The 250-million-year-old date for the Permian extinction, obtained recently by sophisticated radiometric techniques, was known in India before these techniques were developed in the West.
Professor Ludo Rocher of the University of Pennsylvania and many other Sanskrit scholars have claimed that newly-discovered manuscripts of the Puranas, which have been rigorously dated to the medieval centuries, are substantially different from the currently-circulating Puranas. For example, a few years ago, a new manuscript of the Skanda Purana was found in Nepal and dated at 810 A.D. These scholars claim that this manuscript is entirely different from the versions of the Skanda Purana that have been circulating in South Asia from the time of the colonial era. The scholars further claim that four more newly-discovered manuscripts of the Skanda Purana are substantially different from each other. The scholars conclude that this Purana has undergone major editing on at least two occasions. The first occasion was probably before the 12th century, and the second one was sometime in the 15th-16th century. The scholars claim to have evidence that similar changes have occurred in the other Puranas over the centuries. A few of the numerous articles and books written by these scholars include: Rocher, L. “Origin and Growth of the Puranic Text Corpus, With Special Reference to the Skanda Purana,” Journal of the American Oriental Society, volume 125, pages 568-569, 2005; Rocher, L. The Puranas, Otto Harrassowitz Verlag, 1986; Hazra, R. “Discovery of the genuine Agneya Purana, Journal of the Oriental Institute Baroda, volume 4-5, pages 411-416, 1956.
The key point is, even these scholars admit that the most recent editing of the Puranas occurred before the development of radiometric dating in the 20th century. Dates for significant geological and paleontological events in the history of the Earth are recorded in the Puranas. When these dates are multiplied by a factor of two, they closely agree with dates for these events obtained by modern, sophisticated, radiometric dating techniques. An explanation for this factor of two is discussed below.
It is important to recognize that modern radiometric dating techniques are the culmination of hundreds of years of painstaking developments in European physics and chemistry. There is overwhelming historical evidence that such developments never occurred in India (or anywhere other than in Europe during the last few centuries). Therefore, the most rational explanation for the close agreement between Puranic dates and those obtained by radiometric dating is revelation by superhuman beings to Indian savants prior to the development of radiometric dating in the West. As discussed below, analysis of the motives for this revelation indicates that these superhuman beings are servants of a Supreme Being.
We begin with the dating of the primordial global ocean described in Puranic texts and those of modern geology. According to Srimad-Bhagavatam, at the beginning of each Day of Brahma, the earth is entirely covered with water (SB 3.11.28-31). The beginning of the current Day of Brahma occurred nearly two billion years ago. The reference (SB 3.11.28-31) means verses 28 through 31 of Chapter 11 of the Third Canto of Srimad-Bhagavatam. The original Sanskrit (with word-for-word translation into English) of the entire Srimad-Bhagavatam is now available for free at www.vedabase.com
Geologists say that the Earth formed around 4.5 billion years ago but was too hot for oceans to stably exist until approximately 4 billion years ago, when the Earth was completely covered with water for the first time. Both Srimad-Bhagavatam and modern geology agree that continents didn’t emerge until later. Both agree that, after continents emerged, they gradually began to dominate the Earth’s surface, which means that the ratio of land to water steadily increases over billions of years, culminating in the future in the complete absence of oceans.
Paleontologists have identified a number of mass extinctions in Earth history, such as the one that wiped out the dinosaurs approximately 65 million years ago. Out of all these extinctions, the one that paleontologists unanimously agree is by far the most severe was that which occurred at the end of the Permian period. So severe was this extinction that paleontologist D.H. Erwin wrote that life on earth nearly ended at that time (Erwin, D.H., Extinction: How Life on Earth Nearly Ended 250 Million Years Ago (Princeton University Press, 2006). According to Srimad-Bhagavatam, by far the most severe pralaya (mass extinction) in this Day of Brahma is that which occurred at the end of the Caksusa Manvantara, 124 million years ago. This number is obtained by noting that, according to Puranic chronology, we are now 5,000 years into the Kali-yuga of the 28th divya-yuga of the next Manvantara (which is called the Vaivasvata Manvantara), each divya-yuga (consisting of the four yugas Satya, Dvapara, Treta and Kali) lasts 4.32 million years, Kali-yuga lasts 432,000 years, and two Manvantara-sandhyas (each of 1.78 million-year duration) must be added in to bring us back to the end of the Caksusa Manvantara, as required to compare with the modern Western dating of this extinction event, which refers to the end of the Permian period. This pralaya at the end of Caksusa Manvantara is described in the following references (SB 1.3.15, 8.24.10, 8.24.32, 8.24.33, 8.24.37).
Both Srimad-Bhagavatam and modern astrophysics agree that the energy output of the sun will increase in the future, giving rise to an increase in the temperature of the Earth and, thereby, destroying all life on Earth. According to Srimad-Bhagavatam, at the end of this Day of Brahma (SB 12.4.3), which will occur a little more than two billion years from now, the sun will dry up all the oceans and destroy all life on earth (SB 12.4.8). A summary of Srimad-Bhagavatam is called Krsna Book and abbreviated as KB. The following quote is from Chapter 63 of Krsna Book: “It is said that at the end of creation the sun becomes twelve times more scorching than usual.” The entire text of KB is available for free online: www.vedabase.com/en/kb
What does modern astrophysics have to say about this? An article in Wikipedia sums up the consensus among professional astrophysicists: “Four billion years from now, the increase in the Earth’s surface temperature will cause a runaway greenhouse effect, heating the surface enough to melt it. By that point, all life on the Earth will be extinct,” (Wikipedia: “Future of Earth”).
The Puranic prediction of an increase in the energy output of the sun billions of years in the future is counter-intuitive because all physical energy sources with which we are familiar eventually run out of fuel. Thus, it is reasonable to suppose that the authors of the Puranas would have speculated that the sun would run out of fuel and, hence, decrease its energy output in the future. The increase in energy output of the sun wasn’t discovered until the last few decades due to sophisticated developments in astrophysics. There is overwhelming historical evidence that such developments didn’t occur in India before the last few decades.
Not only does this prediction extend the range of concordance between Western and Puranic dates by four billion years (bringing the total range of concordance up to an impressive eight billion years), it is based on a different branch of physics, namely astrophysics. So, not only do radiometric dates agree with Puranic dates, at least one date based on astrophysics does so as well.
Another concordance is the Puranic Dvapara-yuga-to-Kali-yuga transition date of 5,000 years ago which, when multiplied by two, lines up with the Pleistocene-to-Holocene transition date of 10,000 years ago according to Western chronology. Although this transition is often said to be between 11,000 and 12,000 years ago based on studies conducted in North America and Europe, it may have been closer to 10,000 years ago in India (I am researching this and will report shortly). Both the Puranic account (SB 10.52.2) and modern paleontology agree that this transition was characterized by a reduction in the size of mammals and a global increase in temperature.
How do we account for the factor-of-two difference between Puranic dates and those obtained by modern radiometric dating? Let’s first consider sources of error in radiometric dating. Thousands of papers on radiometric dating have been published by geologists in peer-reviewed, professional journals during the last 50 years. A major theme in these papers is a detailed discussion of sources of error in radiometric dating and ways to circumvent them. Consider, for example, the uranium-lead dating method. In the uranium-lead dating method, each sample actually provides two radiometric clocks, one based on the decay of uranium-235 to lead-207 with a half-life of ~700 million years, and the other based on the decay of uranium-238 to lead-206 with a half-life of ~4.5 billion years. These two clocks provide a built-in cross-check that allows accurate determination of the age of the sample even if some of the lead has leaked out of the sample. Moreover, uranium-lead dating is often performed on the mineral zircon (ZrSiO4) which, at the time of formation, readily incorporates uranium atoms into its crystalline structure as a substitute for zirconium, but strongly rejects lead atoms. Thus, zircon is nearly ideal for radiometric dating because it starts out with uranium already incorporated into its structure but virtually no lead, which is the radioactive decay product in both radiometric clocks. Other desirable features of zircon include: (1) a very high closure temperature, which means that the probability of the clock being reset due to heating at a time after the mineral has formed is very low, (2) resistance to mechanical weathering, and (3) very chemically inert.
A recent, easy-to-read article in a professional, peer-reviewed, scientific journal containing the facts described above regarding zircon and the uranium-lead dating method is: MacDonald, J. “Zircon–Earth’s Timekeeper,” Geology Today, volume 29, 2013.
The 40-Argon/39-Argon dating method provides a check on the potassium-argon method. A recent article on potassium-argon dating and 40-Argon/39-Argon dating in a professional, peer-reviewed, scientific journal is: McDougall, I. “Perspectives on 40-Argon/39-Argon dating,” Geological Society of London, Special Publications, volume 378, pages 9-20, 2014.
Despite these ingenious attempts to circumvent sources of error in radiometric dating, there appears to be no way, at present, to prove that the decay “constants” have actually been constant over long periods of time. Could this account for the factor-of-two difference between radiometric dates and Puranic dates? The problem with this hypothesis is that it is difficult to conceive of a physical mechanism that would change decay constants in such a way as to maintain a constant factor-of-two difference with Puranic dates over billions of years.
My explanation for this constant factor-of-two difference is based on a non-intuitive concept in physics known as “higher-dimensional space.” Since most readers aren’t familiar with this concept, before presenting this explanation, I first introduce the concept of higher-dimensional space.
In a famous lecture at the University of Göttingen on June 10, 1854, Bernhard Riemann revolutionized Western geometry by unveiling his “metric tensor,” which provides a detailed description of the curvature of higher-dimensional space by assigning a collection of numbers to each point in that space. Such a collection is called a “tensor.” For example, Riemann showed that, in four spatial dimensions, a collection of ten numbers is needed at each point to describe the properties of a manifold, regardless of how distorted this manifold is. Riemann’s genius was revealed by his prescient realization that a mathematical framework in terms of higher-dimensional space can unify the seemingly disparate forces of nature, such as gravity, electricity and magnetism. Riemann was the first Western mathematical physicist to realize this. His famous lecture was translated into English, French and other European languages, and had a profound effect on the worldview of Western science.
Michael Faraday had already shown that moving a magnet across a wire can produce an electric current in the wire. It was also known that a wire carrying electric current can cause a nearby compass needle to rotate. Riemann recognized that these phenomena indicate that electricity and magnetism are manifestations of the same force. Riemann’s intense desire to discover the field equations that unify electricity and magnetism was thwarted by ongoing struggle with serious illness. In 1865, James Clerk Maxwell succeeded in unifying electricity and magnetism with his four famous partial differential equations. Maxwell was so brilliant that, based solely on these equations, he predicted the existence of electromagnetic waves in 1865, more than 20 years before they were first produced in the form of radio waves by Heinrich Hertz in 1888. Maxwell realized that light is the visible portion of the electromagnetic spectrum. Maxwell and Riemann are now recognized as two of the greatest mathematical physicists of all time.
Thus, Riemann was the first Westerner to suggest using higher-dimensional space to describe physical reality, predating Einstein by 60 years. In fact, Riemann’s metric tensor turned out to be essential in the development of Einstein’s General Theory of Relativity, which was published in 1915. The central concept in the General Theory of Relativity is that, instead of describing gravity as a force in our familiar three-dimensional space, gravity is the result of curvature in four-dimensional space-time. Thus, force in three-dimensional space can be described in terms of geometry in higher-dimensional space.
Although Einstein’s theory was a major step forward in our understanding of gravity, and Maxwell’s theory was a brilliant synthesis of electricity and magnetism, neither of these theories explained the relationship between gravity and electromagnetic forces. In a letter to Einstein in April 1919, Theodor Kaluza wrote down Riemann’s metric tensor in five dimensions and identified portions of it that correspond to gravitational force and portions of it that correspond to electromagnetic forces. Thus, Kaluza showed that a fifth dimension provides a unified geometrical description of electromagnetism and gravity. This is further confirmation of the brilliant and revolutionary idea that a mathematical framework in terms of higher-dimensional space can unify the seemingly disparate forces of nature. Today, physics is dominated by theories that involve higher-dimensional space, such as String Theory and M-Theory.
Some physicists reject Kaluza’s five-dimensional unification of gravity and electromagnetism because, when it is combined with quantum mechanics, the resulting theory isn’t “renormalizable,” which means that its erroneous prediction that certain physical quantities are infinite can’t be modified to make these quantities take on finite values, which is a requirement for a valid physical theory. However, as shown in my article on quantum mechanics below, the problem is with quantum mechanics and not Kaluza’s brilliant, five-dimensional unification of gravity and electromagnetism. Thus, the fact that Kaluza’s unification doesn’t work with quantum mechanics isn’t a disqualification of Kaluza’s work.
Richard L. Thompson of the Bhaktivedanta Institute, who has a Ph.D. in mathematics from Cornell University, pointed out that the Puranic worldview is implicitly higher-dimensional (Thompson, R. Vedic Cosmography and Astronomy, Bhaktivedanta Book Trust, 1986). The Earth in Srimad-Bhagavatam and the other Puranas is an enormous disc the size of the solar system called, in Sanskrit, “bhu-mandala,” whereas the Earth in the astronomical Siddhantas is a globe ~8,000 miles in diameter, which is the same as that of modern astronomy. (This enormous disc occupies the plane of the ecliptic.) Thus, Indian culture had, for many years, two apparently contradictory ways of viewing the solar system. They are not actually contradictory but are, in fact, complementary: the globe is seen by human beings, whereas the huge disk is seen by superhuman beings, who are introduced later in this article. Thus, space is actually higher-dimensional, but human beings are mislead by their brain and senses into believing that space is three-dimensional.
Instead of dismissing Puranic cosmography as mythological, Thompson proposed that it is actually real but inaccessible to the senses of human beings, which means that it is higher-dimensional. This proposal is supported by the correlation between dates obtained by sophisticated radiometric techniques and dates given in the Puranas.
There is an enormous spatial transformation in going from the Earth that we perceive to the Earth that is described in Srimad-Bhagavatam. Considering this enormous spatial transformation, we should hardly be surprised by the paltry factor-of-two transformation in time that is revealed by the factor-of-two difference between modern radiometric dates and Puranic dates for the same geological and paleontological events. Indeed, Srimad-Bhagavatam (9.3.32) describes a much larger transformation in time between two planets than a mere factor of two. Likewise, the phenomenon of “time dilation” in the Theory of Relativity, induced either by travelling near the speed of light or by high gravitational fields, can be many times larger than a mere factor of two.
In the Theory of Relativity, space and time aren’t independent. Thus, transformations in space are generally accompanied by transformations in time. Since there is an enormous spatial transformation between the Earth of our common perception and the Earth of the Srimad-Bhagavatam, it is not surprising that there is a factor-of-two transformation in time as well.
Although an explicit explanation for this factor-of-two transformation in time has, thus far, eluded me, I am sure that there is a clear and simple explanation for it based on our location on the plane of bhu-mandala and the motion of the sun relative to it, as described in the Fifth Canto of Srimad-Bhagavatam. Therefore, I hereby request the help of Puranic scholars to find this simple and clear explanation, since my understanding of the Fifth Canto of Srimad-Bhagavatam has thus far proven inadequate.
Since the authors of the Puranas didn’t use radiometric dating techniques, how did they acquire such accurate knowledge of the dates of highly-specific events that occurred hundreds of millions of years ago? How did they even know that these events had occurred? Would you be able to figure out, by doing nothing more than walking around and looking at things today, that life on Earth all over the planet nearly ended hundreds of millions of years ago? Hardly! Keep in mind the fact that it took the arduous labor of generations of paleontologists to figure out that life everywhere on Earth was nearly wiped out at some time in the distant past, and it took the arduous work of brilliant physicists to develop the highly-specialized equipment required to obtain radiometric dates for this global extinction. Would you be able to figure out merely by walking around and looking at things today that the Earth was entirely covered with water four billion years ago? I don’t think so! Thus, the most rational explanation is that Indian savants received knowledge from superhuman beings before the rise of modern science. In fact, this is the explanation given in Srimad-Bhagavatam itself. According to Srimad-Bhagavatam, there is a hierarchy of superhuman beings (known by names such as deva, prajapati, rishi and Purusha-Avatara) ranging from the human level up to Krishna’s expansion Maha-Vishnu who, according to Krishna’s order, creates innumerable physical universes. Krishna’s purpose in creating physical universes is to offer us the chance to experience ever-increasing pleasure by rendering loving, devotional service to Him. When this service is performed purely to please Krishna, it evokes overwhelming, transcendental ecstasy in the performer, which attracts Krishna Himself. In fact, Krishna is captivated by the love of His pure devotees, and He reciprocates with them, rendering even more service to them than they render to Him! The most confidential aspect of pure devotional service is that it brings the unlimitedly powerful Lord under the control of His servant. (This is described in detail in the fourth article below.) Thus, there is a purpose to the creation, and Krishna arranges for higher knowledge, including significant events in Earth history and the dates at which they occur, to be disseminated in human society through the medium of books such as Srimad-Bhagavatam.
Further evidence for revelation by superhuman beings is found in the Indian astronomical treatise Surya-siddhanta. In order to appreciate this evidence, we need to know how to calculate the diameter of a planet. The angular diameter of a planet is how large the planet appears from a particular vantage point. The actual diameter of a planet is obtained by simple trigonometry using this angular diameter and the distance from this vantage point to the planet. For example, the moon appears to be about the size of a dime held at arm’s length when viewed from the Earth, but it is actually 2,600 miles in diameter. So, to calculate the actual diameter of the moon, we need to know the angular diameter of the moon and the distance between the Earth and the moon.
The angular diameters of Mercury, Venus, Mars, Jupiter and Saturn are obtained by the simple algorithm listed in verse 7.13 of the Surya-siddhanta, and the orbital circumferences of these planets are listed in verses 12.81-12.87 of the Surya-siddhanta. Although these angular diameters are too large, when they are used with these orbital circumferences (which are too small) to calculate the actual planetary diameters, these diameters agree within a few percent with modern values, which are obtained using powerful, modern telescopes (Thompson, R.L., “Planetary Diameters in the Surya-siddhanta,” Journal of Scientific Exploration, volume 11, 1997).
Apparently, the author of the Surya-siddhanta knew very well the correct diameters of the planets and deliberately made the angular diameters too large in order to be accepted by pre-telescopic (naked-eye) astronomers, all of whom (for thousands of years all over the world) consistently over-estimated the angular diameters of the planets. It is now well known that naked-eye estimation of the diameter of a small, distant source of light (which is how a planet appears to observers based on the Earth) is inevitably inaccurate due to the physiology of the human eye. Thus, naked-eye estimation of the angular diameters of the planets always yields an estimate that is too large. Knowing this, the author of the Surya-siddhanta apparently made the orbital circumferences too small so that the calculation yields the correct diameters of the planets. It is important to recognize that, outside of India, all medieval and ancient planetary diameters (including those of the Greeks, Babylonians and Egyptians) were grossly inaccurate (typically in error by over 100%).
Professor Kripa S. Shukla of the Department of Mathematics at Lucknow University wrote that there is an authentic palm-leaf manuscript (No.XXI.N.8) of the Surya-siddhanta (including the famous commentary written on it by the renowned astronomer Paramesvara) in the Adyar Library in Madras (Shukla, K.S. The Surya-siddhanta with Commentary of Paramesvara, published by the Department of Mathematics and Astronomy, Lucknow University, 1957, Introduction, page 1). This manuscript contains verse 7.13 (Shukla, op. cit. 1957, p.41) and verses 12.81-12.87 (Shukla, op. cit. 1957, p.45).
The Surya-siddhanta must be at least as old as the commentary written on it by Paramesvara. The following academic references provide strong evidence that Paramesvara lived from 1380 to 1460 A.D. Professor Kim Plofker of Brown University described in an article in a professional, peer-reviewed journal “a one-point iterative technique for calculating the Sine of a given angle” presented by Paramesvara (Plofker, K. “An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text,” Historia Mathematica, volume 23, pages 246-256, 1996). In this article, Plofker confirmed that Paramesvara lived from 1380 to 1460 A.D. Another scholar who confirmed that Paramesvara lived from 1380 to 1460 A.D. is Professor R.C. Gupta of the Department of Mathematics at the Birla Institute of Technology (Gupta, R.C. “Paramesvara’s rule for the circumradius of a cyclic quadrilateral,” Historia Mathematica, volume 4, pages 67-74, 1977). Finally, the prestigious Biographical Encyclopedia of Astronomers (published in 2007 by the renowned scientific publisher Springer Verlag, New York, page 870) states that Paramesvara lived from 1380 to 1460 A.D.
It should be noted that, before the rise of modern technology, palm-leaf manuscripts of the Surya-siddhanta and other important works had to be regularly hand-copied to circumvent degradation due to high humidity and temperature in India. Thus, although Professor Shukla wrote that there is an authentic palm-leaf manuscript (No.XXI.N.8) of the Surya-siddhanta (with the commentary of Paramesvara) in the Adyar Library in Madras, we can’t exclude the possibility that this manuscript is a copy of the original made at a later date. Unfortunately, Professor Shukla didn’t provide any evidence (for example, radiocarbon dating) that this manuscript is the original one written by Paramesvara himself. Indeed, Professor Shukla wrote that he examined several different manuscripts of the Surya-siddhanta and noted that they have slightly different verse numbers (Shukla, op. cit. 1957, Introduction, p.2), which indicates that those who copied the manuscripts also edited them. For example, in manuscript (No.XXI.N.8) in the Adyar Library in Madras, verses 12.81-12.87 give the circumferences of the orbits of the planets, whereas in the famous translation by E. Burgess, these circumferences are given in verses 12.85-12.90 (Burgess, E. The Surya Siddhanta, New Haven CT, The American Oriental Society, 1858). In the first of these manuscripts, the 12th chapter has only 87 verses, whereas in the second manuscript, it has 90 verses. Clearly, manuscripts of the Surya-siddhanta have been edited over the centuries. Thus, at present, we can’t entirely exclude the possibility of fraudulent interpolation of verses 7.13 and 12.81-12.87 into the text of the Surya-siddhanta after the first telescope was invented in the Netherlands in the year 1608 A.D., which is the time that sufficiently-accurate planetary data first became available in Europe. The prestigious Reflecting Telescope Optics (published in 2004 by the renowned scientific publisher Springer Verlag, New York) confirms that the first telescope was invented in the Netherlands in 1608 A.D.
Thus, it is important to conduct further research in India to find an authentic manuscript of the Surya-siddhanta that can be rigorously dated to a year that was prior to the year 1608, and this manuscript must contain verses 7.13 and 12.81-12.87. If this can be achieved, then the level of accuracy of the diameters of the planets calculated from the information in verses 7.13 and 12.81-12.87 of the Surya-siddhanta strongly supports the hypothesis that these diameters were not obtained by Earth-based observation but, instead, were revealed by the superhuman beings described above.
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Although the evidence discussed in this article makes a strong case that superhuman beings actually exist and revealed sophisticated knowledge to Indian savants, where is the evidence for Krishna (God) Himself? The evidence is found in analyzing the motive for this revelation. History shows that, whenever a technologically superior culture encountered an inferior culture, the superior culture exploited the inferior culture. Three well known examples are: (1) when the Europeans came to Africa and saw the inferior technology of the Africans, they brutally exploited and enslaved them; (2) when the Spanish Conquistadors came to Central and South America five centuries ago, they brutally conquered the native American Indians and confiscated hundreds of pounds of their gold; (3) when British settlers encountered native American Indians in North America, they ruthlessly forced them to move west, ultimately taking away all their land and confining them to “reservations.” So, it’s reasonable to suppose that there is no motivation for superhuman beings to specifically reveal knowledge of planetary diameters, as well as geological, paleontological, and astrophysical events (and their dates of occurrence) to Earthlings unless these superhuman beings are under a higher authority who orders them to reveal it. Superhuman beings who wished to be worshiped as gods by the ancients needed to do nothing more than simply display their powers; there was no need to reveal this kind of detailed and specific knowledge. Superhuman beings who simply wished to exploit the ancients also had no need to reveal this kind of detailed and specific knowledge. Moreover, there is no record in the Srimad-Bhagavatam or Surya-siddhanta of exploitation by the superhuman beings who revealed this knowledge. The revelation of this kind of knowledge only makes sense in a religious context, in other words in a context in which God is revealing specific knowledge that helps human beings to reawaken their loving relationship with Him. One of the major themes of Srimad-Bhagavatam is the undesirable nature of the physical world, which is full of suffering in the form of old age, disease, death, rebirth and envious dealings between materially-motivated people. Since Krishna (God) is very compassionate and doesn’t want us to suffer unnecessarily in this physical world, He desires that we read about the inevitable sufferings of this world in Srimad-Bhagavatam, Bhagavad-gita and similar revealed scriptures, along with the overwhelmingly great pleasure of rendering pure devotional service to Him. Thus, the superhuman beings who revealed this knowledge to the ancient Indians are His servants, and they act according to His orders.
I welcome all serious correspondence. I can be reached at Lenantak at ggmmaaiill dot com. I have written it in this way to confound unscrupulous advertisers, especially machines. It will be clear to human beings how to reach me.