Category Posts
Mathomathis would like to present an article on Navigation, Math’s & Astronomy – The Pagan Knowledge Compiled by D.P. Agrawal Lokvigyan Kendra Almora 263601. It may sound strange that the adventurous sailors like Columbus and Vasco da Gama were no great navigators? The European method of navigation by ‘dead reckoning’ necessarily relied upon maps and charts, so they did not know how to navigate on uncharted seas. Behind this enigma lies the ignorance of maths of the Europeans, and the story of navigation, calendars and clocks. The methods of timekeeping in Europe, whether through mechanical clocks or the calendar, remained remarkably inaccurate until the 16th century CE, when this became a major embarrassment to both church and state. Unlike India which was far better off, the early 16th century Europe was very poor. The most prosperous regions were only Spain and Portugal, just emerging from Arab rule. Trade with the rich states of India and China represented a golden opportunity. Motivated by abject poverty and the hope of future riches, European sailors were ready to run huge risks: approximately a third of them used to die on each successful voyage to India. Ships sank frequently, and a sunken ship meant also loss of valuable cargo. Ultimately, successful trade needs secure trade routes and secure travel from Europe to India or China and back needed, at the least, knowledge of navigation. Navigation was the strategic and economic key to the initial prosperity of Europe through trade and subsequent colonization. Many of us would be surprised to know that Columbus and Vasco da Gama were hardly great navigators, though they certainly were great adventurers. Neither knew the celestial navigation techniques known to their Indian, Arab, and Chinese contemporaries. They had heard of celestial navigation, used by Arab navigators, but did not quite understand it. Columbus’ first recorded attempt at using a quadrant to establish his latitude was on 2ND November when he was off the northern shore of Cuba. This sadly erroneous sighting put him on the latitude of Cape Cod. Even so, Columbus failed to recognize this gross error and instead concluded that he was on the mainland of Cathay. This illustrates Columbus’s serious incompetence in celestial navigation. Columbus tried the quadrant again on 20TH November and came up with the same deplorable result of 42 degrees north latitude, but this time he realized that something was wrong and blamed it on the quadrant which he said was broken and needed repair. How can a quadrant be broken when it has only one moving part and that part is a string with a weight on the end? Similarly, Vasco da Gama used the services of an Indian pilot, Kanha, to ‘discover’ the sea route to India. To determine the latitude at sea, the pilot used an instrument, called kamal or rapalagai. In its simplest form, the instrument consists of a small wooden board and a string graduated with knots. The local latitude is almost the same as the altitude of the pole star, or its angular elevation above the horizon. To determine the altitude of the pole star, the wooden board is held in front of the eye, at an appropriate distance, so that it blocks the portion between the horizon and the pole star, and the distance from the eye is measured. Holding the string between the teeth, and counting the number of knots, one measures the distance. In the Arabic-Malayalam language, the pole star is hence called kau, which also means ‘teeth’. Vasco da Gama, not understanding the principle of the instrument, thought the pilot was telling the distance with his teeth! He further recorded that he carried back a couple of copies of the instrument to get it graduated in inches! (The instrument involves a harmonic scale, whereas inches refer to a linear scale, so that graduating it in inches is intrinsically impossible.) Though the Europeans did not know celestial navigation, their own technique of navigation by ‘dead reckoning’, using maps and charts, was very unreliable. Though a great deal of effort initially went into procuring and making accurate maps, it was eventually understood that, despite accurate maps, the European technique of navigation itself was inaccurate since it required measurement of the speed of the ship. A process called heaving the log measured the ship’s speed: throwing overboard a log tied to a rope, and measuring out the amount of rope taken up in a given period of time. A sailing manual describes how inaccurate this process was, even in 1864: “if the gale has not been the same during the whole hour, or time between heaving the log, or if there has been more sail set or handed, there must be an allowance made for it, according to the discretion of the officer. Sometimes, when the ship is before the wind and a great sea is setting after her, it will bring home the log; in such cases it is customary to allow one mile in ten, and less in proportion if the sea be not so great; a proper allowance ought also to be made if there be a head sea. In heaving the log, great care should be taken to veer out the line as fast as the log takes it; for if the log be left to turn the reel itself, it will come home, and give an erroneous distance.” European ignorance of navigation was widely recognized as a major problem, because the immense economic and strategic importance of navigation for Europe was transparent to all. One sunken ship meant not only a fortune gone, but also more men gone than in a typical war of those times. Consequently, governments in Europe not only officially admitted the European ignorance of navigation, from the 16th to the 18th century they did everything possible to find a better technique of navigation. Pedro Nunes, a professor of mathematics at Lisbon and Coimbra, was appointed royal cosmographer in 1529. Philip II of Spain offered a huge prize […]
Mathomathis would like to present an article on Vimana Shastras or Vymanika Shastras written by the author by Maharshi Bharadwaaja Propounded by Venerable SUBBARAYA SHASTRY Translated into English and Edited, Printed and Published by G.R. JOSYER SCHOLAR, HISTORIAN, ESSAYIST, SANSKRITIST Printed at CORONATION PRESS, MYSORE-4, INDIA. The following article presented in mathomathis was adopted from the website In the following materials, we would constantly using the word author and readers needs to be aware off that author in the following context would be Josyer. Author describes the book is as follows: Sometime in the period just before World War I, a Brahmana named Pandit Subbaraya Sastry began to dictate previously unknown texts in Sanskrit which purported to contain ancient Indian technological knowledge. He in turn, credited a Vedic sage named Maharshi Bharadwaja, as well as other Rishis who appear in legitimate Hindu texts. One of these ‘channeled’ texts was, on its face, a technical manual for the construction and use of ‘vimanas,’ the flying machines of the Vedic sagas. It is unclear as to whether any part of the present work was actually published in print at that time, even though it is implied in the introduction, so it is unclear whether it was published (in the legal sense) prior to 1923. The Sanskrit manuscript of the VS lay unpublished for over fifty years. In 1973, this text was published in a very limited edition by G.R. Josyer, along with a translation which he had produced over a twenty year period. In 1991, the English portion and the illustrations from the Josyer book were reprinted in the above-mentioned Vimana Aircraft of Ancient India & Atlantis. It as if someone in the early 20th century wrote a 100 page book on ancient aircraft in Biblical Hebrew and attributed it to Moses and other prophets. However, the fact that the book was originally written in Sanskrit, while very impressive, isn’t any indication of authenticity. Sanskrit is to some extent still a living language, used everyday in Vedic ritual. It is plausible that a well-educated high-caste Brahmins from that period would be able to compose a Sanskrit text of this length given enough time. If you are looking for an ancient manuscript on this fascinating topic, you’ll need to keep on looking. The Vymanika Shastra was first committed to writing between 1918 and 1923, and nobody is claiming that it came from some mysterious antique manuscript. The fact is, there are no manuscripts of this text prior to 1918, and nobody is claiming that there are. So on one level, this is not a hoax. You just have to buy into the assumption that ‘channeling’ works. On the other hand, there is no exposition of the theory of aviation (let alone antigravity). In plain terms, the VS never directly explains how vimanas get up in the air. The text is top-heavy with long lists of often bizarre ingredients used to construct various subsystems. This includes items such as monkey skin, eagle bones, sea-foam, and many that are only named in Sanskrit. Often the recipes are a mix of plant, animal and mineral ingredients, and involve mixing these ingredients and cooking them at high temperature in a furnace shaped like an animal, such as a frog. One wonders whether we are talking about metallurgy here, or some kind of alchemy. Most of the systems are described as mechanical devices, powered by steam, electricity or even solar power; a number literally involve smoke and mirrors. Vimanas are widely described in the genuine ancient texts such as the Ramayana and Mahabharata, as well as other later texts such as the dramas of Kalidasa. They are not metaphors or hyperbole, nor do you have to be a god to own or ride one as in other mythologies. [Source: wikipedia] The Sanskrit word vi-māna (विमान) literally means “measuring out, traversing” or “having been measured out”. Monier Monier-Williams defines Vimana as “a car or a chariot of the gods, any self-moving aerial car sometimes serving as a seat or throne, sometimes self-moving and carrying its occupant through the air; other descriptions make the Vimana more like a house or palace, and one kind is said to be seven stories high”, and quotes the Pushpaka Vimana of Ravana as an example. It may denote any car or vehicle, especially a bier or a ship as well as a palace of an emperor, especially with seven stories. In some Indian languages like Tamil, Malayalam, Telugu, and Hindi, vimana or vimanam means “aircraft”, for example in the town name Vimanapura (a suburb of Bangalore) and Vimannagar, a town in Pune. In another context, Vimana is a feature in Hindu temple architecture. [Source: wikipedia] Either the way, in the following article, we would describe vimanas as: “aircrafts”, flying vehicles. The pictures shown below are some of the types of vimanas G. R. JOSYER Hon. Director, International Academy of Sanskrit Research writes the following lines (Note: None of the words have been edited). On 25-8-1952 the Mysore representative of the Press Trust of India, Sri N. N. Sastry, sent up the following report which was published in all the leading dailies of India, and was taken up by Reuter and other World Press News Services: “Mr. G. R. Josyer, Director of the International Academy of Sanskrit Research in Mysore, in the course of an interview, showed some very ancient manuscripts which the Academy had collected. He claimed that the manuscripts were several thousands of years old, compiled by ancient rishis, Bharadwaja, Narada and others, dealing, not with the mysticism of ancient Hindu philosophy of Atman or Brahman, but with more mundane things vital for the existence of man and progress of nations both in times of peace and war. “Mr. Josyer’s manuscripts dealt in elaborate detail about food processing from various indigenous materials like grass, vegetables and leaves for human consumption, particularly during times of famine. “One manuscript dealt with Aeronautics, construction of various types of aircraft for civil aviation and for warfare. He showed me plans prepared according to directions contained in the manuscript on Aeronautics of three types of aircraft or […]
Source of Natural and Positive Law The devas or gods and asuras or demons, are allegoric terms, the term asura might stand politically for external invaders; historically for aborigines of India whom the Aryan immigrants had to repel!: socially, for the trash and bad characters; and psychologically, for the perverted tendencies in man. The terms devas and asuras stand broadly to denote respectively the good and the evil aspects in man as well as in nature. The mass extermination of the asuras at the hands of the devi or the goddess, is the victory of order over disorder by operation of natural law in the universe and by operation of positive law, in the society, this provides the metaphysical estimate of the idea of law. The Idea of Law In the field of natural sciences, die idea of law comes from the invariable sequence of events in future. When the recurrence of days and nights is referred to the diurnal motion of the earth, the law refers to the phenomena of causation. When Corin, the Shepherd, in Sakespear’s “As You Like It” understands what the property of fire is to bum and that of water to wet, his knowledge leads to the discovery of law into the uniform behaviour of substances. The human intelligibility of the uniform behavior of a mass of matter, body or substance, makes an association of such uniformity with the consistency of a purpose, as when the diurnal motion causes days and nights, or when fire causes burning or water causes wetting, so that an otherwise manipulation with the cause shall require a violation of law, just when the person desiring to avoid the purpose of burning shall devise to quench fire, or when the purpose of dispensing with the phenomena of days and nights shall necessitate a forcible arrest of earth’s motion. The law is a plan inherent in the ‘principle and its utility lies in the unfoldment of the plan. The plan consists in the realization of some particular nature. The earth realizes its nature in its motion, the fire in burning and the water in wetting. The utility lies in the exploitation of the wealth of a substance, and such exploitation is reconciliation of the nature of the substance. Unrest prevails so long as the purpose is not served, so long as the nature is unrealized. The execution of law is consummation of the purpose. In the consummation of the purpose, the property of a substance is put to test. The law set to realize a given nature abides with its intrinsic purpose. Random deviation in behavior of nature is not enigma. The floods, the epidemics, the holocausts, are just aberrations of nature, as if the nature becomes at times mal-charged. But this mal-charged resulting into abrupt deviations forms the normal course of nature, is part of the scheme of law. The idea of law is not without an idea of its breach, though the breaches in the order of nature are rare whereas breaches in the human order are frequent, and this difference owes itself to degree of freedom endowed’ respectively to nature and to men. The process in nature is not, whereas that in human life, is meditative. The universal nature in comparison to human nature is perfect. The greater degree of imperfection in human nature denotes the higher possibility of lapses serving as trials and errors in the meditative life in its onward march for perfection. The ultimate reality is infinite, and the infinite, by the buoyancy of its law, has to manifest itself and becomes finite. It is by will of its law that the non-self infinite comes down into the multiplicity of finite selves; it is in becoming finite that the infinite realizes its nature. Compelled by its unrest, the infinite releases its wealth and falls into a process. The fall of the perfect entity into a process of imperfection. The operation of law visits the breach of infinite nature by its descent for becoming finite. The function of law is to operate the mechanism of revelation of the infinite through finite means. In becoming finite, the infinite limits itself and this limitation is transference of imperfection in the finite. The finite law carry the philosophy of imperfection on its way to a graduated scheme of perfection. Being perfect, the law of the infinite is immutable. The finite being imperfect, the laws it has, are not immutable. The finite is the end of the infinite, in one epicycle of law, and the infinite is end of the finite in another epi-cycle. The cyclic order of the ultimate law is from the infinite to the finite and from the finite again to the infinite. From unity to multiplicity and from multiplicity again to unity is the course of law which is eternal will of the reality. The reality is an exemplary identity of being and willing. It is exemplary because it postulates infinite freedom. The infinite will and infinite freedom are one. The freedom of being is freedom of willing. Negation of the freedom of will is negation of being itself. There is, however, a different between the infinite and the finite wills. The infinite will is an inner pull of its law. But the finite self can mold and determine its will, in more than one way because of its imperfection. The will, in the finite, amounts only to voluntariness of action, and implies self-determination. The freedom of will of the finite is right of self-vindication or effective manifestation into a desired activity. Manifestation is test of freedom of will. Freedom connotes the willing of anything in any way, and to the extent is possible to separate freedom of activity from freedom of will, any subject finite or infinite, is free to will, meaning thereby that it is free only to will, meaning thereby that it is free only to will. A finite being may although be bound to do in anyway or any way to be […]
The desire to know is the desire to experience, to realize, to become, or to create, as explained in the first part of “Aitareya Upanishad”. In Bible, the first episode of Adam in tasting the forbidden fruit is an offence attributable to the outburst of the creative force. The divine command was conservation of force, which was condition of being. Ingrained into the fancy for the forbidden, lies the assumed awareness of an ideal, and the impairment of the ideal is actual impulse of the dynamicity concentrated in reality. The awareness of the ideal and the aberration for the breach of it, are the two opposites only of a single structural whole, which is real. The real polarizes itself into the ideal and the actual is quaking motion of it. The actual is a strivance for reversal of the ideal of breach thereof. The breach sustains the actual but sanctifies the ideal. If is the possibility of the breach that sustains the ideal and keeps the actual sustainable. The process of breach implicates both the ideal and the actual. There is a breach because of the ideal. The force or the “shakti” breaks its bounds, and it is through the breach that the force becomes intelligible. The breach is basically a device for vindication of the ideal. The breach is real, because it synthesizes, in a dialectical sense, both the ideal and the actual. Each phase of becoming is revelation of the creative force of being and the scheme of becoming synthesizes the ideal and the actual and points the way in which the force is put to test or becomes tested. The force of “shakti” is inherent limitation of the indefinite. It is with accessories of limitations that the infinite reveals itself and becomes finite. In its revelation alone the infinite is apprehended. The limitations are aids to revelation. The limitation is standardized modality of the finite, since the force persists in the revelation of the infinite through finite means. It is in this revelation that the infinite chooses to put its vitality to test. The entire process is an experiment and the creative force is the tested reality, nay the continual testing of hat which is ultimately real. The genesis in the bible, is testimony of the elan of creative energy. It is elan vital in Bergson’s terminology. The fall of Adam is rhetoric revolt against dormancy of the creative force. The divine command depicts the poised rectitude of force. The divine is slumbering state of force which transcends the creative process. The fall of Adam furnishes the restive passion for creation. The fruit which is forbidden is humanity prior to procreation. The deep slumbering pose of the infinite is averse to creation. The divine command is the first awareness instilled in the being as readiness for creation. The divine command was Adam’s anthropomorphy of the infinite withholding its creative power. It was a stage of forbearance, a stage where procreation had to be forsaken. It was a pint of transition in the creative force for its transformation into tire procreative power. The fall of Adam is rhapsodic imagery of a discourse between the creator and the creature. The imbroglio of force was premeditated. The creator was aware of the forbidden, and the creature was made aware of that which was forbidden. The difference is not without meaning. The awareness of God was creative energy, that of Adam was procreative power. God is name for creative agency in nature. Adam is creature or product of nature. The character of God or Adam may be legends, and the episode may be phantasy, but the moral is correct to bear evidence that the reality in its mystery of creation carries the burden of some primaeval force. The procreative pleasure of the creature is accountable to a later formality of the operation of this force. It is this force which throughout persists prior to, or even after, the fleeting flux of the world. It is “Lebnitz” knew this by the name of “conatus” the same what Hindus know by the name of “shakti”. The desire to know as well as the knowledge derived, both refer to this force. The Knowledge Gained The desire to know, in the creature, as instanced by the character of Adam starts from the first-hand information of the forbidden, and the forbidden, in relation to the desire to know, is mere admission of the unknown. The unknown is one which eludes perception. Knowledge is the facultative art of breaking through the barriers of perception and thereby apprehending the casual nucleus of that which is perceived. Infonnation leads to intelligence, intelligence to understanding, understanding leads to learning, learning to wisdom and wisdom to knowledge; and all this, from first to the last, is a gap filed by a process of transfusion of precepts into concepts. The percept of the tree can never become knowledge of the tree without the corresponding concept of seed. The seed is cause of the tree but in knowing the seed as cause of the tree, the knower knows of the latent force in which the tree potentially exists; and what is true of the origin of tree is true of the origin of the entire universe ‘which at one stage lay dormant in a reservoir of force omnipotent. The conatus of Leibnitz, the elan vital of Bergson, the shakti of the Hindus, the forbidden fruit of the genesis, the prakrati of the samkhya, or the Maya of Vedanta, stand all as synonyms of this potential force. Knowledge, leaping back from one posterior phenomenon of force to its prior, that is, from one perceptual event to its antecedent casual potentiality, stabilizes itself in the comprehension of the first cause, which implicates in itself the vision of the law. d Vision of Law the knowledge of this potential force is knowledge of the first cause. Law is but the ingrained tendency of this force. The law of the tree is ingrained in the force […]
Mathomathis would like to present an article on: Yajnavalkya and the Origins of Puranic Cosmology By Author Subhash Kak Department of Electrical & Computer Engineering Louisiana State University Baton Rouge, LA 70803-5901, USA (May 30, 2018) The prehistory of Puranic astronomy is not well understood. Although it is known that the Puranas contain very old material, some modern historians of astronomy have believed that the cosmology presented there has no Vedic antecedents. In this paper, we show that this belief is wrong, and a system similar to Puranic cosmology is described in the Vedic tradition. In the past few years a new understanding of the origins of Indian astronomy has emerged. In various publications, we have sketched a history of Indian astronomy from the earliest Vedic conceptions— as expressed in the astronomy of geometric altars to the classical Siddhantic astronomy. Meanwhile, the use of modern computer packages has made it possible to reexamine the astronomical references in the early texts. Although recent work showed that Puranic and Siddhantic astronomies have several common points, the origins of Puranic astronomy remained unclear. Here author presents Yajnavalkya’s cosmology from Brihadaranyaka Upanishad (BU) 3.3.2 which has hitherto escaped scholarly attention. We show that this cosmology has all the basic features of the later Puranic cosmology and so it may be viewed as the original source. The great Upanishadic sage Yajnavalkya is a major figure in the earliest Indian astronomy, that precedes Lagadha’s Vedanga Jyotisa. Elsewhere, we have noted that in the Satapatha Brahmana, Yajnavalkya speaks of a 95-year intercalary cycle to harmonize the lunar and solar years and he describes the non-uniform motion of the Sun. We showed that these were significant links in the early development of Vedic astronomy. The 19th century European Indologists tended to assign him to around 800 B.C., but a reexamination of the evidence suggests that he should be assigned to around 1800 B.C. However, the chronology of Yajnvalkya is not our concern here, so will not Vedic and Puranic Cosmological Ideas: In brief, the Vedas take the universe to be infinite in size. The universe is visualized in the image of the cosmic egg, Brahmanda. Beyond our own universe lie other universes. The Pancavimsa Brahmana 16.8.6 states that the heavens are 1000 earth diameters away from the Earth. The Sun was taken to be halfway to the heavens, so this suggests a distance to the Sun to be about 500 earth diameters from the Earth. Yajurveda, in the mystic hymn 17, dealing with the nature of the universe, counts numbers in powers of ten upto 1012. It has been suggested that this is an estimate of the size of the universe in yojanas. The Puranas provide material which is believed to be close to the knowledge of the Vedic times. Here author specifically considers Vayu Purana (VaP), Vishnu Purana (ViP), and Matsya Purana (MP). VaP and ViP are generally believed to be amongst the earliest Puranas and at least 1,500 years old. The Puranas instruct through myth and this myth making can be seen in their approach to astronomy. For example, they speak of seven underground worlds below the orbital plane of the planets and of seven “continents” encircling the Earth. One has to take care to separate this imagery, that parallels the conception of the seven centers of the human’s psycho somatic body, from the underlying cosmology of the physical universe of the Puranas, that is their primary concern in their Jyotisha chapters. The idea of seven regions of the universe is present in the Rigveda 1.22.16-21 where the Sun’s stride is described as saptadhaman, or taking place in seven regions. The geography of concentric continents is a representation of the plane of the Earth’s rotation, with each new continent as the orbit of the next “planet”. The different Puranas reproduce the same cosmological material. There are some minor differences in figures that may be a result of wrong copying by scribes who did not understand the material. In this paper, we mainly follow ViP. ViP 2.8 describes the Sun to be 9,000 yojanas in length and to be connected by an axle that is 15.7×106 yojanas long to the Manasa mountain and another axle 45,500 yojanas long connected to the pole star. The distance of 15.7 million yojanas between the Earth and the Sun is much greater than the distance of 0.46 million yojanas used by Aryabhatta in his Siddhanta. (But note that the yojana of the Puranas is different from the yojana of the Siddhantas) This greater distance is stated without a corresponding change in the diameter of the Sun. The size of the universe is described as 500 million yojanas. In VaP 50, it is stated that the Sun covers 3.15 million yojanas in a muhurta. This means that the distance covered in a day are 94.5 million yojanas. MP 124 gives the same figure. This is in agreement with the view that the Sun is 15.7 million yojanas away from the Earth. The specific speed given here, translates to 116.67 yojanas per half-nimes. Author have argued that the speed of 2,202 yojanas in half-nimes. a mentioned by Sayana, may have emerged from the theory that light should travel at a speed that is able to illuminate the entire universe in one day. The size of the universe is described in two different ways, through the “island-continents” and through heavenly bodies. The planetary model in the Puranas is different from that in the Siddhantas. Here the Moon as well as the planets are in orbits higher than the Sun. Originally, this supposition for the Moon may have represented the fact that it goes higher than the Sun in its orbit. Given that the Moon’s inclination is 5◦ to the ecliptic, its declination can be 28.5◦ compared to the Sun’s maximum declination of ±23.5◦. This “higher” position must have been, at some stage, represented literally by a higher orbit. To make sense with the observational reality, it became necessary for the Moon is taken to […]