Thursday, May 21, 2009

Wheels within wheels

Wronski's prognometer - a mathematical oracle


I read about Jozef Hoëné Wronski in the first issue of Les Cahiers de l'Institut (2008), a French magazine dedicated to my favourite subject, the Fous littéraires or litterary insanity - sometimes called kooks. It strikes me how in the drawing by Felix Valotton below he looks like Baudelaire!


It seems Wronski (born Hoëné, 1778-1853) was and still is considered not only a respected metaphysician in Poland, but a respected mathematician, lawyer, physicist and inventor as well. Outside of Poland however generally he is considered completely bonkers. He joined general Kosciuszko in his fight for Polish independance in 1794. They were taken prisoner by the Russians who committed a massacre amongst the population of Warsaw. At age 22, after an early succesful but forced career in the Russian army he started to conceive the idea of a global philosophy. At 32 he moved to Paris and remained there until his death, writing exclusively in French, publishing over 100 books sometimes as Hoëné, sometimes under his nom de plume Wronski but usually as Hoëné Wronski (without a first name) and left even more manuscripts. He studied Kant but Jacob Boehme as well and was familiar with Gnostic and caballistic teachings. He took upon him to reform not only philosophy, but economics, law, psychology and music - in short, he wanted to offer a complete paradigm shift to human knowledge.

After joining the team of the astronomic observatory in Marseille in 1803 he developped a complex theory concerning the structure of the universe. He started to send letters to reputed scientists of his day, many of whom replied. The main base of his theory was of Pythagorean nature, seeing numbers as the essence of life, the universe and everything. He published his results, which were generally dismissed as total rubbish, yet some honorable scientists gave him favorable reviews. More and more he developped an arrogant, paranoid personality. From then on he wanted to apply philosophy to mathematics. In 1809 he made plans to develop a device to determine longitude at sea, but his address "'On the Longitude" to England's Board of Longitude was deemed too philosophical. The Board was unconvinced. Later on he tried to appeal to the Royal Society concerning the value his theories on hydrodynamics to no effect. Both attempts ended in vigorous arguments, one of his hallmarks. In 1812 he wrote "'Résolution générale des équations de tous degrés" claiming to show that every equation had an algebraic solution hereby contradicting Paolo Ruffini's proof (the latter is nowadays accepted). In 1818 Wronski started giving metaphysical lessons to Pierre Arson, a rather naive banker who wanted to learn "'the Absolute" which Wronski claimed to have discovered, as the "knowledge of truth reached through the human reason". At the end of the course, Wronski asked for a tantalous 200.000 francs. The banker refused to pay, Wronski went to the courts and lost. He was ruined but unimpressed. Strangely during the trials Arson was approached by a secret society. He never could make sense of their relationship with Wronski, but later on some thought they were either French Martinists or members of a Polish Saturnian lodge. In 1821 he developed the "Universal Hoëné-Wronski series" in mathematics. Actually after he brought forth his "highest law", giving a general rule to calculate a series of coefficients, these were officially renamed "Wronskians" in mathematics. Starting from 1822 he lost his remaining marbles, with attempts to build a perpetual motion machine, to square the circle and especially he started the construction of a machine to determine the future, which he named the Prognometer. In 1827 he published his "Canons de logarithmes", offering in six compact pages all the common logarithms structured in tables. This might be considered the first attempt at an universal calculator. From 1830 on he had started to imagine several steam-driven vehicles dubbed 'dromads' to compete with the railways which he hated. His Dynamogenic System allowed the engine to dispense with the use of rails. None of these engines were manufactured although at one point he could have become rich had he kept the rights on his railed prototype for the Messageries Générales de France. Somehow he considered it his duty to publish all technical specifications to the engine so the company had no need for him anymore. At the same time he started to consider himself an apostle of Messianism and wrote several books on the subject. In 1837 he introduced mysticism in politics, with his book "the secret politics of Napoleon as the starting point for a world morality". The last three years of Wronski's life were spent in total misery, putting all his remaining energy into initiating a young man named Alphonse-Louis Constant whom he introduced to the world of mathematics and the occult philosophy. Soon the young man would take the alias Eliphas Levi and would become one of the most famous caballists of the 19th century.

Wronski maintained that the goal of man was to become god-like and veiled his ideas under occult layers of mathematics. Because of the complexity of his writings, using mathematical expressions to develop metaphysical ideas, his thoughts often are very hard to understand. But as excentric as he might have been, Wronski never gave up searching and a few of his mathematical ideas are considered nowadays quite valuable. Another important theory of Wronski was that "man could create reality from the total of the impressions of his senses", which seems a very sane statement to this Maybe Logician. The following words are written on his grave (in French): The search of truth is a testimony to the possibility of finding it.

The Prognometer, an infinity probability drive?

Only one prognometer or prognoscope was built. Wronski trusted his secret only to Marquis Sarrazin de Momferrier, whose son-in-law claimed to be the last grandmaster of the Templars. It was bought long after Wronski's death in 1873 in a junk shop by his pupil Eliphas Lévi, who wrote that Wronski "dared to involve himself with inventions, he constructed mathematical machines, revolving axes which were put together in an admirable fashion. But his machines would not work because the copper and bronze of his devices won't acknowledge the truth of his philosophies... His most fevered and most kept investigation was the invention of a divinating machine, also called prognoscope, that calculated all probabilities and drafted equations of all occurrences that had happened in the past, happened now and would happen in the future, in order to establish all possible values." At the base of the prognometer was the desire to find a way to calculate all probabilties and as such, predict certain trends in the history of mankind. Levi: "Nobody saw the design of his machine, but he let the workmen construct the machine in bits and pieces, and being a bit of a mechanic, put the parts together himself". Actually Levi had believed the inventor had dismantled all his machines to sell their copper, and was extremely excited by his discovery. According to his description, it consisted of two metallic globes revolving around a cercle in which small boxes contained, hand-written by Wronski, the principles of all sciences. Structured according to their analogy, the mathematical representation of the same sciences is drawn on a larger, central sphere that can turn around on two axes. It looks a bit like a representation of a planet with two moons circling around it. On one of the smaller globes there's a pyramid (the divine knowledge), on the other a pyramid topped by a hexagram (the human knowledge), turning together but always opposed. Levi: "Man might tour the totality of sciences, he'll never meet god who is always hidden by the central globe, the thickness of all knowledge. At the same time god provides man with balance even in his largest errors".
The god-sphere could be opened and inside was written "All that must be has been, is and will be". Surrounding this globe were four letters in copper, A, B, X and Z, according to Levi equivalent of Yod, He, Vau and He, and two animated metallic arms showing "the proportion of what is above compared to what is below".


The sphere of human knowledge showed the sign of Salomon on top of the pyramid. Towards the central sphere a pentagram is pointed "as a symbol of human autonomy".


When Levi touched the large central globe, "the globe made out of bismuth opened itself and revealed on the inside another globe that was also covered with mathematical equations". Both could revolve both around the horizontal and the vertical axe. The central wheel showed all the astrological signs and was divided into 32 little boxes. On the outside of every little door was written the name of three sciences and inside the boxes were written the fundamental axiomas for each and every one them. A looking glass was needed to be able to read those. Still according to Levi, two sentences were written on the side of the circle: "All sciences are the degrees of a circle revolving on the same axe" and "The future is in the past, but not entirely into the present". The following drawing is by Levi:


Levi died two years after his discovery. The above etching is the only original image of the Prognometer. No one knows what happened to the device.

In 1906 hermeticist Alexandre de Saint-Yves d'Alveydre (1842-1909), famous for being the first westerner to write about the realm of Agartha and to become the teacher of Papus, constructed his own version based on Wronski's design, the Archeometer. This one was even patented.


In 1903 he had written a 500-page book " L'Archéometre, Clef De Toutes Les Religions et De Toutes Les Sciences De L'Antiquité" describing its functioning. On this disk were shown correspondences between numbers, letters, colors and musical notes, the signs of the zodiac and of the planets. Also included was the author's own metric system comparable to J.W. Keely's musical charts below, destined to reform sonometry.




Piotr Pragacz, Notes on the life and work of Jozef Maria Hoene-Wronski

Le prognomètre de Wronski

Theos talk archives

Jean Prieur: "L'Europe des médiums et des initiés"

Hoëné Wronski: "Pétition aux deux chambres législatives de France sur la barbarie des chemins de fer et sur la réforme scientifique de la locomotion"

Three complete books by Wronski (in French) on the Internet Archive:

Hoëné Wronski: "Secret politique de Napoléon, comme base de l'avenir moral du monde"

Hoëné Wronski: "Philosophie absolue de l'histoire; ou, Genèse de l'humanité" Hoëné Wronski: "Nouveaux systèmes de machines à vapeur fondés sur la découverte des vraies lois des forces"

Arkologie fondamentale #19 (1999), pp 6-10

Paul Chacornac: "Eliphas Levi, Renovateur De L'Occultisme en France", 1926

Francesco Lamendola: "Wronski e il Messianismo"

Desiderio Valacco: "From Zarathustra to Ken Wilber. Lives and works of prominent mystical philosophers"

Thursday, May 07, 2009

Cats and curiosity

At my previous dwelling I had used plastic film to cover the windows from  curious passers-by. I had cut holes through to permit my five cats to look outside. The holes up front had the form of three huge cats,  at the side  they looked like books with cat eyes or paws and at the back I had cut out small spirals for myself to look outside.

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