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P. Svarogich

(English editing by Ed Falis)

Principia of polyzodiacal astrology

1. Introduction. History of astrology and medieval primary sources.
Astrology as a knowledge system.
1.1 The age of modern astrological tradition.
1.2 Development of the conceptual framework and calculating algorithms of medieval astrology.
1.3 Astrology in 20th century.
1.4 The conceptual framework of astrology and natural science principles of thinking.

Man has long been interested in the order of the universe and in the place of human beings within that order. A longing for a knowledge, exact knowledge is perhaps the most distinctive characteristic of the human species. Namely cosmogonic hypotheses were among the first significant human descriptions of the surrounding world. Many such systems eventually froze in their development and became systems of doctrine, eventually transforming into religious systems. Such ideologies no doubt met certain human needs for a stable context in which to conduct societal activities. In spite of this tendency, certain communities of people, fulfilling a role similar to that of the modern scientific community, continued to study and develop conceptual frameworks for understanding the world.

In any sufficiently rich and formalized conceptual system it is always possible to find statement that is impossible to prove or disprove within its set of assumptions 1). This characteristic of formal systems guarantees that no definitive and exhaustive description of the universal order can be attained. The Universe, Nature, God is always a developing and self-enriching essence. Not only does our knowledge of the Universe evolve, develop and become more profound, but the Universe itself does as well. We do well to consider the Universe as the development and realization of the divine idea. In the Gospel of John, God is identified with Logos (Greek l o g o V ), a term which is clearly a conceptual framework for the Universe as it is used in the original of that text in ancient Greek.

Among the oldest known doctrines are the Gnostic writings, which are fairly criticized by both modern Christian historians and the ancient representatives of official theology [1]. The ancient Gnostic schemes known today can hardly cause other sensations than of dying or of impending doom. However alongside the dead Gnostic schemes, another form of living and developing knowledge of the Universal order (or God) existed from extreme antiquity – known to us under the name of astrology. The most prominent quality of astrology is its dialecticalness, as its main object of study is time and the qualitative changes of divine creations with time. The structure and essence of the time, the fundamental difference of one moment of time from another, is the main object of astrological study.

The core of astrology is not its calculations or techniques, but its symbolism, the laws and structure of which permeate the world and form the backbone of the Universe. This symbolism allows us to see intrinsic relationships among phenomena based upon their symbolic unity.

Astrology also highlights how the future crystallizes within the past. Our ability to forecast the short-term future that is the scope of a human life, its dynamics, its fullness of events of universal importance or of personal character illustrates of the existence of the future as a seed within the times at which the planets were just being formed. Astrological calculations based on the motions of the planets are in fact “counting sticks” by which we learn the divine idea of which our Universe is woven. In assimilating the rhythms of this weaving, we form inside ourselves the spark of the divine consciousness, becoming like God.

The particular value and distinctiveness of astrology among systems of human knowledge is that the astrological "counting sticks" allow us to most profoundly understand this divine idea of our Universe. Perhaps this is the real reason astrology is the most ancient system of the human knowledge. As the author of this work supposes that we are all doomed (or blessed) to eternal life in this inconceivably old and young, beautiful and horrible world, rather than in some paradise or Hades, the best thing we can do is to penetrate as deeply as possible into God’s idea. We can become active parties in the creative work that is continually taking place in our sight. So, although forecasting and analysing events is not the primary task of astrology, it is one of the best ways on the human plane of evolution to recognize and to integrate the divine idea.

The 20th century is the age of the revival of astrology as a system of exact knowledge. Astrology has been reborn with a substantially changed appearance. It has gained a more humanistic, even humanitarian, nature. To a considerable extent it was revitalized as a conceptual basis of psychology. Some of the outstanding psychologists of 20th century (e.g. Carl Gustav Jung) have found that its notional system for describing human consciousness is very close to the structure of astrological symbolism. The majority of prominent astrologers of the 20th century (e.g. Dane Rudhyar) have been representatives of its psychological branch.

New names have even been invented for astrology such as astrosophy, astropsychology, cosmobiology and so on. Certainly, these names reflect the interests of people using the astrological notional structure and its methods of calculation in their activities. But the use of such euphemistic names in place of “astrology” shows not only the widespread intolerance of astrology, but also the sheer affront that the existence of such a system of knowledge offers to certain powerful communities in the modern world. The Christian fundamentalist communities are a prominent example.

This situation reflects the significant degree of dogmatism in religious doctrines and the drift of religious world-views as forms of knowledge toward becoming the empty shards of their formerly vital engagement with the universal order. The largest astrological organization in the USA carries the faint-hearted and ambiguous name “The National Council for Geocosmic Research”2).

It is quite possible, that the growing influence and authority of the Catholic Church in the 16th and 17th centuries was a contributor to the decline of medieval astrology. Nicholas Campion3) considers that the "denouncement" of astrology by Saint Augustine, one of the most authoritative church fathers, had a significant negative impact on the development of astrology and brought serious problems to the astrologers of Christian Europe [2]. Still, astrology had not completely disappeared; it continued to exist into the 18th and 19th centuries in a form similar to fortune telling. This period left an imprint of charlatanry on astrology, and led to a “cookbook” form of practice. Astrology still has not completely recovered from this heritage of its own "Dark Ages”.

In the 20th century, not only has astrological symbolism been rehabilitated: the methods of astrological calculations as an exact knowledge have also been restored. One of the outstanding figures in the astrology of the 20th century was Alfred Witte (2 March 1878 - 2 August 1941) [3]. While not all the techniques of his “Uranian” school are indisputable, his development of Kepler’s method of discrete symmetries (planetary pictures), his use of zodiacal harmonics, and his simultaneous use of multiple equal house divisions as facets of interpretation, have had a significant effect on the development of astrology, and will continue to do so for the foreseeable future. The second major event in the astrology of the 20th century was the development (or perhaps rediscovery) of the “Topocentric” method of domification as a natural successor to Placidus domification. The Topocentric method was made possible by enhancements to the accuracy and precision of astronomical calculations [4,5].

It is regrettable that astrology as an exact science is unknown not only to the mass of the educated public, but also to the majority of professional astrologers.

Unlike the majority of modern sciences, the history of astrology comprises many centuries. The full reclamation of the achievements and discoveries of medieval and ancient astrologers is impossible without the most attentive study of the history of astrology as it interacts with general history. Among existing disciplines only theology and history compete with astrology in age. But theology discredited itself with dogmatism not only in the view of 20th century intellectuals, but much earlier - in the 18th and 19th centuries. This fact was even reflected in some European languages such as French and Italian (e.g. compare the meaning of words teoretico and teorico in Italian).

At the same time, the discipline of historical study has too often been used as a tool for political domination. Authorities have never been interested in broad (and overdue) revisions to its methods and conclusions. Each generation of politicians has preferred to not touch what their predecessors have done, and has merely modified interpretations of historical periods to suit their own ideological needs. Furthermore the scholastic tradition in science that appeared during the Renaissance perniciously influenced many scientific disciplines for several centuries. Only the physical sciences have completely overcome its influence. Even biology has not completely freed itself from the scholastic tradition.

1.1 The age of modern astrological tradition.

The traditional and generally accepted opinion is that the names of the zodiacal signs are approximately two thousand years old. This dating is calculated from the value of the precession of the equinox of 50" of ecliptic longitude per year and that the signs of the tropical zodiac, representing the 30º sectors of the ecliptic as measured from the vernal equinoctial point, have taken their names from the corresponding constellations superimposed on them at that time and have gone from them by 30°. We can assert with confidence that the existence of the 12-fold division of the ecliptic, together with the widely used names of the zodiacal signs, is a sufficient proof of the age of the fundamental notional system of astrology, despite the loss of this original system.

m a q h m a t i k h s u n t a x i V (i.e. The Mathematical Systematic Treatise), known under the name of the Almagest and ascribed to the ancient astronomer Claudius Ptolemaius from Alexandria, is considered a second proof of the ancient origin of astrology. The "Mathematical Treatise in Four Books", known as the Tetrabiblos (t e t r a b i b l o V ) [6], is also ascribed to Ptolemy. The generally accepted belief in the existence of a developed astrological knowledge system in antiquity is founded on the dating of the Tetrabiblos consistent with the author’s life and with the dating4) of the Almagest.

Almagest is a collection of 13 books of astronomical contents, including the results of astronomical observations. It is alleged that the period of the astronomical observations included in Almagest corresponds to 127-141 CE (or AD – anno domini in latin medieval tradition). These figures are the rationale for dating the writing of the Almagest in the 2nd century CE. However, a modern mathematical analysis of the astronomical observations of the Almagest, carried out by the well-known 20th century astronomer Robert Newton, caused him to conclude that the Almagest was composed in some other epoch. Robert Newton even published the book The Crime of Claudius Ptolemy, in which he attempted to prove that the data of the stellar catalogue was forged and that it was actually the result of recalculation [7].

The astronomical observations of Ptolemy were independently analysed by the Russian mathematician A.T. Fomenko5) and his co-authors [8]. Let us sketch their results. First, the astronomical stellar catalogue of Almagest is a copy of the catalogue of Hipparchus, the ancient Greek astronomer from Rhodes. The traditional chronology places the life of Hipparchus in the 2nd century BCE. Second, the stellar catalogue of Almagest could only have been created over the interval from the 7th through 13th centuries CE. Moreover the most probable time of its creation is the 10th or 11th century. This dating is consistent with the new version of the universal chronology, presented in the works of A.T. Fomenko and his co-workers [9]. From this standpoint Ptolemy was no fraud: he simply lived more than a thousand years later (13th or 14th century) than is accepted in the traditional chronology. But what are we to make of the displacement of the zodiacal signs relative to the corresponding constellations as given in Almagest? The history of the first printed editions of Almagest shed light on this question.

The first edition of Tetrabiblos was printed in Nürnberg in 1535 CE [6] in Greek, but it contained the Latin translation as well. The first edition of Almagest was printed 2 years later in 1537 CE in Cologne in Latin (“Nunc primum edita, Interprete Georgio Trapeuzuntio”) with stellar coordinates given for 16th century. The Albrecht Durer engravings of constellation pictures used within the text to locate stars in the catalogue have original inscriptions dating them at 1515 CE. Therefore, the stellar catalogue description appeared after 1515 CE6). Some of the constellations — Ara and Pegasus - can be seen inverted from their normal appearance in the sky of the northern hemisphere. This absurdity seriously disturbed the medieval astronomers, including Coppernic (1473-1543). Therefore, Durer must have considered his drawings of the constellations only as works of art; he did not even bother to verify how these constellations were seen in the sky. Succeeding editions, including the edition in Greek from Basel (1538), nowadays considered as "original", contain the stellar coordinates in which ecliptic longitudes correspond to those of the 2nd century CE. Perhaps the publisher of the Latin edition was alerted to the discrepancy between the stellar coordinates in the catalogue and the dating of the of Ptolemy’s life; he "corrected" the discrepancy in later editions by shifting the ecliptic longitudes of stars by 20º exactly7). Exactly thus located zodiacal signs (relative to the equinox of the 2nd century CE) could give matching names to the corresponding areas of the starry sky. These collected facts force us to question the approach of the so-called Age of Aquarius. Besides, from our standpoint the zodiac itself and the notion of the equinoctial point as a crossing point of the ecliptic and the celestial equator gives no basis in favour of this generally accepted opinion.

If we reject the legends about astrologers of antiquity of the same ilk as the story about Nectanebus, the astrologer of Philip of Macedonia, who had predicted the birth of Alexander the Great (and who could actually be the father of Alexander), we have then no other reliable material in hand beyond the treatises of the medieval astrologers (astronomers8)), dated not earlier than the 14th century, and Almagest, whose author lived in 13th or 14th century. The dating of the life of Campanus (1239 CE–1296 CE), the author of one of the oldest house systems, is also questionable. It is possible that he lived even before the author of Almagest9). We had no opportunity to get acquainted with Ptolemy’s treatises using the first editions of the 15th century. Judging from the numerous works of later medieval astrologers, devoted to the interpretation and explanation of his methods of astrological calculations, we surmise an absence of clarity and completeness in the description of these techniques as they are presented in his works. In the opinion of one of the most famous French astrologers of 20th century, Alexandre Volguine, the astrological part of Ptolemy’s heritage (Tetrabiblos) is a compilation presenting to the reader three different approaches without stating the author’s position [10]. But this could be caused by the peculiarities of the Tetrabiblos languages, Greek and Latin, as synthetic archaic languages. In our opinion, these languages require not phrasal but block perception of the text. This peculiarity increases the probability of its incorrect interpretation. This may happen either as a consequence of the ancient languages’ evolutions, or due to mistakes in transcription and translation. Without a first-hand acquaintance with the primary sources we do not dare to make even a preliminary judgment on this.

Here it is necessary to note a very interesting characteristic of the stellar catalogue of Almagest [8]. The list of stars and constellations in the catalogue begins from the elevated pole of the celestial equator. This gives grounds to suppose that the measurements in the initial catalogue were carried out in equatorial coordinates, which are much more suitable from the standpoint of measurement technology. The conversion to ecliptic coordinates occurred after the catalogue’s creation. The catalogue begins with a Ursae Minoris, the North Star. But this star came to be nearest to the elevated pole only in the 9th century CE. Before this time, the nearest star to the elevated pole was b Ursae Minoris. Thus, having begun from the North Star, the compiler of the Hipparchus-Ptolemy catalogue has signed out the epoch of his own observations - approximately the 9th century CE or later. This remark is not principal for the dating of Ptolemy’s catalogue. However it allows us to assume the time of creation of its more ancient prototype.

1.2 Development of the conceptual framework and calculating algorithms of medieval astrology.

"Since the moment that the manuscript of Tolomeo made its debut in the world of astrology, many were the people who tried to understand the mysterious directional technique of the grand maestro but who did not arrive at the true result." [11]. It is not an exaggeration to say that the attempt to understand the true techniques of Ptolemy was the leitmotif of most astrological treatises of the 15th through 17th centuries.

Prior to reviewing the history of the development of the ideas and calculation methods of medieval European astrology, we wish to beg the pardon of the reader for the inexactness, even the associativity of what we write on this subject. We have restricted ourselves to our own highly immature version of the development of only European astrology (plus Egypt). This is more a glimpse than a history, and is given only to place the current work into the context of the development of astrological ideas. We have not encountered well-documented versions of the history of the eastern (Chinese and Indian) astrologies in European languages, though we are aware for instance that the Chinese Academy of Sciences has conducted such studies for many years. Even the references to the articles in Chinese are known. With the history of Arabic astrology the situation is much better: the medieval primary sources are known in sufficient detail and quantity. But the familiarity of the author with the history of astrology in the Arab countries is restricted for several reasons. First among these is his ignorance of Arabic language. The experience of working with the primary sources in Latin and Greek demonstrates the necessity of this condition for true understanding of the material. Any translation is fit only for a quick overview and orientation to the material. Second, many Arabic primary sources need to be re-dated. Third, many Arabic archives and documents are not open for use by non-Moslems. Without overcoming these obstacles it is difficult to construct a reasonable picture. Finally, since the purpose of this work is not to present a history of astrology, no attempt has been made to be comprehensive. The medieval methods are used mainly to validate the concept of pinpoint accuracy calculations according to the principle of correspondence.

We note with regret that, unlike in the conventional sciences, even serious researchers of astrological concepts, methods and history rarely make exact references to their sources. We have to take on trust a number of statements on the history of medieval astrology from the publications we cite here. This may have led to mistakes in the following review of the medieval history of European astrology. We hope that eventually we will have a chance using primary sources to verify all facts posited here. The situation with astrological information in our country, as well as throughout the world, arouses our pity and vexation. Many libraries do not subscribe to astrological journals and books. We hope that in the future the traditions of the British Museum’s library and the US Library of Congress — to subscribe to practically all that is published in the world, regardless of ideology — will be supported by the largest Russian libraries, including the Russian state library and the library of the Russian Academy of Sciences.

A small problem in identifying medieval authors is the transliteration of names from national languages to Latin, Greek and Arabic in citations. Most likely, this has not caused problems, but mistakes are possible.

The oldest known system of domification is that of Campanus (Campanus in Latin and Campano in Italian). It is generally agreed that he was a personal astrologer of the Pope and lived from 1239 to 1296 CE. The geometry of the Campanus system of houses gives grounds to believe that it preceded and was an influence on the development of the Regiomontanus system of houses.

The German astrologer Königsberger (Regiomontanus in Latin), known in the history of astronomy under his real name of Johann Muller (1436-1475 CE), developed the house system known by his pseudonym. It is believed [11] that Muller and his contemporaries were certain that this system of houses was used in the calculations described in Tetrabiblos. William Lilly used this system in horary astrology and for primary directions, although he did use other domification methods.

Francesco Giuntini (Junctinus in Latin), the famous Florentine astrologer of the 16th century, also used the Regiomontanus system. He was the author of the treatise "Speculum Astrologiae" [11]. He could not have known the house system carrying the name of Ptolemy (Placidus) since it was not published until 1604 CE by the mathematician from Padova, Giovanni Luciano Magini (Antonius Maginus in Latin10)) under the title translated to English as The Second Measure of Time [12]. It is agreed that the method of Regiomontanus was spatial, but that the method of Ptolemy as interpreted by Maginus was temporal. William Lilly mentioned in his book [13] that a part of the work published by him was based on the treatises and utterances of the famous Tycho Brahe (1546–1601 CE).

Once Placidus de Titi (1606-1668 CE) had used the Ptolemaic system of houses to formulate his new, very exact system of equatorial directions, known in 20th century under the name of “mundane directions of Ptolemy-Placidus” (or “Placidean mundane primary directions”), the majority of astrologers moved to the use of the Ptolemaic domification in its Maginus variant. Now this domification is known as the Placidus domification. The Regiomontanus system of houses leads to significant mistakes in astrological calculations, as noted by Johannes Kepler (1571-1630 CE), the pupil of Tycho Brahe. It is believed that it was for this reason that he rejected the use of houses in astrological calculations. The Regiomontanus system of houses persisted as the most common system of domification up to the end of the 16th century, then almost immediately gave way to the much more exact system of Placidus.

1.3 Astrology in 20th century.

This concludes our overview of the history of European medieval astrology. The Placidus domification and the equatorial directions of Ptolemy-Placidus remained the most exact methods of calculation in the astrology of events until the middle of the 20th century. The development of astronomical calculation methods, the augmentation of accuracy in ephemeris calculations following the discovery by Kepler of his three laws of planetary motion, and later by Newton (and/or by Hooke (1635-1703 CE)) of the laws of gravity has gone apace, but astrology came to a standstill in its evolution for three centuries11). It is necessary to note that there were purely astronomical reasons for this standstill. Formulation of an exact system of astronomical calculations was accomplished only at the beginning of the 20th century in the works of the outstanding American astronomer Newcomb (1835-1909 CE). This formulation permits further development of astrological computing methods and an increase in their accuracy.

"Charlatanry is not only a modern phenomenon,” noted Alexandre Volguine when speaking about texts on astrology and citing an ancient manuscript as an example [10]. We really are more familiar with the charlatanry of our own century. This phenomenon occurs not only in astrology, but in the natural sciences as well. The specific form of charlatanry in the astrology of the 20th century is the invention of a new house system. Altogether there are dozens of house systems. When attempting to understand the underlying geometry of various house systems, we usually find that they have no geometry at all, only an algorithm of obscure origin with an undesignated scope of applicability. Notice here that the house systems we’ve inherited from past centuries all have well-described and comprehensible geometries. Their formulae are secondary and can be derived by any competent mathematician from a description of the geometry. Among the house systems that have appeared in the 20th century, only three have a real geometry: Topocentric, Koch and that of local space.

In the early sixties Koch invented a system of houses [14] that his astrological colleagues have "perfected" by simplification of its calculations [15]. Note that some computer programs compute something different under the name of Koch house cusps. From here on, we will only discuss the Placidus and Topocentric systems.

As mentioned earlier in this work, astrologers tend to lump together distinct concepts under the notion of house system. There are at least two conceptually different constructs indicated by the term “houses”. The first is the collection of Equal House Systems, derived by equal division of the ecliptic. One can use several of these in the analysis of a single chart. These systems are most logically and systematically treated in the Uranian astrology of Witte [3]. It uses sectors of 30° on the ecliptic, starting from the Sun, Moon, MC, Ascendant and other points. Each set of divisions corresponds to a different facet in interpretation. Quadrant (or “unequal”) house systems are constructs of a fundamentally different nature. We also call them systems of domification. In these systems we assign to points on the celestial sphere a longitudinal coordinate, independent of time, in the first equatorial system of astronomical coordinates12) [16]. This mapping is performed in a manner such that the longitudinal coordinate for a point exactly on the celestial equator coincides with its usual uniform angular measure on the equator (i.e. the difference of its right ascension, expressed in degrees, from some predetermined starting point)13). There can only be one such mapping that is correct, just as 2× 2 = 4, and not 3 or 5, depending on the result we seek in order to fit to our preconceptions. Once such a parameterization of the celestial sphere has been determined, we can vary the reference point in a manner similar to that used on the ecliptic in the Uranian techniques.

We did not check whether points such as the Vertex or Antivertex, which are held to be similar to the ascendant and descendant, are effective in astrological forecasting. We surmise that it is possible to introduce another 10 points, complementing the Vertex or Antivertex to a 12-fold division along the prime vertical. However it is not necessary to treat such a partitioning as a house system, since it is yet another completely different construct. The use of the same name to designate it can only increase the terminological mess.

We restrict the term domification to those systems providing a parameterisation of the celestial sphere, independent of time, in the first equatorial system of coordinates and connected with the celestial equator. This is the notion of houses that has its basis in medieval astrological tradition. If the systems of Koch and of local space as 12-fold divisions of the ecliptic are really effective, they are still not house systems in the traditional medieval sense.

With Newcomb’s formulation of the system of astronomical calculations at the beginning of the 20th century, it became possible to advance the accuracy of astrological forecasting techniques. In the early sixties a series of articles appeared in the journal Spica, describing the so-called Topocentric domification [4,5]. It is interesting that the authors understand their system as a house system in the traditional medieval (Ptolemaic) sense: they determine both the house cusps and each planet’s coordinate within the houses. The geometry (reconstructed by the author of the present work according to one of the formulae of the Topocentric system) of this system is uncommonly elegant. It is a natural development of the Regiomontanus domification. But the positions of the house cusps on the ecliptic, and of the planets within houses, are very close to the corresponding positions under the Placidus system. If we consider the positions of the Topocentric house cusps to be the best approximation, given present-day accuracy, to the true geometry that mediates the triggering of events in our world, then the calculation errors of the Placidus method do not exceed 20' even at the latitude of Moscow. In this system, the mathematical and geometric elegance of Regiomontanus has been harmoniously combined with the practical accuracy of Placidus.

Unfortunately the Spica articles describing the system are full of ambiguities and do not contain a description of its underlying geometry. The articles give only some practical formulae for the calculation of the positions of the house cusps on the ecliptic and of the positions of the planets in houses. The declared accuracy of calculations in this system was stated to be 3' – 5'. This is so, as the formula for the positions of the planets in houses is indeed approximate; if it is taken as exact, it actually contradicts the formula for calculation of the house cusps on the ecliptic. The error of the approximation compared with the exact formula (which is consistent with the algorithm for house cusp calculation) is about 5' at middle latitudes.

Furthermore, their algorithm for application of the system within the circumpolar regions is unfortunately absent from the articles. This algorithm, known to the authors but omitted in the articles, is most likely incorrect. There is no description of the algorithm in the articles, but there is mention of the characteristics of its results. The author of the present work has performed a mathematically accurate reconstruction of the geometry of this domification, based on the Topocentric cusp positions on the ecliptic. The exact formula for the calculation of a planet’s position in the houses has been obtained, and the analytical extension of the house system geometry into the circumpolar regions has been constructed. The characteristics of the reconstructed geometry within the Polar circle are radically different from those of the Topocentric domification in the Spica articles. Their confusion of an approximate formula for planetary positions, and its inconsistency with the formula for cusp determination, leads us to doubt the mathematical competence of the authors of these articles. However, as a first approximation adequate for practical calculation without a computer, this formula demonstrates a good understanding of the geometries of both the new house system and of the Placidus system. It also shows the high competence of a man who derived it. We suggest that the reader should make his own conclusion as to the possible reasons for this ambiguous situation.

This situation has compelled the author of the present work, in order to avoid misunderstanding, to use a different name for the house system reconstructed on the basis of the cusp formula of the Topocentric domification. We propose to name it the Zodiacal house system. One of the main tasks of the present work is to provide an accurate mathematical description of the characteristics of the Zodiacal house system, and to derive the formulae for practical calculations. The word Zodiacal has not been chosen lightly. From our standpoint the houses are the result of the accurate projection of one zodiac onto another. The geometry and formulae derived below are a consequence of this conceptual orientation to domification. In the perspective of this work, the generally accepted notion of houses is a projection of the terrestrial (earth) zodiac into the solar (conventional) zodiac.

1.4 The conceptual framework of astrology and natural science principles of thinking.

The main task we have put before ourselves is to reformulate both astrological calculations and the concepts upon which they are based in accordance with the notional systems of the physical sciences of the 20th century.

The phenomenologicalness (i.e. the absence of a physical basis for its rules) of modern astrology is its essential and as yet insurmountable defect. This defect cannot be considered grave: physics itself does not answer the question "why"; it only describes "how". When we find an answer to the question "why", physics transforms into mathematics. It is agreed that we know why 2·2 = 4. In this sense, the general theory of relativity, correctly named geometrodynamics, is the mathematics describing the spacetime of the world. Newton’s law of gravitation, on the other hand, was physics. Since geometrodynamics is no longer physics, but the mathematics of spacetime, it is necessary for consistency to describe all phenomena occurring in space and time in accordance with its conceptual basis14). Here we have in mind not the relativistic laws of coordinate transformation, nor the curvature of space, nor Einstein’s equations, but the basic notional system underlying the language in which these concepts are expressed15).

In order to achieve this goal, we first need to articulate a fundamental principle, in accordance with which astrological laws manifest in the Universe. We need to clearly understand the nature of the phenomena represented by astrology. Holistic philosophy provides the best language in which to examine this question.

In holistic philosophy the world comprises different wholes interacting with each other, coming into existence and passing away in the course of their interaction. Furthermore a whole is an ideal object. In some sense, real objects cannot exist in time. The moving hand of a clock exists only as an abstraction, though it allows us "to measure time". For the purpose of measuring time we treat it as a certain kind of abstracted or ideal object, whose spatial attitude changes with respect to the face of the clock. Such a clock hand described to an accuracy of one atom does not exist as such: it is impossible to determine a discrete boundary between it and the surrounding world. However, the fact that we manage to perceive the clock hand as a whole, and to use its changing attitude relative to another whole to measure time, shows that this ideal object is real.

Since wholes are born, persist and die in time, it is possible to treat time as an internal measure of wholeness. It is interesting that while the clock hand dies on one level of abstraction and becomes a different whole when a piece breaks off, on another level it continues as a whole that can be used to measure time. In other words, several wholes manifest or live within the same clock hand, each of which has its own lifetime. It’s no large leap to say that it is precisely its moments of birth and death that define and designate the specific whole with which we are dealing.

While time can be used as an internal measure of wholeness, space can assume an analogous role as an external measure - a measure of simultaneity. For the measurement of distance between two wholes it is necessary to have a metric – yet another whole.

From the standpoint of astrology an event is the death of one whole and the birth of another. An event occurs at a particular place and time, thus complying with the notion of event in the theory of relativity as a collection of spatial and temporal coordinates. For astrology, time and space cannot be continuous - they are like the set of rational numbers. In astrology two moments of time are distinguished by the wholes that are born or die within them. To emphasize this point in this perspective, if from one moment of time to another nothing has been born or died, then there is no third temporal point between the two16). Yet at the same time between them there exists a certain measure of continuous physical time. The same can be said about space. Note that one of the basic concepts for understanding space is the notion of simultaneity.

The closest scientific analogue to the astrological notion of event is the idea of catastrophe - a leap in a system’s state under continuous (smooth) variation of its parameters. In astrology, we understand an event as the same kind of discontinuous change: one whole at its death is transformed into another being birthed.

We are now ready to characterize astrology as a knowledge system:
Astrology is a science connecting the events taking place in the world with the motion of heavenly bodies.

When Einstein created geometrodynamics, his guiding philosophy was Mach’s principle [17]. Mach’s principle is extremely important in the interpretation of the Universal order. It reveals the deepest conceptual basis of the natural-scientific world-view. Einstein aspired to develop a theory in which Mach’s principle would be physically expressed. He did not achieve this, but the theory he constructed with its inspiration turned out to be true. Mach held that space is created by matter. But the "ether drag" by ordinary matter (e.g. the Earth) within the framework of geometrodynamics is extremely small: for the Earth the ratio of its size to its gravitational radius is approximately equal to 10–9. Mach’s principle also posits that long-range action, which is formally denied by modern science, lies at the base of modern physical concepts. All observed physical phenomena are described within the framework of a maximum speed of interaction propagation; but the notion of simultaneity is used as the interpretative basis of modern physical theories.

For our work Mach’s principle is very important because it puts a question of the theoretical necessity for the existence of long-range phenomena. Let us briefly formulate here the relevant argument. Let an astronaut fly in a rocket a sufficient distance from any significant accumulation of matter. If he ignites the engine, he feels an acceleration that presses him into the chair. Observing carefully, he notices that he feels a pressure when he moves with acceleration relative to the remote matter (i.e. he feels the influence of this matter on himself). Moreover this influence is a long-range phenomenon, since he feels the pressure immediately upon starting the engine, as though he were in the immediate vicinity of the accumulation of matter. This effect indicates that matter can act in some long-range way currently unknown to us. Einstein’s geometrodynamics imply that the Earth’s part in the formation of the space-time at the distance, equal to its size, is about 10–9.

In the 20th century many attempts have been made to explain astrological rules in terms of the known types of physical interactions. All of these attempts have failed. One can, of course, set one’s hopes on the discovery of an additional type of interaction. It seems to us, however, that the physical phenomenon lying at the base of astrology is not connected to either a particular type of interaction or to their joint effects. The responsible phenomenon could turn out to be long-range. It is interesting that the preliminary analysis of astrological observations performed on the basis of the concepts formulated in this work supports this opinion. That is to say: the planetary configurations causing one or another event are calculated for the time of a coming event without taking into account the effects of planetary and stellar aberration (i.e. without taking into account the finite velocity of interaction propagation — the velocity of light). This simultaneity is taken from the standpoint of the frame of reference of the native with whom the described event occurs.

A zodiacal circle, the main instrument in astrological calculation and interpretation, must be generated by a material body according to the above understanding of astrology. The conceptual object we call the Zodiac with a capital letter is the way to describe the astrological influences on surrounding wholes from the Sun. The relative dynamics of the Sun and a native, whose events we study, define its geometry.

The house cusps on the conventional zodiacal circle are projections of the zodiac generated by the Earth onto the solar zodiac. This sense of two “zodiacs” has been known from antiquity. Numerous attempts have been made to define the lunar zodiac (i.e. the zodiac generated by the Moon [18]). However no event calculations have been attempted with the resulting constructs.

We now understand how to describe the terrestrial and solar zodiacs in a unified way, using a common model and derivation despite the apparent differences in their geometries. Having developed this common model, we also know how to derive the zodiac of any massive heavenly body. It is clear a priori that the greater the distance of a body from the Earth, or the smaller its mass, the less effect it will have on the events of the native. From this standpoint, it seems necessary to derive and work with a properly constructed zodiac of the Moon, as it is the closest body to us after the Earth.

If we study the events taking place in a person’s life, we become inclined to think that the person’s spirit uses planetary configurations taken in the context of one or several zodiacs as potential turning points in his evolution. These opportunities are realized as events. When such events are frequently and obviously indicated in a given zodiac, we have more reason to use that zodiac in our calculations and interpretation.

From this perspective on time and events the astrologer’s stance toward each instant of time (epoch in astronomical terminology) becomes clear. Each instant of time differs from the next not quantitatively, but qualitatively, as characterized by the wholes that come into existence or pass away with it. Astrology is precisely the study of the qualitative description of each moment of time17).

The whole paradigm of astrology is built on the idea of the presence of the divine, ideal order in the material world. The Zodiac is a reification of the dialectical, evolutionary idea within the framework of the idealist Weltanschauung of the Universe. Even a materialist will not argue with the statement that the world is ordered by primary principles, fundamental laws of nature – what an idealist would name ideas, forms or eternal truths. Materialism only allows a certain degree of free will in its view of the world. Moreover, it admits free will only in the form of chaos, or as rebellion against the divine idea, rather than as a participation in the divine work. From the astrological perspective, order in the material world is no less harmonious and complete than in the ideal; the apparent chaos of the material world is merely an indicator of our own inability to grasp this order as it is manifested.

It is possible that the notion of causality can be understood more profoundly in the astrological perspective than within the framework of the modern natural-scientific Weltanschauung. The future continuously and inevitably crystallizes in the past; the closer the moment of an event, the less opportunity there is to change its character. The only way to exercise true free will, rather the illusion of it, is to foresee the possibilities of the future insofar as possible, and to become aware of the remote consequences of our actions.

It is important to note that one of the most difficult problems in all branches of the modern natural sciences is forecasting the evolution of long duration of a system. Attempts to solve this problem always seem to expose fundamental technical or conceptual difficulties. This comes as no surprise to the astrologer: permanent evolution is overwhelmingly determined by the laws of the spirit or Logos and is effected by means of material influences.

1. In mathematics this statement is known as Gödel’s Theorem.
2. Let us note here that the loss of a true name can be sufficient cause for the loss of the essence of an organization.
3. The president of the Astrological Association of England.
4. We mean dating based upon its astronomical catalogue.
5. Currently a member of the Russian Academy of Sciences.
6. The description of the stars’ positions in the sky, provided by the catalogue, uses small details of the constellation pictures in Durer’s engravings.
7. Furthermore, in the Basel edition, the declinations of the stars were corrected. This is connected with a more precise determination of the ecliptic position in the sky [8]. In other words, the publisher of the Almagest did not consider it as a relic of past, and it was updated to include the results of contemporary measurements.
8. We should note that before the 18th century, scientists were not divided into astronomers and astrologers; in Spanish dictionaries, it is even specified that in old texts under the word ‘astrologer’ it is necessary to understand an astronomer.
9. This is provided that Ptolemy really existed and was the author of the Almagest. As is well known, no biographic data on him exists.
10. Note that we are not confident that this is the same person.
11. This statement follows from the date of the publication of the Topocentric house system - the beginning of the 1960s. However, we cannot dismiss the feeling that the geometry of the Topocentric house system is much older and was elaborated 1-2 centuries before its publication by Vendel Polich and Nelson Page.
12. Throughout this work widely known astronomical notions are used without references (e.g. the first equatorial system of astronomical coordinates). The reader can find their definitions in any textbook on general astronomy.
13. Note that the oldest of the medieval systems — that of Campanus, satisfies the first requirement, but not second. The medieval astrologers after Campanus noticed that the house system must be naturally connected with the rotation of Earth around the Polar axis and consequently with the celestial equator. Campanus is a division of the prime vertical.
14. If our attempt here to describe the computing methods of astrology consistently with the notional system of the theory of general relativity has been successful, then astrology really has not "lagged behind" the other natural sciences. The International Astronomical Union only adopted the theory of general relativity as the conceptual basis of its measurements in 1992 (!).
15. Note that the accurate calculation of the space-like geodesic could be necessary in the situation of a conjunction of a planet with the Sun (superior conjunction for inferior planets), if the accuracy of calculations must be on the order of 1” or less. The accuracy of the system of calculations proposed in this work is not less than 10”. It is probably possible to improve the accuracy of these calculations by 1-2 orders of magnitude with no change to the conceptual basis. Current impediments to such improvement are discussed below.
16. Indeed, it is not a continuum, but a denumerable set. If we limit the denominator of the rational numbers we consider, as is done in astrology by a practical limitation of the harmonic numbers considered when using aspects, the situation of absence of a third point between two others divided by the finite interval becomes possible.
17. This is most obvious in horary astrology. The practice of horary astrology is the best way to learn to conceive the character of time.
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