming Pluto in Cancer into a catalyst for both herself and Egypt. farida ii.png  

Cave-in, Larksville PA 1922


The history of the event

We have highlighted another cave-in around the Northeastern Pennsylvania area that was a large mining district because of its hard firing, cleaning-burning coal:  the best coal ever discovered throughout the world.  This one, in 1922 in nearby Larksville, destroyed a high school on August 24, 1922.  There are no casualties mentioned and while school does start earlier in Pennsylvania than most states, before Labour Day, that is usually the last week of August, or a week after the accident.

larksville map.png

The T-Square from Uranus opposing Mercury show the suddenness of the event. but the houses are key here.  First we have a preponderance of planets in earthy Virgo, making the tenth house of “dreams and aspirations” they keystone of the chart.  Virgo is the ruler both the month of August and hidden earth works both of which work well here, as the even happened not only during the rulership of Virgo but in the month of August; the piers that collapsed were underground that supported the structure.  Another thing that could be implicated here are the “inspectors” that viewed the woodwork — they too are ruled by Virgo — thus with Virgo afflicted by Uranus in Pisces in the hidden northern hemisphere,  the idea  that the inspectors did shoddy work takes hold.

39700661_2097963386903142_2842953116532342784_n.jpg

Mars typically in the first house suggests according to Martha Lang Westcott, a traumatic event that leaves scars; Alan Leo simply says that this position gives a scar to the face.  The point focus of Uranus opposing Mercury (chosen because it is the closest opposition, all others are translations of light) is at Mars 20.18 Sagittarius in the first house.  This aspect highlights that the cave-in will mark the land but not swallow it whole, leaving remnants or scars above.  Sagittarius rules schools  & traveling and is trine the underground god Neptune at Leo 16.16 that rules earthquakes and earth ruptures.  It is also semisextile Saturn, the ruler of caves and underground earthworks, in Libra highlighting that the piers were not sound.  Saturn is then sextile Neptune showing that it will earth not water that will be at the root.

larksville cave in

Here is the article on the accident from the Wilkes Barre Sunday Independent, August 27, 1922.  The paper is now defunct.

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Prohibition Starts midnight 6-30-1919


prohibition with asteroids.png

prohibiton.png

Basically this chart is a bundle with an Uranian handle in the sixth house.  Uranus is also the only retrograde planet in the chart.  The asteroid chart is supplied above and has an interesting aspect between asteroid Li and Venus suggesting that the legislators were quite aware that this would not work.

The ascendant is 22 Virgo, that has the Hyperion Symbol of “a small bowl with a sacrificial food within” that supports that aspect because it has the meaning of a “great gift” of willing devotion that was not the case because it was squared the Midheaven of 21 Gemini or a “lost dog trying to find its way.”  Despite the great humanitarian wish of Uranus the Ascendant opposing it, meant it would never be anything but a “small offering” to the Great Temperance Movement.

#292 Vernon California, Boxing & Jack Doyle


The city of Vernon is best known today for its meatpacking plants and slaughterhouses, but nearly a century ago vied with Madison Square Garden for the title of “Boxing Capital of the World.” In his Vernon Arena, promoter Jack Doyle staged 20-round world championship fights and, between bouts, allowed the sporting set to refresh itself in a saloon with the “longest bar in the world” and the battleground for some of America’s greatest fighters, including Sam Langford, Joe Rivers, Joe Gans, Willie Richie, Benny Leonard, Bert Colima, Mickey Walker and Jack Dempsey.

willard ko
willard ko

But not everything was so rosy for on Aug. 22, 1913, future heavyweight champion Jess Willard knocked out Bull Young in the 11th round. Young died the next day. Two years later, in response to Young’s death, California legislators limited boxing matches to four rounds and forbade promoters to offer more than a $35 prize (usually a medal). This led fighters to ask “How much medal do I get?”

doylesarena
doyles arena

Prohibition pretty much spelled the end of Doyle’s watering hole, though it went out in a big way. The night before the national law went into effect, June 30, 1919, more than 60 bartenders patrolled the bar, doling out drinks to an estimated 1,000 customers in what was the ultimate “last call.”

prohibition.png

A few years later, Doyle tore down the old arena and built a 10,000-seat indoor coliseum in just 35 days. He replaced the four-legged stool in the boxers’ corner with padded seats that swung out of sight between rounds, and the unsightly and unsanitary water buckets were replaced with modern plumbing carrying running water.

When Doyle replaced the wooden benches with orchestra seats, Arbuckle had a special one built for himself, about 50% wider than the average. Chaplin sat ringside. Fans watched him rise from his seat to duck, swing, shout and dodge blows, as if he were in the ring himself. He even refereed a match for one of his favorite boxers, Frankie Dolan.

In 1924, when the Los Angeles Olympic committee was seeking a venue for wrestling and boxing, it lent some financial help to Doyle, who built today’s Olympic Auditorium just south of downtown. A year later, Doyle spent thousands of dollars lobbying the Legislature to allow the return of 10-round bouts. In 1927, Doyle’s Vernon indoor coliseum, where amateurs rose to become world champions, burned when the adjacent baseball park caught fire.

jack doyle placidus
jack doyle in placidus and a see-saw.

When he died in 1944, lucky Jack Doyle was rich and long retired from his pugilistic empire. He’d struck gold in the ring, but not nearly as much as he found when he struck gold a second time–the black gold still being pumped from beneath Signal Hill.

from the L. A. Times obituary.

Attached is Marc’s data for Jack Doyle that was missing the birthplace, so it is in Placidus format to match his 1000 Notable Nativities. Retrosheet.org supplied the place but has different data, October 25, 1869. Kilgorin was then part of the United Kingdom – Ireland did not procure its freedom until Easter Sunday 1916 so the Retrosheet version is in the colours of the Union Jack,

jack 1869
jack 1869 a locomotive.  Our preferred chart and the Astro.com one.

We would if asked, go with the 1869 date as it shows his loyalty to his brother and a strong aspect to the Galactic Center. We supplied the KO for August 22 1913 as that chart is quite remarkable, post the opposition and yod point to the Midheaven with Pluto and Neptune in semi-sextile aspect.