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Tag: Sanatana Dharma

  • Kerala Calculus Precedes Western Calculus

    Kerala Calculus Precedes Western Calculus

    Vedic mathematics and science are ancient Indian systems of knowledge that have been passed down through generations. These systems originated in the Vedas, which are a collection of ancient Indian scriptures. Vedic mathematics is a system of mathematical calculations based on 16 sutras, or word-formulas, and 13 sub-sutras, or corollaries. This system is known for its simplicity and efficiency, as it allows for faster calculations and mental math techniques.

    Vedic science, on the other hand, is a system of knowledge that encompasses a wide range of subjects, including astronomy, astrology, medicine, and philosophy. It is based on the principles of the Vedas and the Upanishads, which are ancient Indian texts that contain philosophical and spiritual teachings.

    One of the key principles of Vedic science is the idea of interconnectedness between all things, known as the principle of unity. This principle suggests that everything in the universe is connected and that there is a fundamental unity underlying all of existence.

    Another important principle of Vedic science is the idea of balance, or the principle of equilibrium. This principle suggests that in order for an individual or society to achieve health and well-being, there must be a balance between different aspects of life, such as work and rest, or physical and spiritual pursuits.

    Overall, Vedic mathematics and science offer unique insights into ancient Indian knowledge systems and can provide useful tools and perspectives for modern-day learning and living.

    Before I write on what Kerala Calculus is, I feel it is necessary to remind us Indians of the fact that our continued ignorance, indifference reluctance to learn our highly scientific texts have resulted in the Myth of Aryan Invasion Theory by the Eurocentric colonialists gained currency and it has taken a lot of efforts to deny the theory which attempted to deny India its glorious past.

    There are other insidious attempts too.

    That the scientificancient texts are vague, they do not really talk about science and people use it, after the modern science discovers something,Indians say that the facts were mentioned in the Hindu Texts.

    And another ingenious attempt to deny India its rich scientific heritage is by stating that the data referred to in the tests were not used by the ancient Indians !

    The only way one can counter these arguments is for us to study the original texts and bring into light the scientific thoughts found in our Texts.

    I am trying to instill a sense of pride in our heritage by posting articles on various astounding facts in out texts, our stupendous Temples Astronomy.

    It is for the specialists to delve deep into the Texts and reveal what they contain.

    Unfortunately those who know Sanskrit are not generally aware of advanced modern Scientific Theories and those familiar with modern concepts do not know Sanskrit.

    My request is that both the groups must get familiar with what they do not know or get together to highlight the highly advanced scientific nature of Hindu Thought.

    I shall continue to post articles giving general directions.

    Now to Calculus.

    ‘

    Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves),and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot.

    Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called “the calculus of infinitesimals”, or “infinitesimal calculus”. The word “calculus” comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and process calculus.”

    The Kerala Calculus.

    The Kerala school of astronomy and mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently created a number of important mathematics concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (c. 1500 – c. 1610), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha.

    Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation and integration, nor is there any direct evidence of their results being transmitted outside Kerala ..

    The Kerala school has made a number of contributions to the fields of infinite series and calculus. These include the following (infinite) geometric series:

    \frac{1}{1-x} = 1 + x + x^2 + x^3 + \dots for <img class="mwe-math-fallback-image-inline tex" src="https://upload.wikimedia.org/math/1/1/2/112f97d0a5732861bb9297b7d2c3e631.png&quot; alt="|x|

    This formula, however, was already known in the work of the 10th century Iraqi mathematician Alhazen (the Latinized form of the name Ibn al-Haytham) (965-1039).[8]

    The Kerala school made intuitive use of mathematical induction, though the inductive hypothesis was not yet formulated or employed in proofs. They used this to discover a semi-rigorous proof of the result:

    1^p+ 2^p + \cdots + n^p \approx \frac{n^{p+1}}{p+1} for large n. This result was also known to Alhazen.

    They applied ideas from (what was to become) differential and integral calculus to obtain (Taylor-Maclaurin) infinite series for \sin x, \cos x, and \arctan x.TheTantrasangraha-vakhya gives the series in verse, which when translated to mathematical notation, can be written as:

    r\arctan(\frac{y}{x}) = \frac{1}{1}\cdot\frac{ry}{x} -\frac{1}{3}\cdot\frac{ry^3}{x^3} + \frac{1}{5}\cdot\frac{ry^5}{x^5} - \cdots , where y/x \leq 1.
    r\sin \frac{x}{r} = x - x\cdot\frac{x^2}{(2^2+2)r^2} + x\cdot \frac{x^2}{(2^2+2)r^2}\cdot\frac{x^2}{(4^2+4)r^2} - \cdot
    r(1 - \cos \frac{x}{r}) = r\cdot \frac{x^2}{(2^2-2)r^2} - r\cdot \frac{x^2}{(2^2-2)r^2}\cdot \frac{x^2}{(4^2-4)r^2} + \cdots , where, for r = 1 , the series reduce to the standard power series for these trigonometric functions, for example:

    \sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots and
    \cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots (The Kerala school did not use the “factorial” symbolism.)

    The Kerala school made use of the rectification (computation of length) of the arc of a circle to give a proof of these results. (The later method of Leibniz, using quadrature (i.e.computation of area under the arc of the circle), was not yet developed.) They also made use of the series expansion of \arctan x to obtain an infinite series expression (later known as Gregory series) for \pi:

    \frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \ldots

    Their rational approximation of the error for the finite sum of their series are of particular interest. For example, the error, f_i(n+1), (for n odd, and i = 1, 2, 3) for the series:

    \frac{\pi}{4} \approx 1 - \frac{1}{3}+ \frac{1}{5} - \cdots (-1)^{(n-1)/2}\frac{1}{n} + (-1)^{(n+1)/2}f_i(n+1)

    where f_1(n) = \frac{1}{2n}, \ f_2(n) = \frac{n/2}{n^2+1}, \ f_3(n) = \frac{(n/2)^2+1}{(n^2+5)n/2}.
    They manipulated the terms, using the partial fraction expansion of :\frac{1}{n^3-n} to obtain a more rapidly converging series for \pi:[1]

    \frac{\pi}{4} = \frac{3}{4} + \frac{1}{3^3-3} - \frac{1}{5^3-5} + \frac{1}{7^3-7} - \cdots

    They used the improved series to derive a rational expression, 104348/33215 for \pi correct up to nine decimal places, i.e. 3.141592653 . They made use of an intuitive notion of a limit to compute these results. The Kerala school mathematicians also gave a semi-rigorous method of differentiation of some trigonometric functions, though the notion of a function, or of exponential or logarithmic functions, was not yet formulated.

    The works of the Kerala school were first written up for the Western world by Englishman C. M. Whish in 1835, though there exists another work, namely Kala Sankalita by J. Warren from 1825 which briefly mentions the discovery of infinite series by Kerala astronomers. According to Whish, the Kerala mathematicians had “laid the foundation for a complete system of fluxions” and these works abounded “with fluxional forms and series to be found in no work of foreign countries.” However, Whish’s results were almost completely neglected, until over a century later, when the discoveries of the Kerala school were investigated again by C. Rajagopal and his associates. Their work includes commentaries on the proofs of the arctan series in Yuktibhasa given in two papers, a commentary on the Yuktibhasa’s proof of the sine and cosine series and two papers that provide the Sanskrit verses of the Tantrasangrahavakhya for the series for arctan, sin, and cosine (with English translation and commentary)..

    The following notes by westerners would justify what I had written at the beginning of the Post.

    “

    1. (Bressoud 2002, p. 12) Quote: “There is no evidence that the Indian work on series was known beyond India, or even outside Kerala, until the nineteenth century. Gold and Pingree assert [4] that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use.”
    2. Jump up^ Plofker 2001, p. 293 Quote: “It is not unusual to encounter in discussions of Indian mathematics such assertions as that “the concept of differentiation was understood [in India] from the time of Manjula (… in the 10th century)” [Joseph 1991, 300], or that “we may consider Madhava to have been the founder of mathematical analysis” (Joseph 1991, 293), or that Bhaskara II may claim to be “the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus” (Bag 1979, 294). … The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). … It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian “discovery of the principle of the differential calculus” somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential “principle” was not generalized to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here”
    3. Jump up^ Pingree 1992, p. 562 Quote: “One example I can give you relates to the Indian Mādhava’s demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by Charles Whish, in the 1830s, it was heralded as the Indians’ discovery of the calculus. This claim and Mādhava’s achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the Transactions of the Royal Asiatic Society, in which Whish’s article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series without the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava’s mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution.”

    Reference and citation.

     

    https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_mathematics

  • Pravaras Why Three Five Rishis

    In Hinduism there is the practice of introducing oneself with reference to his ancestors.

    It is logical to refer to oneself with them as it makes it easier to identify.

    Without reference to them, we are not here, which many do not seem to acknowledge.

    Brahmin Gotras.Jpg
    Brahmin Gotras.

    It is customary for Ancient Indian writers to refer either to parents or their preceptor/s, as they were placed in a Higher Status than parents,.

    Thus we have the parent,Grand parent referred to in Slokas and Stuthis.

    Vyaasam Vasishta Napthaaram, Sakthe Pauthra Kalmasham,

    Parasaraathmajam Vande Sukha Naadham Thapo Nidhim-Vishnu Sahasra Naama.

    Here the author Vyasa introduces himself as,,

    Great Grand son of Vasishta,

    Grand son of Sakthi,

    Son of Parasara, and

    Father of Sukha.

    How logically the terms are arranged.

    Great Grand Father, Grand Father, Father, Self and son!

    For Guru reference,

    Adi Shankaracharya never mentions himself directly in his works.

    ‘Sri Govinda Bhagavatpaada Sishya,’

    Disciple of the Noble Govinda Bhagavatpaada”

    This system has been in place from the early period of the Vedas.

    The founders of the Humanity, as far as Hindu Texts go, are the Saptha Rshi, the Seven Sages , after whom the lineage is from.

    And they are referred to in introducing oneself.

    This system is called the Gotra.

    This is patrilineal.

    Then there is Pravara.

    ”

    a Pravara (Sanskrit for “most excellent”) is a particular Brahmin’s descent from a rishi (sage) who belonged to their gotra (clan). In vedic ritual, the importance of the pravara appears to be in its use by the ritualist for extolling his ancestry and proclaiming, “as a descendant of worthy ancestors, I am a fit and proper person to do the act I am performing.” Generally, there are either three or five pravaras. The sacred thread yajnopavita worn on upanayana has close and essential connection with the concept of pravaras related to Brahmin gotra system. While tying the knots of sacred thread, an oath is taken in the name of each one of these three or five of the most excellent rishis belonging to one’s gotra.

    The full affiliation of a brāhamana consists of (1)gotra, (2)sutra (of Kalpa), (3)shakha, (4)pravaras .

    (Example 🙂 A brahmana named ‘Rama’ introduces himself as follows : I am ‘Rama’, of Shrivatsa gotra, of Āpastamba sutra, of Taittiriya shākha of Yajurveda, of five pravaras named Bhārgava, Chyāvana, Āpnavan, Aurva and Jāmdagnya (This example is based upon the example given by Pattābhirām Shastri in the introduction to Vedārtha-Pārijata, cf. ref.).’

    It may be noted in the Pravara,three or Five Rishis are mentioned.

    For example, Kasyapa, Apasthara, Naithruva’

    This is different from Kasyapa Gotra.

    There is another Pravara for Kasyapa Gotra as well.

    Kasyapa, Aavatsaara, Daivala.

    The same with the other Rishis.

    Sometimes three Rishis are mentioned and at times Five.

    Why?

    One view is that these references are to the excellent ancestors from the Gotra.

    My view is that , if that be case the first Rishi should always be the founder.

    But , as in Nythruva Kasyapa, Kasyapa does not appear as the First Rishi but it is Naithruva.

    Reason is that many Rishis have more than one wife and many children through each of them.

    Kasyapa had more than one wife.

    The Prajapati Daksha gave his thirteen daughters (Aditi, Diti, Kadru, Danu, Arishta, Surasa, Surabhi, Vinata, Tamra, Krodhavasha,Idā, Vishva and Muni in marriage to Kashyapa.

    Though the Father is one, mother differs.

    To identify and emphasize the differentitae, the three or Five Rishis are mentioned.

    Traditionally the first wife’s son carries the Father’s name as Gotra and the others the son of the Second or third wife and but to make the reference correct the founder is mentioned later in the Pravara.

    The pravara identifies the association of a person with two, three (or sometimes five) of the above-mentioned rishis. It also signifies the Sutras contributed to different Vedas by those rishis.

    For example, Kashyapa Gothram has 3 rishis associated with it viz. Kashyap, Nidruva and Avatsara

    In a court case “Madhavrao vs Raghavendrarao” which involved a Deshastha Brahmin couple, the German scholar Max Mueller’s definition of gotra as descending from eight sages and then branching out to several families was thrown out by reputed judges of a Bombay High Court. The court called the idea of Brahmin families descending from an unbroken line of common ancestors as indicated by the names of their respective gotras and pravaras impossible to accept. The court consulted relevant Hindu texts and stressed the need for Hindu society and law to keep up with the times emphasizing that notions of good social behavior and the general ideology of the Hindu society had changed. The court also said that the mass of material in the Hindu texts is so vast and full of contradictions that it is almost an impossible task to reduce it to order and coherence.

     

    Citation and Refeernce.

    https://en.wikipedia.org/wiki/Pravaras

    For details of Pravaras  https://www.trsiyengar.com/termsandConditions.shtml

  • Hindu Kings Of Iraq Turkey Syria Lebanon Egypt Italy Mitanni Empire

    I have written about the Mitanni People and the Mitanni Empire.

    The Mitanni Empire covered what is now known as Iraq, Turkey Syria, Lebanon,Egypt and included Italy.

    They were the ancestors of these people.

    Mitanni were the ancestors of the Egyptians as well.

    Mittani Empire.png Mittani Empire. “Near East 1400 BCE” by User:Javierfv1212 – http://en.wikipedia.org/wiki/File:Near_East_1400_BCE.png. Licensed under CC BY-SA 3.0 via Wikimedia Commons – http://commons.wikimedia.org/wiki/File:Near_East_1400_BCE.png#/media/File:Near_East_1400_BCE.png

     

    ‘These Kings and even a Roman Emperor sported Thiruman, The Vaishnavite marks on their Body.

     

    The Sun King Akhenaten of Egypt who ruled between 1352-1336 BC was a son-in-law of Tushratta, the Mitanni king. The name Tushratta has been recorded in the Hittite cuneiform script.

     

    Some have suggested that the Sanskrit origin of Tushratta is Dasaratha, a few others that it is Tvesaratha (having splendid chariots), a name which is attested in the Rigveda.

    “The first Mitanni king was Sutarna I (good sun). He was followed by Baratarna I (or Paratarna great sun), Parasuksatra(ruler with axe),…. Saustatar (Sauksatra, son of Suksatra, the good ruler), Artadama (abiding in cosmic law)..Tushratta (Dasaratha), and finally Matiwazza (Mativaja, whose wealth is thought) during whose lifetime the Mitanni state appears to have become a vassal to Assyria”. Subhash Kak traces the ‘arna’ syllable in the names of the kings to ‘araNi’ (अरणि) meaning ‘sun’…

    (Akhenaten, Surya, and the Rigveda’, Prof Subhash Kak (an Indian American computer scientist, previous Head of Computer Science Department, Oklahoma State University)

    ‘ “A number of Indo-European sounding words have been identified in the cuneiform documents of the Mitanni kingdom (1500-1200 BC). In addition to nouns and adjectives with parallels in Sanskrit this Hurrian speaking kingdom had kings with Indo-Aryan names and two documents even list the main Gods of the Indian pantheon….”

     

    The kingdom of the Mitanni Indo-Iranian dynasty that ruled in the land of the Hurrians was in the upper Euphrates-Tigris basin – land that is now part of northern Iraq, Syria and south-eastern Turkey.

    At its greatest extent (for a brief period at the height of its dynastic power), Mitanni territory extended to the Mediterranean coast and into northern Assyria / Mesopotamia, it’s south-eastern neighbour.

    Mitanni’s north-western border with theHattian kingdom of the Hittites was fluid and constantly subject to aggression except when the two rivals concluded a peace treaty – one that invoked the Indo-Iranian pantheon of Mitra, Varuna, Indra and the Nasatyas – but also one that marked the decline of the Mitanni kingdom and a decrease in size. The Mitanni and Hittites were closely related. The Hittites used the Hurrian language extensively in their inscriptions. They also shared in the development of the light chariot whose wheels used spokes .

    The Hurrian lands are today a part of Greater Kurdistan….

     

    Despite Tusratta’s problems, he was not beyond offering his daughter Tadukhipa in marriage to the King Amenhotep III of Egypt for a large quantity of gold. The tablet seen to the right is a letter from Tusratta to Amenhotep in which he asks for “gold in very great quantity” as a bride price, supporting his request with the comment, “Gold is as dust in the land of my brother.”

    The beleaguered Tusratta was then murdered by his son in a palace coup. Tusratta’s other son, Prince Shattiwaza, fled Mitanni and was eventually given sanctuary by the Hittite King Suppiluliuma with whom he concluded a treaty c. 1380 BCE, which we know as the Suppiluliuma-Shattiwaza Treaty (discovered in 1907 CE in Hattusa, near present-day Bogazkale(Boğazkale, formerly Bogazköy) in north-central Turkey. In the treaty, the Hittite King Suppiluliuma agreed to assist Shattiwaza gain the Mitanni throne and invaded Mitanni. The Hittites captured the Mitanni capital Wassukanni after a second attempt and installed Shattiwaza as a vassal king.

    The Suppiluliuma-Shattiwaza Treaty is a source of considerable information about the Mitanni. In addition, it gives us some astonishing information about the religious practices of the Mitanni for it invokes the Indo-Iranian pantheon of asuras and devas Mitras(il) (Mitra), Uruvanass(il) (Varuna), Indara (Indra) and theNasatianna (Nasatyas) (Ashwins).

    Following the capture of Wassukanni, the Hittites installed new rulers in Mitanni towns while the Assyrians regained control of the territory they had lost to the Mitanni. Tusratta was killed and his son Shattiwaza became a vassal of the Hittite Suppiluliuma (c.1344 – 1322 BCE). At the same time, the rebellious Artatama became a puppet king of a reborn Assyria, led by king Assur-Uballit I (1364-1328 BCE). Wassukanni was sacked again by the Assyrian king Adad-Nirari I around 1290 BCE, after which very little is known of its history.

    In our page on the Hittites, we note:
    “In the Bogazkale archives, native Hurrian is used frequently for a wide range of non-official texts such as those on rituals and even the Epic of Gilgamesh – more so than native Hattian. Native Hurrian texts have been found throughout the region. One such text dated to 1750 BCE was found at Tell Hariri (ancient Mari), a Middle Euphrates site, and another at Ras Shamra (Ugarit) on the Syrian coast indicating Hurrian i.e. Mitanni influence in the region preceded the rise of Hittite power. A similar language to Hurrian is the language of Urartu located to the west of the Hittite lands at the headwaters of the Euphrates and around Lake Van. According to the literature (cf. The Hittites by O. R. Gurney, Penguin Books 1981), The Hurrians were migrants to the Upper Euphrates and Habur basin from the Elburz Mountains east across the Taurus Mountains from about 2300 BCE onwards.”

    The Mitanni name for chariot warriors was maryanna or marijannina, a form of the Indo-Iranian term marya meaning ‘young man,” used in the Rig Veda when referring to the celestial warriors assembled around the Vedic deity Indra.The Mitanni were famed charioteers. They are reported to have spearheaded the development of the light war chariot with wheels that used spokes rather than solid wood wheels like those used by the Sumerians.

    Tushratta's letter to Amenhotep III of Egypt Amarna from Tell el-Amarna. Housed at British Museum WAA 29791.jpg Tushratta’s letter to Amenhotep III of Egypt Amarna from Tell el-Amarna. Housed at British Museum WAA 29791
    The Hittite archives of Hattusa, near present-day Bogazkale contained what is the oldest surviving horse training manual in the world. The elaborate work was written c. 1345 BCE on four tablets and contains 1080 lines by a Mitanni horse trainer named Kikkuli. It begins with the words, “Thus speaks Kikkuli, master horse trainer of the land of Mitanni” and uses various Indo-Iranian words for horse colours, numbers and names. Examples are:

    assussanni a form of the Sanskrit asva-sani meaning ‘horse trainer’,
    aika wartanna meaning one turn (cf. Vedic Sanskrit ek vartanam),
    tera wartanna meaning three turns (cf. Vedic Sanskrit tri vartanam),
    panza wartanna meaning five turns (cf. Vedic Sanskrit panca vartanam),
    satta wartanna meaning seven turns (cf. Vedic Sanskrit sapta vartanam), and
    navartanna meaning nine turns (cf. Vedic Sanskrit nava vartanam).
    [Regrettably, writers do not mention the Old Iranian equivalents.]

    A Hurrian text from Yorgan Tepe also uses Indo-Iranian words to describe the colour of horses, words such as babru for brown, parita for grey, and pinkara for a reddish hue.

    The Kikkuli manual for training chariot horses highlights the links between the Mitanni and Hittites. Even though they were rivals at times, the two groups also collaborated frequently. The fact that the Hittites employed a Mitanni as a master trainer of horses may indicate that it was the Mitanni who were the regional experts in horse training especially for military purposes (in a manner similar to the Sogdians in the East) and that the Mitanni in turn had brought the expertise with them in their migration westward.

    The methods used in the Kikkuli method enabled horses to be trained without injury. The text detailed a 214-day training regime using interval training and sports medicine techniques such as the principle of progression, peak loading systems, electrolyte replacement, fartlek training, intervals and repetitions and was directed at horses with a high proportion of slow-twitch muscle fibres. the Kikkuli horses were stabled, rugged, washed down with warm water and fed oats, barley and hay at least three times per day.

    Kikkuli’s interval training technique stressed the leading of horses at a trot, canter and gallop, before subjecting them to the weight bearing stress of a rider, driver or chariot. Workouts sometimes numbered three a day with scheduled rest days. Kikkuli’s interval training contained three stages – the first two for developing strong legs and a strong cardio-muscular system, and the third for increasing neuromuscular conditioning. His workouts included brief recoveries to lower the heart rate. Swimming was also included in intervals of three to five sessions, with rest periods after each session. The horses were also subject to warming down periods and the method’s example of cantering included intermediate pauses to lower the heart rate partially and as the training advanced the workouts included intervals at the canter.

    Mitanni Indo-Iranian Names

    The names of the Mitanni kings and their capital city were of Indo-Iranian origin. For instance, Tueratta was a form of the Indo-Iranian Tvesa-ratha meaning ‘Possessor of a Chariot’. The name S’attuara was a form of Satvarmeaning ‘warrior’ and the name of the Mitanni capital Wassukanni, was a form of Vasu-khani meaning ‘wealth-mine’.

    The names of proto-Indo-Iranian dieties are also found to form the names of the Kassite rulers of Babylonia.

    Arta

    Several Mitanni names contained the Old Persian term arta, a derivative of asha via arsha, meaning cosmic order and truth (arta transforms to the Sanskrit r’ta). Arta is found used in Old Persian Achaemenian names (e.g. Artakhshassa c.450 BCE) and in the Sogdian Avesta as well. Asha is the central ethical concept of the Avesta.

    Philologists trace the Mitanni names to the Vedic equivalents. For instance, they note that the royal name Artatama was a form of the Indo-Iranian R’ta-dhaanman meaning ‘the abode of rta’, and the name Artas’s’umara was a form of Rta-smara meaning ‘remembering r’ta’.

    However, for some reason, none of the writers that we have come across link the name to their Old Iranian or Old Persian equivalents – equivalents that will be closer to the Mitanni names as we have demonstrated with the use of arta above.

     

    Reference and Citation.

    http://www.heritageinstitute.com/zoroastrianism/ranghaya/mitanni.htm#dynasty

  • Indra In Incas Peru Viracocha Ramayana, Upanishad

    Viracocha of South America tradition, is the great creator deity in the pre-Inca and Inca mythology in the Andes region of South America. Full name and some spelling alternatives are Wiracocha.

    Viracocha god of Incas.Image,jpg
    Viracocha, of Incas.
    Image credit.wiki.

    Tiqsi Huiracocha may have several meanings. In the Quechua language tiqsi means foundation or base, wira means fat, and qucha means lake, sea, or reservoir.Viracocha’s many epithets include great, all knowing, powerful, etc. Wiraqucha could mean “Fat (or foam) of the sea”.

    The name is also interpreted as a celebration of body fat (Sea of fat), which has a long pre-Hispanic tradition in the Andes region as it is natural for the peasant rural poor to view fleshiness and excess body fat as the very sign of life, good health, strength, and beauty.

    Another interpretation of the word is ‘The word ‘Vira’ (वीर) means ‘brave, heroic, powerful, strong’. ‘Kocha’ (कोच) means a ‘man of Mixed Ancestry.

    He reminds of Indra,the Chief of Devas.

    Like Indra Viracocha wields Thunderbolt and the chief Deity among the Incas, pre-Inca Pantheon.

    According to Puranas Indra and Virochana both studied under Prajapathi.

    While Indra advocated the worship of the Atman, The Self as the goal of Life, Virochana worshiped Sarira, the Human Body.

    Hence he was not considered as a Deva in Sanatna Dharma, though his story is narrated in the Puranas and the Ramayana.

    In the Valmiki Ramayan of India, Virochana (Sanskrit: विरोचन), was the first great Asura king with supernatural powers. (Asuras were power seeking deities). The Upanishads say that Virochana and Lord Indra together were taught at the feet of Prajapati. However, contrary to what he was taught, Virochana preached the Asuras to worship the ‘sharira’ (body) instead of the ‘atman’ (absolute consciousness)…

    Scholars say today, the megaliths of South America, such as the Temple of ‘Kalasasaya’ (which houses an idol of Viracocha) in Bolivia, could not have been made without alien help.

    Investigations in Assyrian mythology prove the existence of a tradition in Assyrian history of such a king called Berosus – a distortion of Virochana and Viracocha – as it has often been reiterated ‘b’ and ‘v’ are commutable. According to Swami Vivekananda “the western nations are the children of the great hero Virochana.” (Source: Talks with Vivekananda: Publisher- Advaita Ashram, Mayavati, Himalayas, January 1939.)’

    I have posted about the origin of the Incas as being the Tamils of India.

    The Incas celebrated the Makara Sankaranti in the South Indian Style.

    ‘Most of you in India are familiar with the Charak Puja ceremonial observed in Bengal and several States in South India. This Hindu Ceremonial also observed in Mexicohistorian call it the mexicon and peru. The Spanish Valador ritual. A relief of Bayon central temple of Angkor Thom inCambodia represents a rite similar to the Mexico Valador. The use of parasol (Chhatra) is an age-old sign of royalty and rank in India, Burma, China and Japan. The Maya Astec and the Incas also used it as a sign of royalty. Frescoes of Chak Multum in Yucatan show two types of parasols both of which correspond to types still in use in South-East Asia.’

    Incas celebrated it as “Inti Raymi”

    Makara Sankaranthi in Peru

    For more on this Google Incas ramanan50.

    Reference and citation.

    http://vediccafe.blogspot.in/2012/07/in-valmiki-ramayan-of-india-virochana.html

  • Lord Krishna Present Many Places Same Time Quantum Validates.

    Hindu Puranas/The Ithihasas ,Ramayana and Mahabharata speak of people being present at two different places at the same time. Popular exampe is of Lord Krishna being present ,at the same time, with his 16000 wives.

    On Krishna’s wives,please read my Post.

    The Rasa krida of Krishna.jpg
    Dance sport ,Rasa Krida of krishna

     

    Now Scientists at The University on Bonn have devised a new method of measuring Atoms.

    They have shown that an Atom can be present at two places at the same time!

    Jan 20, 2015 The Bonn team has developed a measurement scheme that indirectly measures the position of an atom. In essence, one looks where the Caesium atom is not. The image clarifies this procedure. Let us assume that two containers are in front of us and a cat is hidden under one of them (a). However, we do not know under which one. We tentatively lift the right jar (b) and we find it empty. We, thus, conclude that the cat must be in the left jar and yet we have not disturbed it. Had we have lifted the left jar instead, we would have disturbed the cat (c), and the measurement must be discarded. In the macro-realist’s world, this measurement scheme would have absolutely no influence on the cat’s state, which remains undisturbed all the time. In the quantum world, however, a negative measurement that reveals the cat’s position, like in (b), is already sufficient to destroy the quantum superposition and to influence the result of the experiment. Credit: Andrea Alberti / http://www.warrenphotographic.co.uk Can a penalty kick simultaneously score a goal and miss? For very small objects, at least, this is possible: according to the predictions of quantum mechanics, microscopic objects can take different paths at the same time. The world of macroscopic objects follows other rules: the football always moves in a definite direction. But is this always correct? Physicists of the University of Bonn have constructed an experiment designed to possibly falsify this thesis. Their first experiment shows that Caesium atoms can indeed take two paths at the same time. Almost 100 years ago physicists Werner Heisenberg, Max Born und Erwin Schrödinger created a new field of physics: quantum mechanics. Objects of the quantum world – according to quantum theory – no longer move along a single well-defined path. Rather, they can simultaneously take different paths and end up at different places at once. Physicists speak of quantum superposition of different paths. At the level of atoms, it looks as if objects indeed obey quantum mechanical laws. Over the years, many experiments have confirmed quantum mechanical predictions. In our macroscopic daily experience, however, we witness a football flying along exactly one path; it never strikes the goal and misses at the same time. Why is that so? “There are two different interpretations,” says Dr. Andrea Alberti of the Institute of Applied Physics of the University of Bonn. “Quantum mechanics allows superposition states of large, macroscopic objects. But these states are very fragile, even following the football with our eyes is enough to destroy the superposition and makes it follow a definite trajectory.” Do “large” objects play by different rules? But it could also be that footballs obey completely different rules than those applying for single atoms. “Let us talk about the macro-realistic view of the world,” Alberti explains. “According to this interpretation, the ball always moves on a specific trajectory, independent of our observation, and in contrast to the atom.” But which of the two interpretations is correct? Do “large” objects move differently from small ones? In collaboration with Dr. Clive Emary of the University of Hull in the U.K., the Bonn team has come up with an experimental scheme that may help to answer this question. “The challenge was to develop a measurement scheme of the atoms’ positions which allows one to falsify macro-realistic theories,” adds Alberti. The physicists describe their research in the journal Physical Review X: With two optical tweezers they grabbed a single Caesium atom and pulled it in two opposing directions. In the macro-realist’s world the atom would then be at only one of the two final locations. Quantum-mechanically, the atom would instead occupy a superposition of the two positions. “We have now used indirect measurements to determine the final position of the atom in the most gentle way possible,” says the PhD student Carsten Robens. Even such an indirect measurement (see figure) significantly modified the result of the experiments. This observation excludes – falsifies, as Karl Popper would say more precisely – the possibility that Caesium atoms follow a macro-realistic theory. Instead, the experimental findings of the Bonn team fit well with an interpretation based on superposition states that get destroyed when the indirect measurement occurs. All that we can do is to accept that the atom has indeed taken different paths at the same time. (more…)