The paper argues that the depiction of the Mediterranean coast of Africa in Ptolemy’s Geography was based on a source similar to the Stadiasmus of the Great Sea. Ptolemy’s and the Stadiasmus’ toponymy and distances between major points are mostly in good agreement. Ptolemy’s place names overlap with those of the Stadiasmus by 80%, and the total length of the coastline from Alexandria to Utica on Ptolemy’s map deviates from the Stadiasmus data by only 1% or (...) 1.5%. A number of serious disagreements between Ptolemy’s map and the Stadiasmus regarding the length of particular coastal stretches can be explained by assuming that Ptolemy had to tailor the distance data derived from periploi to his other sources, especially, to the longitudes of the key reference points, such as Cape Phyces, Cyrena, Berenica, Aesporis, Thena, and Carthage. A notable stretching and the subsequent contraction of the coast between Alexandria and Cyrenaica, as are exhibited by Ptolemy’s map relative to the Stadiasmus’ data, can be explained by assuming that several points on this coast were tied to the position of Crete, which was moved to the west being pushed by the westward shift of Rhodes. A sharp contraction of the two coastal stretches of the Great Sirte, oriented along the north-south direction, can be explained by Ptolemy’s erroneously underestimated value for the circumference of the Earth. The analysis of this contraction, as well as of the east-west stretching of the coast between Alexandria and Cyrene in angular terms relative to the modern map, makes it possible to assess the magnitude of Ptolemy’s error and to determine the length of his stade. This analysis shows that Ptolemy’s value for the circumference of the Earth must have been underestimated by approximately 20–27%, and Ptolemy’s stade must have been approximately 175–185 m length. Comparison of the Stadiasmus distance data with the modern map shows that the average length of the stade was close to 179 m or to the “common” stade of 185 m for the stretch between Alexandria and Berenice. (shrink)

The model of scientific revolution genesis and structure, extracted from Einstein’s revolution and described in author’s previous publications, is applied to the Copernican one . In the case of Einstein’s revolution I had argued that its cause consisted in the clash between the main classical physics scientific programmes: newtonian mechanics, maxwellian electrodynamics, classical thermodynamics and statistical mechanics. Analogously in the present paper it is argued that the Copernican revolution took place due to realization of the dualism between mathematical astronomy and (...) Aristotelian qualitative physics in Ptolemy’s cosmology and the corresponding efforts to eliminate it. The works of Copernicus, Galileo, Kepler and Newton were all the stages of the mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on divine phenomena. (shrink)

We present our Special and General Epigenetic Theories of Astrology based both on the most recent genetic research and on authors Cicero, Ptolemy, Sahl, Ezra, Morin, Selva, and Weiss. Key words: astrology; natal horoscope; epigenetics; genetics; DNA; methylation; environment; human development; thought experiment; determinism; free will; quantum indeterminacy; controlled variables; independent variable; dependent variable; general and special epigenetic theories of astrology.

Fermat’s Least Time Principle has a long history. World’s foremost academies of the day championed by their most prestigious philosophers competed for the glory and prestige that went with the solution of the refraction problem of light. The controversy, known as Descartes - Fermat controversy was due to the contradictory views held by Descartes and Fermat regarding the relative speeds of light in different media. Descartes with his mechanical philosophy insisted that every natural phenomenon must be explained by mechanical principles. (...) Fermat on the other hand insisted an end purpose for every motion. For example, least time of travel and not the least distance of travel is the end purpose for motion of light. This implied a thinking nature, which was rejected by Descartes. Surprisingly, with contradictory assumptions regarding the relative speeds of light in different media, both Descartes and Fermat came to the same result that the ratio of sines of angles of incidence and refraction is a constant. Fermat’s result came to be known as the ‘Fermat’s least time principle’. We show in this article that Fermat’s least time principle violates a fundamental theorem in geometry – the Ptolemy’s theorem. That leads to the invalidity of Fermat’s principle. -/- . (shrink)

Leibniz proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or spherical (concave (...) or convex) surfaces. The extremal time path avoided the criticism that Fermat’s least time path was subjected to, by Cartesians who cited examples of reflections at spherical surfaces where light took the path of longest time. Thereby it became the standard method of demonstration of Snell’s Laws. Ptolemy’s theorem is a fundamental theorem in geometry. A special case of it offers a method of finding the minimum sum of the two distances of a point from two given fixed points. We show in this paper that Leibniz’s calculus proof of Snell’s Laws violates Ptolemy’s theorem, whereby Leibniz’s proof becomes invalid. (shrink)

Recently, a number of authors have suggested that we understand scientific models in the same way as fictional characters, like Sherlock Holmes. The biggest challenge for this approach concerns the ontology of fictional characters. I consider two responses to this challenge, given by Roman Frigg, Ronald Giere and Peter Godfrey-Smith, and argue that neither is successful. I then suggest an alternative approach. While parallels with fiction are useful, I argue that models of real systems are more aptly compared to works (...) that portray real people, like the Emperor Claudius. This approach will allow us to avoid problems with fictional characters. (shrink)

SUMMARY. The works of Alexander of Aphrodisias were written a few decades after the publication of the most successful -astrology hand- book in antiquity, Ptolemy's Tetrabiblos Syntaxis, which attempts to naturalize astrology, i.e. to make it agree with Aristotelian theory of science. A comparison of the doctrines between the Tetrabiblos and some passages of Alexander'p works on fate demostrates a noteworthy con¬vergere of the two scholars, and probably a dependence of the lasi great greek Aristotle's exegete on the theories (...) of Ptolemaic astrology, at least in reference to three points: theory of fate; justification of de- vining as a technical and naturai conjecture about man's fate; ana¬lysis of the stars' influence on the sublunary world in physical and phi¬losophical terms. (shrink)

This analysis of Ptolemy's Teatriblos deals with how the social and cultural role of astrology changed between lì and III century a D.: from a practice hard fought, although successful, to a generally accepted branch of knowledge. In Ptolemy's treatise astrology is shown to be not a science but an art: a techne" fallible but not controvertible. As the basis for such a project of reforming common opinion about astrol¬ogy, we find a quiet yielding attitude toward sceptical antidogmatism, (...) and a non-deterministic way of conceiving man 's naturai relationship with heavenly bodies. (shrink)

What were the reasons of the Copernican Revolution ? How did modern science (created by a bunch of ambitious intellectuals) manage to force out the old one created by Aristotle and Ptolemy, rooted in millennial traditions and strongly supported by the Church? What deep internal causes and strong social movements took part in the genesis, development and victory of modern science? The author comes to a new picture of Copernican Revolution on the basis of the elaborated model of scientific (...) revolutions that takes into account some recent advances in philosophy, sociology and history of science. The model was initially invented to describe Einstein’s Revolution of the XX century beginning. The model considers the growth of knowledge as interaction, interpenetration and unification of the research programmes, springing out of different cultural traditions. Thus, Copernican Revolution appears as a result of revealation and (partial) resolution of the dualism , of the gap between Ptolemy’s mathematical astronomy and Aristotelian qualitative physics. The works of Copernicus, Galileo, Kepler and Newton were all the stages of mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on skies. The model elaborated enables to reassess the role of some social factors crucial for the scientific revolution. It is argued that initially modern science was a result of the development of Christian Weltanschaugung . Later the main support came from the absolute monarchies. In the long run the creators of modern science appeared to be the “apparatchics” of the “regime of truth” built-in state machine. Natural science became a part of ideological state apparatus providing not only scientific education but the internalization of values crucial for the functioning of state. -/- . (shrink)

This work describes the main basic concepts of the astrological work of Ptolemy, through an analysis of his Tetrabiblos. Comparing his ideas to those of other authors of his time, it is shown that Ptolemy does not present stoic influences, as claimed by some historians. The conclusion of the article is that the basis of Ptolemy's astrology was Aristotle's physics.

The model of scientific revolution genesis and structure, extracted from Einstein’s revolution and considered in my previous publications, is applied to the Copernican one . According to the model, Einstein’s revolution origins can be understood due to occurrence and partial resolution of the contradictions between main rival classical physics research programmes : newtonian mechanics, maxwellian electrodynamics, thermodynamics and Boltzmann’s statistical mechanics. In general the growth of knowledge consists in interaction, interpenetration and even unification of different scientific research programmes. It is (...) argued that the Copernican revolution also happened due to realization of a certain dualism – now between mathematical astronomy and Aristotelian qualitative physics in Ptolemy’s cosmology and the corresponding efforts to eliminate it. The works of Copernicus, Galileo, Kepler and Newton all were the stages of the mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on divine phenomena. Yet the very realization of the gap between physics and astronomy appeared to be possible because at least at its first stages modern science was a result of Christian Weltanschaugung development with its aspiration for elimination of pagan components. -/- Key words: scientific revolution, modernity, Christian Weltanschaugung, Copernicus, Ptolemy. (shrink)

This article seeks the origin, in the theories of Ibn al-Haytham (Alhazen), Descartes, and Berkeley, of two-stage theories of spatial perception, which hold that visual perception involves both an immediate representation of the proximal stimulus in a two-dimensional ‘‘sensory core’’ and also a subsequent perception of the three dimensional world. The works of Ibn al-Haytham, Descartes, and Berkeley already frame the major theoretical options that guided visual theory into the twentieth century. The field of visual perception was the first area (...) of what we now call psychology to apply mathematics, through geometrical models as used by Euclid, Ptolemy, Ibn al-Haytham, and Descartes (among others). The article shows that Kepler’s discovery of the retinal image, which revolutionized visual anatomy and entailed fundamental changes in visual physiology, did not alter the basic structure of theories of spatial vision. These changes in visual physiology are advanced especially in Descartes' Dioptrics and his L'Homme. Berkeley develops a radically empirist theory vision, according to which visual perception of depth is learned through associative processes that rely on the sense of touch. But Descartes and Berkeley share the assertion that there is a two-dimensional sensory core that is in principle available to consciousness. They also share the observation that we don't usually perceived this core, but find depth and distance to be phenomenally immediate, a point they struggle to accommodate theoretically. If our interpretation is correct, it was not a change in the theory of the psychology of vision that engendered the idea of a sensory core, but rather the introduction of the theory into a new metaphysical context. (shrink)

Is vision merely a state of the beholder’s sensory organ which can be explained as an immediate effect caused by external sensible objects? Or is it rather a successive process in which the observer actively scanning the surrounding environment plays a major part? These two general attitudes towards visual perception were both developed already by ancient thinkers. The former is embraced by natural philosophers (e.g., atomists and Aristotelians) and is often labelled “intromissionist”, based on their assumption that vision is an (...) outcome of the causal influence exerted by an external object upon a sensory organ receiving an entity from the object. The latter attitude to vision as a successive process is rather linked to the “extramissionist” theories of the proponents of geometrical optics (such as Euclid or Ptolemy) who suggest that an entity – a visual ray – is sent forth from the eyes to the object. The present paper focuses on the contributions to this ancient controversy proposed by some 13th-century Latin thinkers. [...]. (shrink)

Levi ben Gerson (1288–1344) was a medieval astronomer who responded in an unusual way to the Ptolemaic tradition. He significantly modified Ptolemy’s lunar and planetary theories, in part by appealing to physical reasoning. Moreover, he depended on his own observations, with instruments he invented, rather than on observations he found in literary sources. As a result of his close attention to the variation in apparent planetary sizes, a subject entirely absent from the Almagest, he discovered a new phenomenon of (...) Mars and noticed a serious flaw in Ptolemy’s treatment of the Moon. (shrink)

Origins of the Copernican Revolution that led to modern science genesis can be explained only by the joint influence of external and internal factors. The author tries to take this influence into account with a help of his own growth of knowledge model according to which the growth of science consists in interaction, interpenetration and unification of various scientific research programmes spreading from different cultural milieux. Copernican Revolution consisted in revealation and elimination of the gap between Ptolemy’s mathematical astronomy (...) and Aristotelian qualitative physics. But the very realization of the gap between physics and astronomy appeared to be possible because at least at its first stages modern science was a result of Christian Weltanschaugung development with its aspiration for elimination of pagan components. Of all the external factors religion was the strongest one. Key words: scientific revolution, Christian weltanschaugung, modernity, Copernicus, Ptolemy. (shrink)

The article includes a short biography of Hermann of Dalmatia and gives an account of his translations and philosophical and scientific work. In order to have a better understanding of Hermann’s philosophy, a reminder of Greek and Arabic philosophy of nature, on which he relies in his interpretation of the world picture, needs to be presented. Cosmological models by Plato, Aristotle, Eudoxus, Heraclides of Pont, Apollonius of Perga, Hipparchus, Ptolemy, and the Arab scientist Abu Ma’shar, are presented. The main (...) focus of interest is on Hermann’s translations. The immense importance of his translations from Greek and Arabic into Latin is due to the fact that some of the seminal Greek and Arabic works became known in Western Europe in the middle of the twelfth century. Hermann is also important as the author of the original work De essentiis, which presented a blend of Platonian and Aristotelian as well as Western European and Arab traditions. (shrink)

Divus Augustus Pater. The cult of divine Augustus under the rule of the Julio-Claudian dynasty -/- Summary The cult of divine Augustus was one of the most important phenomena of ideological nature under the rule of the Julio-Claudian dynasty. The crucial point of its development was the apotheosis conducted on 17 September 14 AD. The new cult was derived greatly from numerous borrowings from the rites of various gods of the Roman Pantheon. As divus, Augustus received a separate priest, a (...) private priestess, and a college of priests. The first flamen Augustalis became Germanicus. The holder of this title enjoyed many privileges. It seems unlikely, however, that flamen Augustalis controlled the entire cult of divine Augustus. This was the role of the emperor as both the supreme priest and the inheritor of political power. Sodales Augustales also had special cult functions. This religious fraternity had a mixed private-state character just like many of the institutions of the early principate. It was a cult college of gens Iulia and, most of all, of Augustus. From its beginning it enjoyed high prestige. The members of this religious fraternity were recruited among the Senate elite and the family of the emperor. Sacerdos divi Augusti occupies a different place in the priesthood established to worship Augustus. This female priesthood, despite its humble cult and political role, is of great interest to scholars. In spite of discerning investigations by researchers, there seem to have been only two priestesses in the Julio-Claudian dynasty – Julia Augusta, the widow of the creator of the principate, and Antonia Augusta. There is even no certainty that the latter had preformed the function at all. Augustus, as a god, was given a separate temple under a Senate decree. However, the construction work went slowly ahead. Therefore, divus Augustus was initially worshipped in other places of worship. At first, it was the temple of Mars Ultor. He was also worshipped in the sacrarium on the Palatine. One encounters certain difficulties when trying to identify the places of Augustus’ worship in Rome. Ultimately, there seem to have been two sacraria in the capital of the Empire. There is no certainty, however, whether yet another temple was located next to the templum novum divi Augusti on the Palatine. In trying to analyse the phenomenon of the divinity of the Roman emperors, and Augustus in particular, it is necessary to refer to the genesis of Emperor worship. Within the framework of official religion it is important to distinguish such elements as genius and numen. Although the consecratio act conducted by the Senate meant the crossing of the boundary between the human Augustus and the divine Augustus, it is important to remember that Augustus had prepared his apotheosis for a long time and already enjoyed divine honours during his lifetime. Certain elements of Augustus worship developed under his rule continued to exist for some time after the death of the creator of the principate. Augustus divinity was guarded by the law of maiestas. At the beginning of the rule of Tiberius it mostly protected divus Augustus himself. Gradually, despite some opposition, the law began to serve the ruling emperor. There is little certainty of how many cases were brought under the crimen laesae maiestatis against those who insulted the divine Augustus. The issue of trials for offending the law of maiestas is accounted for one-sidedly by ancient historians, which complicates the work of contemporary researchers. There is, however, no denying that for Tiberius (Augustus’ successor) the trials on the charge of maiestas turned out to be a trap. The cult of divus Augustus was approved throughout the Empire. Nevertheless, some weaker voices of opposition could be heard. These were present in the Senate circles cherishing the memory of the last defenders of the Republic, as well as among some ethnic and religious communities. The latter included Judaism and emerging Christianity. The political consequences of Augustus’ deification were very serious. He significantly contributed to the ruling of the Julio-Claudian dynasty for over 50 years. The main reason for that was the fact that in the Rome of that time the tradition of power succession was not yet well-grounded. Directly after the principate creator’s death, his consecratio took place – he was assigned priests and many godly honours and a temple was erected in his honour. These actions obviously took place under Augustus’ successor Tiberius who, during his rule, constantly tried to emulate the divine predecessor and referred to his decrees on numerous occasions. Tiberius was the emperor who contributed to the cult of his adoptive father to the greatest extent. However, one cannot fail to notice that his actions were somehow ambiguous. It has to be remembered that, in addition to his sincere respect for the divine Augustus, Tiberius also tried to use the authority of the creator of the principate to strengthen his power. This is exemplified by the motto imprinted on coins: DIVVS AVGVSTVS PATER. Caligula took a different approach to the Augustan cult. When assuming power after Tiberius, he was in a different position. The 20-year rule by Augustus’ successor greatly contributed to the strengthening of the idea of the principate ’s stability in the minds of the Romans. This allowed Caligula to pay less heed to the Senate aristocracy, as well as other institutional elements of the Republic. Under these circumstances, the cult of Augustus underwent modifications. Divus Augustus still remained at the heart of the religious propaganda of the Roman state and gens Iulia, but also other members of the family of the young Emperor received a number of honours drawing them closer to the world of gods. Drusilla, for that matter, was made a diva. By this, the idea of domus Augusta received a new confirmation. Caligula himself did not cease to participate in, and support, the rites performed to worship his divine grandfather. The available sources lead us to believe that Augustus constituted for the young princeps a role model and a character to which he often compared himself with. For Claudius, the use of the cult of divine Augustus was important as a tool to strengthen political power. But due to the fact that his personal links with divus Augustus were rather weak, Claudius focused on the cult of his grandmother Livia, Augustus’ wife. He also emphasised the function of sacerdos divi Augusti which his mother Antonia Augusta was to fulfil. Claudius faced the task of the ‘reconstruction’ of the cult of Augustus which had deteriorated, especially during the second part of Caligula’s rule. Claudius took a different direction in imitating Augustus than his two predecessors. Augustus’ model was very capacious, allowing him to find examples which could be adjusted to fit his own political goals and personality. Claudius avoided the stiffness characteristic of Tiberius and, at the same time, respected Augustus’ traditions which he Caligula inadvertently abused. Claudius’ attitude to Augustus is not quite clear. Undoubtedly he kept alive the memory of the first princeps, however, there is a lack of testimony about the new honours conferred on divine Augustus during the rule of this Emperor. Almost all of them concentrate around the person of Claudius or his family. There are, however, no honours conferred on the creator of the principate. This type of attitude caused the cult of divine Augustus to be eclipsed by the cult of the ruling Emperor. Nero, the last representative of the Julio-Claudian dynasty descended, unlike Claudius, directly from the line of Augustus. The new emperor deified his predecessor by using the model of Augustus’ apotheosis. In the first part of his rule he drew greatly from the Augustus model of exercising power. Nero ’s ideological platform seems to be the richest in comparison with other emperors of the Julio-Claudian dynasty. The tradition of links with divus Augustus was, however, only one of many different elements. With time, the tradition appeared to play a still smaller role. The departure from the Augustus model took place on many levels. Some of the steps were very radical, whereas others were less significant. The most serious was the elimination of the members of gens Iulia and gens Claudia, and those who could prove their kinship with both the houses. The devastation in Nero ’s closest family put an end to the concept of domus Augusta. Formally, the Emperor did not renounce the divine creator of the principate but, in practice, the idea of the new domus Augusta no longer aimed at presenting Augustus’ descendants united in a single family. Nero was now alone and any creation of ideological concepts of power under those circumstances had to be based around him. These actions ended in disaster. By giving up the Augustan model, Nero lost the support of the army and, as a result, lost power. Apart from the worship of the state religion in the capital, divus Augustus was the subject of a provincial and municipal cult. Here, the worship of divine Augustus was often a continuation, sometimes in an extended form, of the honours Augustus had been granted during his lifetime. In the cult of divus Augustus, in the provinces one can observe a mutual interweaving of elements copied from the capital model and local traditions. The beginning of the provincial cult of Augustus dates back to the rule of Tiberius. The crucial point for the establishment of the provincial cult in the West was the request of the citizens of Hispania Tarraconensis to build a temple for divine Augustus. It is important to emphasise here that he was appointed on a local initiative. In the East, the genesis of the provincial cult is related to the functioning of koinon. In comparison with the western regions, the cult here was characterised not only by longer history but also an extensive system of priesthood and rich ritual. The intensity of development of municipal and private cult in the West depended on the level of social and economic development of the regions. It assumed the most complex forms in the provinces with well-developed city life – generally in the eastern provinces. Whereas the cult of divine Augustus in the western municipal provinces was similar in character to the cult of the principate’s creator in Italy. The greatest testimony to the cult’s development comes from relatively strongly romanised and, at the same time, the wealthiest regions which had been part of the Empire for a long time. These included the mainly proconsular Africa, Spain and Narbonese Gaul. The sources coming from these regions constitute not only an illustration of the development of the cult of divine Augustus and members of domus Augusta, but are also a sign of the processes of romanisation of great numbers of city populations. It is necessary to note that outside Rome we do not encounter an isolated cult of divine Augustus. Whenever we deal with information concerning temples or rituals dedicated to the deified creator of the principate, other members of the family are also worshipped. In fact, during the whole rule of the Julio-Claudian dynasty we actually deal with the cult of divine Augustus in close association with the worship of domus Augusta – domus divina. (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...) this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)