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- The dreadful apport
- Some ruminations on asteroids and meteoritic falls
- Comet C/2022 E3 (ZTF)
- The Vyomavyāpin in the Pāśupata-tantra and a discursion on nine-fold Rudra-mantra-s
- Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x
- Origins of the serpent cult and Bhāguri’s snake installation from the Sāmaveda tradition
- Two simple stotra-s, sectarian competition, and the Varāha episode from the archaic Skandapurāṇa
- The zombie obeys: a note on host manipulation by parasites and its ecological consequences
- Cārucitrābhisambodhi
- RV 10.78
- The turning of the yugacakra
- A sampler of Ramanujan’s elementary results and their manifold ramifications
- A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
- The wink of the Gorgon and the twang of the Lyre
- Some poems
- The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā
- Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
- Vikīrṇā viṣayāḥ: India and the Rus
- Alkaios’ hymn to the Dioskouroi: Hindu parallels
- Some notes on the Indo-European aspects of the Anatolian tradition
- The death of Miss Lizzie Willink
- Indo-European expansions and iconography: revisiting the anthropomorphic stelae
- Geopolitical summary: March 2022
- Human retroviruses, sociology of science, and biographical ruminations
- Transcripts of conversations: the addiction principle:
- Phantom impressions-1
- A note on Śrī, Viṣṇu and śṛṅgāra
- Are civilizational cycles the norm?
- On the rise of the mātṛkā-s and the goddess Cāmuṇḍā
- Huns, Uralics, and empires of the steppe
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Search this Blog
Archives
mAnasa-taraMgiNI supplement
- The number of RTs the original twt shows the H in rather dim light twitter.com/goghritaM/stat… 6 hours ago
- A long story if you'd like to read: The dreadful apport manasataramgini.wordpress.com/2023/04/02/the… 6 hours ago
- BRICS to bricolage? 7 hours ago
- RT @blog_supplement: Some ruminations on asteroids and meteoritic falls manasataramgini.wordpress.com/2023/02/20/som… 7 hours ago
- It looks as though after a brief respite with the vi-grahaNa by muShkavAn kastUrI, the "algorithm" has caught up with our account recently. 2 days ago
Top Posts
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Recent Posts
- The dreadful apport
- Some ruminations on asteroids and meteoritic falls
- Comet C/2022 E3 (ZTF)
- The Vyomavyāpin in the Pāśupata-tantra and a discursion on nine-fold Rudra-mantra-s
- Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x
- Origins of the serpent cult and Bhāguri’s snake installation from the Sāmaveda tradition
- Two simple stotra-s, sectarian competition, and the Varāha episode from the archaic Skandapurāṇa
- The zombie obeys: a note on host manipulation by parasites and its ecological consequences
- Cārucitrābhisambodhi
- RV 10.78
- The turning of the yugacakra
- A sampler of Ramanujan’s elementary results and their manifold ramifications
- A catalog of attractors, repellors, cycles, and other oscillations of some common functional iterates
- The wink of the Gorgon and the twang of the Lyre
- Some poems
- The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā
- Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
- Vikīrṇā viṣayāḥ: India and the Rus
- Alkaios’ hymn to the Dioskouroi: Hindu parallels
- Some notes on the Indo-European aspects of the Anatolian tradition
- The death of Miss Lizzie Willink
- Indo-European expansions and iconography: revisiting the anthropomorphic stelae
- Geopolitical summary: March 2022
- Human retroviruses, sociology of science, and biographical ruminations
- Transcripts of conversations: the addiction principle:
- Phantom impressions-1
- A note on Śrī, Viṣṇu and śṛṅgāra
- Are civilizational cycles the norm?
- On the rise of the mātṛkā-s and the goddess Cāmuṇḍā
- Huns, Uralics, and empires of the steppe
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April 2023 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Category Archives: Heathen thought
The dreadful apport
Vrishchika had just finished her work on the diagnosis and possible treatment plan for a pediatric neurological patient on whom she was consulted. She had inferred that the child’s condition arose from a mutation in the TANC2 gene and it … Continue reading
Posted in art, Heathen thought, History, Life
Tagged ancient Hindu thought, fake science, fake scientist, religion, Story
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Comet C/2022 E3 (ZTF)
The dispiriting cloud cover lifted briefly on two nights (Wed 8/2/2023 and Fri 10/2/2023) finally giving us an opportunity to catch the latest Agni-putra-ketu in the welkin, Comet C/2022 E3 (ZTF). On the first night, there was still some haze, … Continue reading
Posted in Heathen thought, Life, Scientific ramblings
Tagged astronomy, Comet, Comet C/2022 E3 (ZTF), Hindu knowledge, Hindu ritual
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The Vyomavyāpin in the Pāśupata-tantra and a discursion on nine-fold Rudra-mantra-s
The Pāśupata-tantra is a poorly understood śaiva text that is believed to be affiliated with the Pāśupata tradition of Lakulīśa. While the colophons of some manuscripts present it as “Lakulīśa-pravartita-Pāśupata-tantram”, internally, it presents itself as a teaching of Nandin to … Continue reading
Posted in Heathen thought, Life
Tagged ancient Hindu thought, Hindu, Indo-Aryan, Indo-European, Indo-Iranian, kaula, mantra, mantra-sAdhana, mantra-shAstra, pA~ncharAtra, religion, rudra, saiva, shaiva, shiva, tantra, tantra age
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Bhāskara-II’s polygons and an algebraic approximation for sines of pi by x
Unlike the Greeks, the Hindus were not particularly obsessed with constructions involving just a compass and a straightedge. Nevertheless, their pre-modern architecture and yantra-s from the tāntrika tradition indicate that they routinely constructed various regular polygons inscribed in circles. Of … Continue reading
Origins of the serpent cult and Bhāguri’s snake installation from the Sāmaveda tradition
Mathuran Nāga installations From the few centuries preceding it down to the first few centuries of the Common Era we see numerous installations of snake deities, i.e., Nāga-s, at various archaeological sites throughout northern India (most famously at the holy … Continue reading
Posted in Heathen thought, History
Tagged ancient Hindu thought, atharvaveda, balabhadra, Hindu, Indo-Aryan, mahAbharata, mantra, mantra-sAdhana, mantra-shAstra, religion, Rigveda, Samaveda, saMkarShaNa, shiva, snake, tantra, tantra age, tantras, vaiShNava, Veda, viShNu, Yajurveda
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Two simple stotra-s, sectarian competition, and the Varāha episode from the archaic Skandapurāṇa
The Ur-Skandapurāṇa (SkP) or the “archaic” Skandapurāṇa ( the Bhaṭṭārāi edition known as the Ambikā-khaṇḍa) is a Śaiva text with affinities to the Pāśupata branch of that tradition. Though it is aware of the mantra-mārga traditions like the Mātṛ-tantra-s and … Continue reading
Posted in Heathen thought
Tagged gods, Hindu, Hindu knowledge, Hindu ritual, indra, kumAra, narasimha, nR^isiMha, padma purana, purAna, purANas, rudra, saiva, shaiva, shiva, skanda, skandapurANa, vaiShNava, vamana, vamAna-purANa, varAha, viShNu
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RV 10.78
RV 10.77 and 10.78 are similarly themed sūkta-s to the Marut-s by our ancient clansman Syūmaraśmi Bhārgava. He is mentioned twice by authors within the RV – in RV 1.112.16 by Kutsa Āṅgirasa and in RV 8.52.2 by Āyu Kāṇva. … Continue reading
Posted in Heathen thought
Tagged ancient Hindu thought, atharvaveda, Greek, Hindu, Indo-Aryan, Indo-European, Indo-Iranian, marut-s, Rigveda, rudra, skanda, skandapurANa, Veda
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The wink of the Gorgon and the twang of the Lyre
The discovery of the archetypal eclipsing binary Algol The likes of Geminiano Montanari are hardly seen today. This remarkable Italian polymath aristocrat from the 1600s penetrated many realms of knowledge spanning law, medicine, astronomy, physics, biology and military technology. Having … Continue reading
Posted in Heathen thought, History, Scientific ramblings
Tagged Algol, astronomy, beta Lyrae, eclipsing binary, gravity, physics, stars, variable stars, W Ursae Majoris
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The Kaumāra cycle in the Skandapurāṇa’s Śaṃkara-saṃhitā
Many khaṇḍa-s, māhātmya-s and saṃhitā-s attach themselves to the sprawling “Mega-Skandapurāṇa”. We use this term to distinguish it from the “Ur-Skandapurāṇa”, which was first published by Bhaṭṭārāi in the late 1980s and is now known to survive as three related … Continue reading
Posted in Heathen thought
Tagged gods, heathen, Hindu, Hindu ritual, karttikeya, kaumAra, kaumAra ritual, kumAra, kumArasaMbhava, mantra, purAna, purANas, rudra, saiva, shaiva, shiva, shiva purana, skanda, skandapurANa, tantra, tantras, viShNu
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Alkaios’ hymn to the Dioskouroi: Hindu parallels
In this note we shall see how even a short “sūkta” of the yavana Alkaios to the Dioskouroi (individually named Kastor and Polydeukes), the Greek cognates of the Aśvin-s, offers several parallels to the Hindu tradition in the Veda. In … Continue reading
Posted in Heathen thought
Tagged ashvins, Greek, Greek thought, Hindu knowledge, Hindu ritual, Indo-Aryan, Indo-European, Rigveda, Roman, Veda
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Phantom impressions-1
Lootika had gotten her kids engaged with the beauty of the connections between multiplication tables, division and geometry. Leaving them to their labors, she went over to Somakhya’s desk to bring him to join her for the afternoon tea. Lootika … Continue reading
A note on Śrī, Viṣṇu and śṛṅgāra
yaḥ pūrvyāya vedhase navīyase sumaj-jānaye viṣṇave dadāśati । yo jātam asya mahato mahi bravat sed u śravobhir yujyaṃ cid abhy asat ॥ RV 1.156.2 Whoever repeatedly performs rituals to the wise one to the ancient and the new one, Viṣṇu, … Continue reading
Posted in Heathen thought
Tagged ancient Hindu thought, goddesses, gods, Hindu, Hindu ritual, Indo-Aryan, Indo-European, religion, Rigveda, Veda, vedic, viShNu
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On the rise of the mātṛkā-s and the goddess Cāmuṇḍā
The roots of the mātṛkā-s in the śruti and the Kaumāra tradition The standard list of 7/8 goddesses known as the mātṛkā-s is a hallmark feature of the classical religion: Brāhmī, Māheśvarī, Kaumārī, Vaiṣṇavī, Vārāhī, Indrāṇī, Cāmuṇḍā, sometimes with the … Continue reading
Posted in Heathen thought, History
Tagged bhairava, bhairava temple, erotic, evolution of religions, goddesses, gods, Hindu, Hindu ritual, kaula, kaumAra ritual, kumAra, mantra, mantra-sAdhana, mantra-shAstra, mathurA, mAtR^ikA, matsya purANa, religion, ritual, rudra, saiva, seven goddesses, shaiva, shakta, shatarudrIya, shiva, temple, twelve goddess
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Huns, Uralics, and empires of the steppe
A map by Savelyev et al. for the geographic orientation of the reader of the below article. The Huns of Europe “The lord of the Huns, King Attila, born of his father Mundzuk, lord of the bravest tribes, who with … Continue reading
Subjective and objective insight
The black American scientist Sylvester Gates mentioned a curious personal anecdote in a talk. To paraphrase him, when he was in college, he had to take a calculus course. He mentioned how he could cut through differentiation as it was … Continue reading
Posted in Heathen thought, History, Life, Scientific ramblings
Tagged consciousness, DMT, first-person, ghosts, history of science, mathematics, objective, subjective
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The Rāmāyaṇa in numbers: meters, sarga- and kāṇḍa- structure
In the extant Indo-European textual corpus, only in the Hindu collection do we find two complete early epics to complement the śruti. The Iranian epics come from a much later age than the core Avestan corpus, and in the Greek … Continue reading
Posted in Heathen thought, History
Tagged epics, Hindu, Indo-Aryan, Indo-European, Indo-Iranian, kavI, kAvya, rAmAyaNa
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Sneha, snowstorms, the sun and the moon in enigmatic ṛk-s
That the Indo-European homeland was a cold place with snow is evidenced by widespread survival of two hon-homologous words for snow. Recently, a discussion on one of these words, sparked by some linguist, landed on my timeline on Twitter. From … Continue reading
Posted in Heathen thought, History
Tagged astronomy, atharva veda, atharvaveda, gods, Hindu, Hindu knowledge, Hindu ritual, Indo-Aryan, Indo-European, Indo-Iranian, indology, linguistics, Rigveda, Sanskrit, Veda, vedic, Yajurveda
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The strange case of the Āpastamba sprite
This is the second of the two stories that arose from incidents during the visit of Yaśaśravas, Somakhya’s cousin. With the autumnal vacations, Somakhya was having a good time with his visiting cousin, giving him lectures on the theory and … Continue reading
Agni as the divine commander in the Veda and the Purāṇa
With the Sākamedha-parvan with the oblations to Agni Anīkavat having just passed, we present a brief note on Agni as the general of the deva army. Agni is presented as the commander of the deva-s in the brāhmaṇa literature. For … Continue reading
Posted in Heathen thought, History
Tagged agni, Aryan, atharva veda, atharvaveda, brahmana, gods, harivaMsha, Hindu, Hindu ritual, Indo-Aryan, Indo-European, kaumAra ritual, purAna, purANas, Rigveda, ritual, soma ritual, Veda, vedic, Yajurveda
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The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
This note has its origin in a conversation with Sharada. We originally intended to incorporate the core of it into one of our usual fantastical stories. However, following a second conversation with her, we decided that it might be best … Continue reading
Some biographical reflections on visualizing irrationals
In our childhood, our father informed us that, though the school told us that , it was not valid. However, he added that for “small fractions” [Footnote 1] it was a great approximation. Moreover, the numerical problems, which we would … Continue reading
Turagapadādi
This note stems from a recent conversation with a friend, where he pointed out that the graph representing all possible positions the horse (knight) can take on the chessboard from a given starting square produces interesting graphs. It struck us … Continue reading
Twin Āditya-s, twin Rudra-s
This note originated as an intended appendix to the article on Rudra and the Aśvin-s we published earlier. The first offshoot from that work, which we published separately, explored the links between Rudra, Viṣṇu and the Aśvin-s in the śrauta … Continue reading
Posted in Heathen thought
Tagged ancient Hindu thought, atharva veda, atharvaveda, evolution of religions, gods, Hindu, Hindu ritual, Indo-Aryan, Indo-European, Indo-Iranian, religion, Rigveda, saiva, Veda, vedic, Yajurveda
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Bhairavānanda’s wicks: a retelling
It was early in the school year and the last class for the week, the English class. The students were restless as the sea at the time of the tide from the pull of the impending weekend. For the first … Continue reading
Some further notes on the old Mongol religion-2
O fire mother, whose father is flint, whose mother is pebble, whose meal is yellow feather grass, whose life is an elm tree. An incantation to the Fire Goddess Ghalun-eke; translation from the Mongolian by Yönsiyebü Rinchen This note revisits … Continue reading
Posted in Heathen thought, History
Tagged bauddha, buddha, buddhism, buddhist, China, Chinese belligerence, Chinese incursion, Ching, Chinggis Khan, evolution of religions, Hindu, Khan, Mongol, Mongol religion, Mongolia, Mongols, ritual
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Some talks at the Indic Today portal
We had a chat with with C Surendranath, Contributing Editor and (in part with) Yogini Deshpande, Editor in Chief of Indic Today. It is divided into four parts: 1) https://www.indictoday.com/videos/manasataramgini-civilization-counter-religion-continuity-collapse-i/ A few clarifications for this part: 1) We do not … Continue reading
Posted in Heathen thought, History, Politics
Tagged Abrahamism, Abrahamistic vandalism, ancient Hindu thought, China, Ching, Chinggis Khan, Hindu, India, Japan, religion, Russia, world history, World War 2
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Matters of religion: Varuṇāvasiṣṇavam, Agnāvasiṣṇavam and the vyahṛti-s
Like the clouds lifting after the monsoonal deluge to unveil the short-lived comforts of early autumn, the metaphorical pall over the nation cast by the engineer’s virus was lifting. Somakhya and Lootika were at the former’s parents’ house, relieved that … Continue reading
Posted in Heathen thought
Tagged atharva veda, atharvaveda, evolution of religions, goddesses, gods, Hindu, Hindu knowledge, Hindu ritual, Indo-Aryan, Indo-European, Indo-Iranian, marut-s, religion, Rigveda, rudra, Samaveda, skanda, Story, Veda, vedAnta, vedic, viShNu, Yajurveda
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The phantoms of the bone-pipe-2
Vidrum had been introduced to a synesthetic patient by a neurologist colleague. The patient’s manifestation of synesthesia left a rather profound impact on him; thus, when he had a break of an hour in his duties, wanting to explore the … Continue reading
Posted in art, Heathen thought, Life
Tagged biochemistry, chemistry, death, ghost, ghosts, pandemic, Story
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Making an illustrated Nakṣatra-sūkta and finding the constellation for a point in the sky
The illustrated Nakṣatra-sūkta Towards the latter phase of the Vedic age, multiple traditions independently composed sūkta-s that invoked the pantheon in association with their home nakṣatra-s as part of the śrauta Nakṣatreṣṭi or related gṛhya homa-s. Of these oldest and … Continue reading
Posted in art, Heathen thought, History, Scientific ramblings
Tagged astronomy, atharva veda, atharvaveda, globular clusters, history of science, nakShatra-s, nebula, nebulae, Rigveda, stars, Veda, vedic, Yajurveda
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Johannes Germanus Regiomontanus and his rod
Even before we had become acquainted with the trigonometric sum and difference formulae or calculus are father had pointed to us that there was an optimal point at which one should stand to observe or photograph features on vertical structures, … Continue reading
A great statistician, and biographical, numerical musings on ancient game
Recently my friend brought it to my attention that C. Radhakrishna Rao had scored a century. Born in 1920 CE to Doraswamy Nayadu and A. Laxmikanthamma from the Andhra country, he is one of the great mathematical thinkers and statisticians … Continue reading
Huntington and the clash: 21 years later
This note is part biographical and part survey of the major geopolitical abstractions that may be gleaned from the events in the past 21 years. Perhaps, there is nothing much of substance in this note but an uninformed Hindu might … Continue reading
Posted in Heathen thought, History, Life, Politics
Tagged Abrahamism, Abrahamistic vandalism, Chinese belligerence, Chinese incursion, clash of civilizations, Hindu, India, mlechCha, war
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The phantoms of the bone-pipe
As Vidrum was leafing through some recent case studies to gather the literature for his own production, he received a call from his chauffeur. He had fetched Vidrum’s new car. Vidrum went out to take a look at it. As … Continue reading
Posted in Heathen thought, History, Life
Tagged bhairava, bhairava temple, death, ghost, ghosts, gupta, Hindu ritual, kaumAra ritual, mAtR^ikA, Rigveda, ritual, skanda, Story, upanisad, upaniShad, Veda, vedAnta
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Some notes on the Brahmayajña brāhmaṇa and Uttama-paṭala of the Atharvaṇ tradition
PDF version The Brahmayajña brāhmaṇa (1.1.29 of the Gopatha-brāhmaṇa) of the Atharvaveda provides a glimpse of the Vedic saṃhitā canon as known to the brāhmaṇa authors of the AV tradition. The Brahmayajña might be done as part of the basic … Continue reading
Posted in Heathen thought, History
Tagged atharva veda, atharvaveda, brahmana, Indo-Aryan, Indo-European, Indo-Iranian, Rigveda, Samaveda, Sanskrit, Veda, vedAnta, vedic, Yajurveda
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Yajus incantations for the worship of Rudra from the Kāṭhaka ritual manuals
This article is available as a pdf document. The notes from it are appended below. The loss of the northern and northwestern Kṛṣnayajurveda traditions due to the Mohammedan depredations of Northern India (aided an abetted by the predatory Anglospheric regimes) … Continue reading
Posted in Heathen thought, History
Tagged atharva veda, atharvaveda, Indo-Aryan, Indo-European, Indo-Iranian, Kashmir, kaTha, Rigveda, rudra, Samaveda, shatarudrIya, Veda, vedic, Yajurveda
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RV 10.5
The Ṛgveda is replete with obscure sūkta-s but RV 10.5 might easily take a place in the top tier of those. One might even ask why even attempt to write a commentary on this. We admit we could be plainly … Continue reading
Posted in Heathen thought
Tagged Aryan, atharva veda, atharvaveda, evolution of religions, gods, Greek, Greek thought, Indo-Aryan, Indo-European, Indo-Iranian, Iranian, mantra, mantra-sAdhana, mantra-shAstra, religion, Rigveda, Veda, vedAnta, vedic
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Bṛhaspati-śanaiścarayor yuddham-2020 ityādi
The below is only for information. Parts of it should not be construed as any kind of prognostication on our part. The great Hindu naturalist Varāhamihira describes various kinds of planetary conjunctions or grahayuddha-s in his Brihatsaṃhitā (chapter 17) thus: … Continue reading
Posted in Heathen thought, History, Scientific ramblings
Tagged astronomy, constellations, geometry, Greek, Greek thought, Hindu knowledge, Hindu science, planets, sky, stars
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Bhāskara’s dual square indeterminate equations
PDF for convenient reading Figure 1. Sum and difference of squares amounting to near squares. In course of our exploration of the bhūjā-koṭi-karṇa-nyāya in our early youth we had observed that there are examples of “near misses”: . Hence, we … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged arithmetic, bhAskara, Euler, fibonacci, figurate numbers, Geometric construction, geometry, Hindu knowledge, Hindu mathematics, history of science, irrational numbers, line, mathematics, numbers, Pythagorean triples, recreational geometry, square, square root, squares
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Counting pyramids, squares and magic squares
Figure 1. Pyramidal numbers The following note provides some exceedingly elementary mathematics, primarily for bālabodhana. Sometime back we heard a talk by a famous contemporary mathematician (M. Bhargava) in which he described how as a kid he discovered for himself … Continue reading
The tale of the dolmen-dweller
The exams were over and the last semester of toil was all that stood between Vidrum and the dim glimmer he saw at the end of his metaphorical tunnel. He finally had some free time that he wished to savor … Continue reading
Posted in art, Heathen thought, Life
Tagged Army of Islam, communism, ghost, ghosts, Marxism, social parasitism, socialism, society, Story
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Matters of religion-4
Pinakasena was visiting Somakhya and Lootika. He was seeking instruction on the Sadyojāta-mantra from his hosts: “O Ātharvaṇa and Śāradvatī, I wish to learn the rahasya-s pertaining to the deployment of the Sadyojāta-mantra to the great god Kumāra, the patron … Continue reading
Posted in Heathen thought
Tagged evolution of religions, goddesses, kaumAra ritual, kumAra, kumArasaMbhava, religion, rudra, skanda, Story, twelve goddess
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Generalizations of the prime sieve and Pi
PDF version for better reading Eratosthenes, the preeminent yavana philosopher of early Ptolemaic Egypt [footnote 1], composed a hymn to the god Hermes of which only some fragments have come down to us. This connection to Hermes is evidently related … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged approximation for pi, circle, geometry, Greek, Greek thought, mathematical entity, mathematics, numbers, pi, prime numbers, sequence
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Rāsabha-nyāya-śikṣā
Vrishchika had been seeing several kids of patients affected by the chemical leak that had happened sometime ago. While she saw some purely for routine clinical practice, she was also particularly interested in the several cases exhibiting heterotaxy and had … Continue reading
Notes on miscellaneous brāhmaṇa passages from the Yajurveda
The upasthāna ritual is performed to let the sacrificial fire remain in residence after the primary oblations are complete. In the triple-fire śrauta rite this is done at the āhavanīya altar with several incantations specified in the saṃhitā-s of the … Continue reading
Posted in Heathen thought, History
Tagged Hindu, Hindu knowledge, Hindu mathematics, Hindu ritual, religion, Rigveda, ritual, Veda, vedic, Yajurveda
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Snatches
Vidrum had called on his friends Somakhya and Lootika on a quiet afternoon to accompany him for a climb on the trails of Vidrumavistāra that lay beyond Viṣṭhaparvata. The fierce fighting arising from a surprise ghazvat of the makkha-viṣaya-dānava-s had … Continue reading
Posted in Heathen thought, History, Life
Tagged fiction, Hindu knowledge, history of science, knowledge production, knowledge systems, Story
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The Aśvin-s and Rudra
The twin Aśvin-s and Rudra are both Indo-Aryan reflexes of two deity-classes which can be reconstructed as likely being present in the Proto-Indo-European religion. Both are likely to have even deeper roots going back to even earlier religious traditions across … Continue reading
Posted in Heathen thought, History
Tagged archaeology, ashvins, astronomy, atharva veda, atharvaveda, Hindu, Indo-Aryan, Indo-European, religion, Rigveda, Veda, vedic, Yajurveda
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The roots of Vaiṣṇavam: a view from the numerology of Vedic texts
While glorified with a 1000 names in the famous stotra of the early Sātvata tradition of the Mahābharata, in the texts of an even earlier period the god primarily went under that name Viṣṇu. Indeed, even the litany of the … Continue reading
Posted in Heathen thought, History
Tagged Hindu, Hindu ritual, Hindus, Indo-Aryan, Indo-European, Indo-Iranian, Iranian, religion, vaiShNava, viShNu
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Matters of religion-3
Lootika seeing Somakhya contemplating something remarked: “That great clash of men is upon us, where, as the śruti says, our flag will be mingled with that of the enemy in close combat.” Somakhya: “It’s almost as if your mind is … Continue reading
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Tagged atharva veda, atharvaveda, Hindu, Hindu ritual, Indo-Aryan, Indo-European, Indo-Iranian, Iranian, religion, Rigveda, ritual, Story, Veda, vedic, Yajurveda
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Some Nārāyaṇa-like convergents and their geometric and trigonometric connections
While playing with an iterative geometric construction in our youth we discovered for ourselves a particular right triangle whose sides are in the proportion , where is the Golden Ratio. This triangle is of course famous as being the basis … Continue reading
The minimal triangle circumscribing a semicircle
Consider a fixed semicircle with center at and radius . Let be the isosceles triangle which circumscribes it (Figure 1). Figure 1 What will be the characteristics of the minimal form of the said triangle, i.e. triangle with minimum perimeter, … Continue reading
A modern glance at Nārāyaṇa-paṇḍita’s combinatorics-1
For improved reading experience one may use the PDF version. Students of the history of Hindu mathematics are well-acquainted with Nārāyaṇa-paṇḍita’s sophisticated treatment of various aspects of combinatorics and integer sequences in his Gaṇita-kaumudī composed in 1356 CE. In that … Continue reading
Kaiṭabha, poison and death: meanderings through tradition
For better reading try PDF version The medical Suśruta-saṃhitā, kalpasthāna, chapter 3 contains an unusual mythologem about the origin of poison. It clearly belongs to the Prājāpatya tradition and presents some unusual features. It presented in full below: prajām imām … Continue reading
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Tagged atharvaveda, brahmA, brahmana, death, Hindu, poison, religion, Rigveda, Samaveda, Veda, vedic, Yajurveda
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Big fruits and dead giants
The fruits of the elephants nāgo bilvam ivākramya pothayiṣyāmy ahaṃ śiraḥ | alabhyām icchatas tasya kīcakasya durātmanaḥ || Like an elephant seizing a bilva [fruit] I will crush the head of that evil Kīcaka who desires that which ought not … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged elephant, extinction, fossils, human existence, mammoths, mastodonts, megafauna, Megatherium, proboscidea, proboscidean, sloths
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Pearl necklaces for Maheśvara
Śrīpati’s pearl necklace for Maheśvara The brāhmaṇa Śrīpati of the Kāśyapa clan was a soothsayer from Rohiṇīkhaṇḍa, which is in the modern Buldhana district of Maharashtra state. Somewhere between 1030 to 1050 CE he composed several works on mathematics, astronomy … Continue reading
Nārāyaṇa’s sequence, Mādhava’s series and pi
The coin-toss problem and Nārāyaṇa’s sequence If you toss a fair coin times how many of the possible result-sequences of tosses will not have a successive run of 3 or more Heads? The same can be phrased as given tosses … Continue reading
Posted in Heathen thought, History, Scientific ramblings
Tagged approximation for pi, coin toss, constant, Euclid, fibonacci, Geometric construction, geometry, Golden Ratio, hexagon, Hindu mathematics, history of science, mAdhava, mathematics, nArAyaNa, pentagon, pi, sequence, series sum, tribonacci
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Matters of religion: the Vāyavīyaṃ Kaubera-vratam
The bus came to halt at the underground stop. Vrishchika of pretty tresses got off the bus and walked up the stairs to reach the over-bridge. She reached the middle of the bridge and stood there looking out expectantly at … Continue reading
Posted in Heathen thought, Life
Tagged atharvaveda, evolution of religions, goddesses, gods, Hindu ritual, Indo-Aryan, Indo-European, Indo-Iranian, kubera, religion, Rigveda, rudra, shiva, Story, varuNa, vAyu, Veda, Yajurveda
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The Platonic culmination of Euclid and the pentagon-hexagon-decagon identity
Why did great sage Pāṇini compose the Aṣṭādhyāyī? There were probably multiple reasons but often you hear people say that he wanted to give a complete description of the Sanskrit language. That was probably one of his reasons but was … Continue reading
Posted in Heathen thought, Life
Tagged Geometric construction, geometry, Golden Ratio, Greek, Hindu, Plato, polygons, polyhedra, recreational geometry, religion, triangles, trigonometry
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Śiva-gaṇa-s and Andhakāsura-vadha in the Vāmana-purāṇa
On Twitter, one of our acquaintances going by the name @GhorAngirasa had a discussion on the significance of the number 66 in śaiva tradition. That reminded us of an unfinished article where we had noted this number in the context … Continue reading
Posted in Heathen thought, History
Tagged Hindu, Hindu ritual, indra, pAshupata, purAna, purANas, religion, shaiva, shiva, vamAna-purANa, viShNu
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Notes on the Bhadra-sūkta, a hymn for felicity to the Vedic pantheon
For better type-setting and Devanagari rendering use PDF version. Introduction Several sub-schools of the Taittirīya school of the Kṛṣṇayajurveda possess their own collections of mantra-s distinct from their saṃhitā-s known as the mantra-pāṭha-s. These include mantra-s that are often found … Continue reading
Posted in Heathen thought
Tagged atharvaveda, deities, deva, devI, goddesses, gods, Indo-Aryan, Indo-European, Indo-Iranian, religion, Rigveda, Samaveda, sanAtana-dharma, Veda, vedic, Venus, Yajurveda
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The maṅgalācaraṇam of the Mānasollāsa
In PDF format A conversation with a friend brought my mind back to the Mānasollāsa, the encyclopedia of the great Cālukya emperor Someśvara-deva. Below is the maṅgalācaraṇam of that work. The last verse is where the author announces himself. There … Continue reading
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Tagged goddesses, gods, Hindu, poem, religion, Sanskrit
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Reflections on our journey through the aliquot sums and sequences
The numerology of aliquot sums and perfect numbers The numerology of the Pythagorean sages among the old yavana-s is one of the foundations of science and mathematics as we know it. One remarkable class of numbers which they discovered were … Continue reading
The ghost in the tattered Gattermann
Vidrum had dropped by to see Somakhya and Lootika when they had just started their household together. They had reconstituted a fairly elaborate lab in the biggest room of their home. They had also completely set up their fire room, … Continue reading
Posted in Heathen thought, Life, Scientific ramblings
Tagged biochemistry, biology, fiction, Gatterman, ghosts, religion, Story
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A poll on peoples’ beliefs on reincarnation
Using the Twitter’s poll tool we conducted a poll which gave the below results: Reincarnation happens: Believe so but there is no evidence for it: 52% Sure, have the evidence for it: 20% No, just mumbo-jumbo: 11% Do not know: … Continue reading
Posted in Heathen thought, Life
Tagged beliefs, Hindu, Hindus, reincarnation, religion
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Making of a modern-day mantra-śāstra pamphlet
Originally, all mantra instructions were oral, keeping with the spirit of the śruti. But over time, starting probably around the Mauryan age, written manuals began to supplement the oral teachings. Thus, through the ages practitioners of the mantra-lore have made … Continue reading
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Tagged atharvaveda, Indo-Aryan, Indo-Iranian, mantra, mantra-sAdhana, mantra-shAstra, religion, Rigveda, Veda, Yajurveda
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Some words on mathematical truth, scientific conviction and the sociology of science
Sometime in the bronze age more than one group of humans, including our own Aryan ancestors, discovered that the squares of the two legs of a right triangle sum up to the square of the hypotenuse. This is the famed … Continue reading
A note on āmreḍita-s in the Ṛgveda and issues of word distribution
sa darśataśrīr atithir gṛhe-gṛhe vane-vane śiśriye takvavīr iva । janaṃ-janaṃ janyo nāti manyate viśa ā kṣeti viśyo viśaṃ-viśam ॥ RV 10.91.2 by Aruṇa Vaitahavya He, with visible auspiciousness, a guest in house after house, in forest after forest lurking like … Continue reading
Posted in Heathen thought, History
Tagged grammar, Hindu, Hindu ritual, Hindus, Indo-Aryan, Indo-European, Indo-Iranian, Iranian, linguistics, mantra, religion, Rigveda, ritual, Veda, vedic
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The amazonian banana republic: the strī-rājya in Hindu tradition
The śaiva tradition shows a dichotomy with respect to the role of the sex in ritual and purity. The earlier antimārga or pāśupata tradition focused on abstinence and the so-called “upward flow” or ūrdhvaretas. This indeed the underlying idea behind … Continue reading
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Tagged amazons, gorakSha, Greek, Greek thought, Indo-Iranian, Iranian, kadalirAjya, matsyendra, natha yogin, strIrAjya
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Sītā in the pyre
It was quiet, early Saturday evening. Vidrum, Jukuta, Sharvamanyu and Lootika were hanging out on the parkway of Somakhya’s house. They had assembled there for some curricular preparation on differentiation. Somakhya and Lootika had covered the chain rule and the … Continue reading
Posted in Heathen thought, Life
Tagged fiction, Hindu, leftists, religion, secularism, socialism, society, Story
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A problem from 600 CE and some curiosities of Āryabhaṭa’s kuṭṭaka algorithm
Around 600 CE in the examinations of one of the Hindu schools of mathematics and astronomy one might have encountered a problem such as below (given by Bhāskara-I in his commentary on Āryabhaṭa’s Āryabhaṭīya): dvayādyaiḥ ṣaṭ-paryantair ekāgraḥ yo ‘vaśiṣyate rāśiḥ … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged AryabhaTa, Golden Ratio, Hindu mathematics, kuTTaka, mathematics, prime numbers
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Frustrations and ramblings ensuing from Cretaceous amber
Time and again I have been frustrated by the inability of Hindus to make the most of the riches that are available in their own land or right next to them. One such case is that of Cretaceous amber from … Continue reading
Posted in Heathen thought, History, Life, Scientific ramblings
Tagged amber, birds, buddhism, dinosaurs, elektron, fossil, Hindu, kavI, kAvya, poetry
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Of lives of men; of times of men-II
Of lives of men; of times of men-I Vidrum: “When we attended the discussions at the Right Wing Debate club we heard the president Rammandir Mishra repeatedly emphasize that South Asian civilization was not a ‘history-centric’ civilization and that history-centricism … Continue reading
Posted in Heathen thought, History, Life
Tagged ancient Hindu thought, Euler, Gauss, Hindu, Hindu knowledge, Hindu science, Hindus, history, Ramanujan, Riemann, Story, world history
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Of lives of men; of times of men-I
Sharvamanyu and Vidrum arrived at the campus where Somakhya and Lootika were in their final days of college. Sharvamanyu had already been working for several months while Vidrum had just completed the last but one of his major exams for … Continue reading
Posted in Heathen thought, History, Life, Politics
Tagged Abrahamism, Aryan, Egypt, Hindu, Indo-Aryan, Iranian, religion, Story, war
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Triangles, Hexes and Cubes
One philosophical question which we have often ponder about is: Are numbers “real”? One way to approach this question is via figurate numbers, where numbers directly manifest as very tangible geometry. This idea has deep roots in our tradition: as … Continue reading
A rambling talk on the śaiva mantra tradition
A rambling talk we had given on the śaiva tradition. Talking is easier but less precise than writing. So please be aware of the insufficiency that goes with the domain of any talk while perusing this material. Part 1; Introduction to … Continue reading
Citrabhānu’s cubes
The Hindus unlike their yavana cousins preferred algebra to geometry. Yet on occasions they could indulge in geometric games for demostrating proofs of algebraic relations. We see a bit of this in the Āryabhaṭa school and the great Bhāskara-II, but … Continue reading
Make your own sky map
We live in the age of photo-realism, be it for maps of the world or of the sky – it is a realism that not long ago was beyond the reach of even our vision. That is why even though … Continue reading
Posted in Heathen thought, Life, Scientific ramblings
Tagged astronomy, globular clusters, nakShatra-s, nebulae, open clusters, sky, star chart, stars, variable stars
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A note on the cow, the horse and the chariot in the Ṛgveda
yasmai tvaṃ sukṛte jātaveda u lokam agne kṛṇavaḥ syonam | aśvinaṃ sa putriṇaṃ vīravantaṃ gomantaṃ rayiṃ naśate svasti || For whom you will make a pleasant world, O Jātavedas! as he does correct rituals for you, O Agni! He endowed with … Continue reading
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Tagged chariot, cow, holy cow, horse, Indo-Aryan, Indo-European, Indo-Iranian, indology, Rigveda, Veda, vedic
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The Rāmāyaṇa and a para-Rāmāyaṇa in numbers-II: Evolving early Indo-Aryan warfare
This article might be read in as a continuation of this earlier one. The methods/caveats mentioned therein apply here too. Some of the counts mentioned in this article might be approximate but should be generally in the correct range, i.e. … Continue reading
Posted in Heathen thought, History
Tagged archery, arrow, bow, chariot, Indo-European, Indo-Iranian, rAmAyaNa, Veda, war, weapons
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Leaves from the scrapbook-2
As described here these entries are from the scrapbook of Somakhya. Entry 11; Arasa, year Pramādin of the first cycle: It was our first day at Kshayadrajanagara. I had exhausted all that was there to talk with my cousins Mandara … Continue reading
Posted in Heathen thought, Life, Scientific ramblings
Tagged ellipse, Geometric construction, geometry, recreational geometry, Story
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A note on the asterisms forming the nakṣatra-s
In Hindu tradition the ecliptic is divided into 27 parts of which correspond to 27 asterisms known as the nakṣatra-s. In the earliest extant layers of our tradition this number is 28 implying division into sectors of or insertion of … Continue reading
Posted in Heathen thought, Scientific ramblings
Tagged asterisms, astronomy, constellations, Hindu, Hindu science, Indo-Aryan, Indo-Iranian, religion, stars
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Some biological analogies for certain sociopolitical issues
In Hindu society we often see certain relatively straightforward sociopolitical issues endlessly debated. A person with relatively commonplace IQ should in principle easily arrive a correct apprehension of these issues by applying correct analogy and/or logic. However, due to emotionalism … Continue reading
Posted in Heathen thought, History
Tagged analogical thinking, biology, Indo-Aryan, language, relgion, Sanskrit
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The magic of the deva-ogdoad
Classical Hindu tradition holds that the ogdoad of deva-s corresponding to their directions is: Indra: East; Agni: Southeast; Yama: South; Nirṛti: Southwest; Varuṇa: West; Vāyu: Northwest; Kubera: North; Īśāna: Northeast. The central position might be occupied in certain traditions by … Continue reading
Trigonometric tangles-2
We had earlier described our exploration of the spirograph, hypocycloids, epicycloids and related curves. In course of our study of the śaiva tantra-s of the kaula tradition we started thinking about a remarkable piece of imagery mentioned in them. Tantra-s … Continue reading
Posted in art, Heathen thought, Life, Scientific ramblings
Tagged circles, circular waves, curves, epicycloid, Generative Art, hypocycloid, mathematics, religion, trigonometry
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Śarabha vidhi
The account of this rite continues from the prefatory narrative. Lootika: “There are several ways in which Rudra is worshipped as Śarabha conceived as the great dinosaur. We shall follow the way which is appropriate for us brāhmaṇa-s who observe … Continue reading
Posted in Heathen thought
Tagged maNDala, mantra, mantra-sAdhana, mantra-shAstra, religion, shaiva, sharabha, Story, tantra
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Some visions of infinity from the past and our times
The great Hindu mathematician and astronomer Bhāskara-II’s work preserves a high-point of Hindu knowledge. His work contains ideas that are often seen as characterizing “modern” scientific understanding i.e. what in the west would seen as starting with Leibniz and Newton … Continue reading
Āryabhaṭa and his sine table
Everyone and his son have written about Āryabhaṭa and his sine table. Yet we too do this because sometimes the situation arises where you have to explain things clearly to a layman who might have some education but is unfamiliar … Continue reading
Early Hindu mathematics and the exploration of some second degree indeterminate equations
The following is merely a record of our exploration as a non-mathematician/non-computer scientist of a remarkable (at least to us) class of numerical relationships. An equation like can be solved to obtain specific solutions as: . However, if we have … Continue reading
The Rāmāyaṇa and a para-rāmāyaṇa in numbers-I: epic as religion
This note may be read as part of our studies on the Rāmāyaṇa and para-Rāmāyaṇa-s of which an earlier part is presented here. A study of the epic in Indo-European tradition suggests that there were two registers of the old … Continue reading
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Matters of religion: “he becomes Naravāhanadatta”
Somakhya’s mother (SM) and Lootika’s mother (LM) ran into each other during their visit to the shrine of Rudra beside the river on a Monday evening. They sat at the platform below the vast aśvattha tree beside the subsidiary Viṣṇu … Continue reading
Posted in Heathen thought
Tagged Hindu, Hindu ritual, Japan, kubera, religion, Story, yakSha
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Matters of religion: discussion on vāyavya offerings
Somakhya and Lootika had revived the private one day rite in the manner of their ancestors as had been ordained by the youthful sage Śunaḥśepa Ājigarti. They were resting at the corner of their fire-room in the interval between the … Continue reading
Posted in Heathen thought, History
Tagged Ape, Hanumat, Hindu ritual, indra, rAmAyaNa, religion, shastra, soma, Story, vAnara, vAyu, Veda
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Syllable, number and rules in the ideal realm
This note is neither meant to be complete exposition of this matter nor a complete view of all what we have realized in this regard. Nor can it be completely understood by those who are not insiders of the tradition. … Continue reading
Posted in Heathen thought, Life, Scientific ramblings
Tagged art, biology, curlicue, fractal, fractals, geometry, Hindu, mathematical entity, mathematics, pi, Plato, Platonic ideals, proteins, religion, science
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Chaos in the iterative Hindu square root method of the gaṇaka-rāja
For Hindus big numbers always mattered and our mathematics is quite reflection of this fascination. Since the earliest times, Hindus devised various methods to obtain square roots of numbers, especially approximations of irrational roots correct to multiple decimal places. The … Continue reading
Some meanderings among golden stuff
There are some angles that we often encounter in the construction of the golden ratio and its use in religious art. The first is the most obvious is the angle which is the angle made by the diagonals connecting a … Continue reading
mAnasa-taraMgiNI 