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- primes of the form p= x^2+y^2+1 for x,y->1:100 is it true that the richest line in this range is 99^2+y^2+1; https://t.co/SkvPfAkhGT 1 week ago
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- 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
- Some observations on the Lekkerkerker-Zeckendorf decomposition of integers
- Subjective and objective insight
- On the passing of E.O. Wilson
- Some words on mleccha cartels
- Relationships between incircles of the “equilateral triangles in a square” system
- The Rāmāyaṇa in numbers: meters, sarga- and kāṇḍa- structure
- Sneha, snowstorms, the sun and the moon in enigmatic ṛk-s
- The strange case of the Āpastamba sprite
- Agni as the divine commander in the Veda and the Purāṇa
- The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
- The rise of Navyonmāda, the subversion of the Mahāmleccha-s, Cīnānusāra and beyond
- Some biographical reflections on visualizing irrationals
- Turagapadādi
- Asians and Pacific Islanders: The triangle
- The shape of dinosaur eggs
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Search this Blog
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mAnasa-taraMgiNI supplement
- RT @shrikanth_krish: What's interesting is that learning outcomes in rural areas is actually pretty good in North India relative to South,… 1 week ago
- I wish they published better images of such historically significant finds c.f. https://t.co/HjjSpgDIdR twitter.com/Akshai1993/sta… 1 week ago
- primes of the form p= x^2+y^2+1 for x,y->1:100 is it true that the richest line in this range is 99^2+y^2+1; https://t.co/SkvPfAkhGT 1 week ago
- Will the arithmetic mean of successive primes be most frequently divisible by 3? 1 week ago
- When the air is humid getting vaishvAnara to chomp on the idhma up can be a pain -- v1 troubles -- but we labored o… twitter.com/i/web/status/1… 1 week ago
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Recent Posts
- 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
- Some observations on the Lekkerkerker-Zeckendorf decomposition of integers
- Subjective and objective insight
- On the passing of E.O. Wilson
- Some words on mleccha cartels
- Relationships between incircles of the “equilateral triangles in a square” system
- The Rāmāyaṇa in numbers: meters, sarga- and kāṇḍa- structure
- Sneha, snowstorms, the sun and the moon in enigmatic ṛk-s
- The strange case of the Āpastamba sprite
- Agni as the divine commander in the Veda and the Purāṇa
- The birth defects of Dhṛtarāṣṭra and Pāṇḍu and related matters
- The rise of Navyonmāda, the subversion of the Mahāmleccha-s, Cīnānusāra and beyond
- Some biographical reflections on visualizing irrationals
- Turagapadādi
- Asians and Pacific Islanders: The triangle
- The shape of dinosaur eggs
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Author Archives: mAnasa-taraMgiNI
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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Some notes on the runiform “Altaic” inscriptions and the early Turk Khaghanates: Orkhon and beyond
The early Turkic inscriptions from Mongolia and their discovery On February 27th, 731 CE (17th day of the Year of the Sheep), Kül Tegin, the great hero of the second Gök Türk (Blue Turks) empire, passed away in his 47th … Continue reading
Posted in Life
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Vikīrṇā viṣayāḥ: India and the Rus
Our sleep was disturbed by a dream with a circulating motif whose exact story line, if any, was lost upon awakening. It started with a tall elderly man of West African ancestry playing cricket (batting) with the swagger of a … Continue reading
Posted in History, Politics
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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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The death of Miss Lizzie Willink
Late that spring, Somakhya and Lootika were visited by their mleccha friend Irmhild. Letting her sleep off the jet lag, they left for work. Given the good weather, Lootika returned early to check on their friend and go out with … Continue reading
Posted in Life, Politics
Tagged English, English tyranny, entomology, Hindu, history, mlechCha, religion, religiosity, Story
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Geopolitical summary: March 2022
The autumn dawn As the 40th day of the autumn of 2016 CE dawned, the mahāmleccha left-liberals were sunning themselves in the last rays of the setting Ardhakṛṣṇa. He was the hero of the age for them, a veritable yuganātha, … Continue reading
Posted in History, Politics
Tagged Abrahamism, Abrahamistic vandalism, American, China, Chinese belligerence, Chinese incursion, Geopolitics, Japan, mlechCha, Russia
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Human retroviruses, sociology of science, and biographical ruminations
We learnt via a recent obituary that the French researcher Luc Montagnier died a month or so ago after living for nearly 90 years. He along with his compatriot and erstwhile colleagues, Françoise Barré-Sinoussi and Jean-Claude Chermann discovered HIV-1. Subsequently, … Continue reading
Posted in History, Life, Scientific ramblings
Tagged AIDS, biography, biological conflict, biological patterns, biologists, biology, HIV, virus, viruses
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Transcripts of conversations: the addiction principle:
A friend recorded some of our verbalizations and made transcripts of them. He sent them to us to and we decide to edit them and post them as and when we get the chance — not out of a narcissistic … Continue reading
Posted in History, Life, Politics, Scientific ramblings
Tagged Geopolitics, history, toxins, war
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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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Are civilizational cycles the norm?
Nearly two and half decades back, we used to have several conversations with a late śūlapuruṣīya professor, mostly on topics with a biological angle. While not a mathematician, he had a passing interest in dynamical systems, for he felt that … Continue reading
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
Some observations on the Lekkerkerker-Zeckendorf decomposition of integers
In our youth, we learned of a nice arithmetic theorem of Lekkerkerker (more popularly known after Zeckendorf; hereinafter L-Z) that relates to the famous Mātrā-meru sequence : 0, 1, 1, 2, 3, 5, 8… defined by the recurrence relationship . … 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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On the passing of E.O. Wilson
E.O. Wilson, one of the great biologists of the age, has fallen to the noose of the king, the black son of Vivasvān. He lived a long, productive, and eventful life, just 8 years shy of a century. He was … Continue reading
Posted in History, Life, Politics, Scientific ramblings
Tagged ants, bees, biology, eusociality, history of science, hymenopterans, isopterans, social parasitism, society, sociobiology, sociology, Superorganism, Watson, Wilson
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Some words on mleccha cartels
An embedded anthropological study of social substructures is vital to grasp some of their features that seem baffling to the outsider or the “uninitiated” insider. Much of what we will be talking about here has been said in some form … Continue reading
Posted in Life, Politics
Tagged Anglosphere, Anti-Hindu, Anti-India, Geopolitics, mlechCha, social parasitism, socialism, society, sociology
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Relationships between incircles of the “equilateral triangles in a square” system
This note relates to geometric relationships that may be likened to the Japanese temple-tablet problems. The inspiration for discovering and exploring it came from an origami construction presented by the pioneer in that field, Sundara Rao of Kumbhaghoṇa, in the … Continue reading
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
Posted in Heathen thought, History, Life
Tagged abhichAra, Hindu, Hindu ritual, history, Maratha, ritual, shaiva, shiva, tantra, tantras, Yajurveda
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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
The rise of Navyonmāda, the subversion of the Mahāmleccha-s, Cīnānusāra and beyond
The past The dynamics of the establishment of the counter-religious unmāda-s are of some interest. The pūrvonmāda of pharaoh Akhenaten arose from the moha in his own head and was imposed on the populace due to his imperial power. It … Continue reading
Posted in History, Life, Politics
Tagged Abrahamism, Anglosphere, Chinese belligerence, Chinese incursion, Geopolitics, Hindu, leukosphere, mlechCha, world history, World War 2
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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
Asians and Pacific Islanders: The triangle
In our youth, we read with great excitement old books on anthropology obtained from a library with considerable difficulty. The excitement was primarily from learning about the osteology of extinct apes and monkeys, including the closest sister groups of Homo … Continue reading
Posted in History, Scientific ramblings
Tagged ancient India, Aryan, Aryan Invasion, Asia, Asian, Australia, Austro-Asiatic, Austronesians, China, DNA, genetics, genomics, Japan, Korea, Papuans
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The shape of dinosaur eggs
Readers of these pages will know that we have a special interest in the geometry of ovals. One of the long-standing problems in this regard is: what is the curve that best describes the shape of a dinosaurian egg? While … 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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Self, non-self and segregation: a very basic look at agent-based lattice models
In our college days, a part time physics teacher from an old and respected V clan used to chat with us about issues of mutual interest that were beyond that of the rest of the class (or for that matter … Continue reading
Posted in Life, Scientific ramblings
Tagged cellular automata, geometry, Ising, lattice models, mathematics, Schelling, self/non-self, society, sociobiology, sociology
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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
Pandemic days: bālabodhana
As the pandemic grinds to a close or at least to a pause in some parts of the world, there is a certain fear from new mutants threaten that threaten break current the status quo. The strain that arose in … Continue reading
Posted in Scientific ramblings
Tagged biochemistry, biology, disease, pandemic, science, virus, viruses
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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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The cicadas return
Seventeen years after we first saw them emerge, like a great horde of Cīna-s invading Tibet, the cicadas of Brood X reemerged. 17 years is a good amount of time, making one pause to reflect on what has passed by … Continue reading
Posted in Life, Scientific ramblings
Tagged animal, animals, cicadas, insects, life expectancy, wildlife
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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, Veda, vedAnta, vedic, viShNu, Yajurveda
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Two exceedingly simple sums related to triangular numbers
This note records some elementary arithmetic pertaining to triangular numbers for bālabodhana. In our youth we found that having a flexible attitude was good thing while obtaining closed forms for simple sums: for some sums geometry (using methods of proofs … Continue reading
Posted in Scientific ramblings
Tagged geometry, Hindu mathematics, mathematical entity, mathematics, proof, sequence, series sum, sum
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Pandemic days: Vaccines and war
In American history-writing we come across various attempts to the justify the use of nuclear weapons on Japan in the closing phase of WW2. We often hear the claim that by using the nukes they avoided a large number of … Continue reading
Posted in History, Politics, Scientific ramblings
Tagged Anglosphere, China, Chinese belligerence, Chinese incursion, disease, Geopolitics, immunity, leukosphere, mlechCha, virus, viruses
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Generating simple radially symmetric art
Many people experience beauty in structures with bilateral, radial and rotational symmetries with or without recursion. The recursive or nested structure are the foundation of the beauty in fractal form, the generation of which has become increasingly easy for the … Continue reading
Posted in art, Life
Tagged art, art and science, Generative Art, Geometric construction, geometry
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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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Pandemic days: Galtonism hits India
At some point last year, we stopped writing any further dispatches regarding the pandemic catastrophe from the disease because everything was playing out more or less as laid out in the earlier notes. There was the whole public drama around … Continue reading
Posted in History, Politics
Tagged American, China, Chinese belligerence, clash of civilizations, mlechCha
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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
Modulo rugs of 3D functions
Consider a 3D function . Now evaluate it at each point of a integer lattice grid. Compute corresponding to each point and plot it as a color defined by some palette that suits your aesthetic. The consequence is a what … Continue reading
Posted in art, Scientific ramblings
Tagged arithemetic, factorization, mathematical entity, mathematics, modulo, prime numbers, recreational geometry
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A guilloche-like trigonometric tangle
Coprimality, i.e., the situation where the GCD of 2 integers is 1 is one of the fundamental expressions of complexity. In that situation, two numbers can never contain the other within themselves or in multiples of them by numbers smaller … Continue reading
Posted in art, Scientific ramblings
Tagged arithmetic, curves, mathematical entity, mathematics, prime numbers, recreational geometry, spirograph, trigonometry
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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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Some notes on the Henon-Heiles Hamiltonian system
Anyone familiar with dynamical systems knows of the Henon-Heiles (HH) system. What we are presenting here is well-known stuff about which reams of material have been written. However, we offer certain tricks for visualizing this system that make it easy … Continue reading
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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The cosine principle, radial effect and entropy in the generalized Lozi map
The generalized Lozi map is a good way to illustrate the cosine principle and the radial effects (in lay circles to which I belong in this regard, as opposed to mathematicians). The generalized Lozi map is a 2-dimensional map defined … Continue reading
Posted in Life
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Prakīrṇaviṣayāḥ: Life, brains, warfare and society
1 On big brains An occidentally conditioned person remarked that “we were making bad use of the great brains we have evolved. Instead of using it for human betterment, we were expending it on killing each other with sophisticated weapons.” … Continue reading
The old teacher
The summer of the year after the tumultuous events, Lootika and Somakhya were traveling to visit their parents. They were supposed to attend the marriage of Somakhya’s cousin Saumanasa but they found social engagements with a subset of the clan … Continue reading
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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Pandemic days-6: Genetic risk factors
The coronavirus that made its way to humans aided by the Cīna-s at Wuhan has now been with us for nearly an year. Right from the early days of this outbreak, one thing has been notable about this virus: some … Continue reading
Posted in Scientific ramblings
Tagged evolution, genetics, human existence, pandemic, proteins, virus, viruses
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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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Ruminations on meteorites, organics and water
In our times the Christian Anglo-Saxons were famous for their “war on drugs”. However, in the 1800s, when they lorded over India, they were famous as global drug dealers. On the morning of August 25, 1865 CE around 9:00 AM, … Continue reading
Posted in History, Scientific ramblings
Tagged astronomy, biochemistry, biology, chemistry, Earth, geology, Life, meteorite, meteoroid, meteors, origins
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Winners and Losers
Somakhya and Lootika were visiting the Śūlapuruṣadeśa for work reasons. Unlike their ārya ancestors, they did not like being on the move much. It was a rare occasion that both had been able to travel together and it brought them … Continue reading
Posted in History, Life, Politics
Tagged American, China, Chinese belligerence, Chinese incursion, fiction, Germans, Germany, history, Japan, Story, war, world history
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An arithmetic experiment and an unsolved problem
We realized that a simple arithmetic experiment we had performed in our youth is actually related to an unsolved problem in number theory. It goes thus: consider the sequence of natural numbers Then find the distance of to nearest prime … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, arithmetic mean, geometric mean, mathematical entity, mathematics, numbers, prime numbers, sequence
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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, twelve goddess
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Conic conquests: biographical and historical
PDF file of same article Studying mathematics with our father was not exactly an easy-going experience; nevertheless, it was the source of many a spark that inspired fruitful explorations and life-lessons. We recount one such thread here, and reflect on … Continue reading
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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Pandemic days: the fizz is out of the bottle
Just this morning our brother remarked that the fear of the virus has inverted this month with respect to the actual infection. We literally hear this: in the past few months, while home-bound, we at least had aural quietness for … Continue reading
Posted in History, Life, Politics
Tagged Abrahamism, Abrahamistic vandalism, American, ape behavior, communal riots, evolution of religions, Geopolitics, mlechCha
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A simple second order differential equation, ovals and chaos
In our youth as a consequence of our undying fascination with ovals we explored many means of generating them. In course of those explorations we experimentally arrived at a simple second order differential equation that generated oval patterns. It also … Continue reading
Viṣṇu, the Marut-s and Rudra
This note might be read as a continuation of the these two earlier ones: 1) The Aśvin-s and Rudra 2) The roots of Vaiṣṇavam: a view from the numerology of Vedic texts In the Ṛgveda (RV), the Marut-s are seen … Continue reading
Posted in Life
Tagged agni, ashvins, Indo-Aryan, Indo-European, Indo-Iranian, indra, Rigveda, rudra, shatarudrIya, varuNa, ved, Veda, vedAnta, vedic, viShNu, Yajurveda
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Pandemic days-4: viruses get new hosts
That we have come to be in these pandemic days evokes some wonderment or even disbelief among laypeople. The general thinking of a large section of the populace is that this event is something completely unexpected or out of the … Continue reading
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
Chaotic behavior of some floor-squared maps
Consider the one dimensional maps of the form: , where is the fractional part of What will be evolution of a under this map when or ? We can see that for it will tend converge. However, the behavior is … Continue reading
Posted in Scientific ramblings
Tagged attractors, chaos, fractal, fractals, geometry, Golden Ratio, mathematics, numbers
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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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The culmination of Galtonism or pandemic days-3
We saw a list of famous elderly people whom the virus has already placed in the abode of Vaivasvata at the time of writing. We recognized at least two names: (1) Robert Carroll the paleontologist, whose hard to find book … Continue reading
Posted in Life, Politics, Scientific ramblings
Tagged China, Chinese belligerence, Geopolitics, Han imperialism, memetic virus, Mycobacteria, virus, viruses
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The culmination of Galtonism or pandemic days-2
Ensconced in the apparent safety of the 4 walls the mind looks out into the completely silent streets with hardly a soul or even a passing ratha — a mere 120 days have made the world look and sound different. … Continue reading
Posted in Life, Scientific ramblings
Tagged China, disease, Han imperialism, virus, viruses
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The culmination of Galtonism or pandemic days-1
While many thoughts crowd our mind we have hardly felt the drive to put them down on a more visible medium. Such is the nature of the times when things happen reminding you of the inexorable turning of the yuga-cakra. … Continue reading
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 Plague: historical, biographical and current: a brief roundup
Globalization is not a new thing. The Indo-European empire of the steppes was perhaps the first one. In addition to having a serious component of our genetic ancestry and most of our memetic inheritance in it, we can still see … Continue reading
Two squares that sum to a cube
Introduction This note records an exploration that began in our youth with the simple arithmetic question: Sum of the squares of which pair integers yields a perfect cube? Some obvious cases immediately come to mind: . In both these cases … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, Brahmagupta, cube, Euler, Gauss, Hindu mathematics, mathematical entity, mathematics, numbers, prime numbers, Ramanujan, square
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Difference of consecutive cubes, conics and a Japanese temple tablet
Introduction In our part of the world, someone with even a nominal knowledge of mathematics might be aware of the taxicab number made famous by the conversation of Ramanujan and Hardy: the smallest number that can be expressed as the … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, cube, ellipse, geometry, history of science, Japan, mathematics, numbers, parabola, recreational geometry, square
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The Mātrā-meru and convergence to a triangle
What is presented below will be elementary for someone with even just the mastery of secondary school mathematics. Nevertheless, even simple stuff might present points of interest to people who see beauty in such things. Consider the following question: Given … Continue reading
Posted in Scientific ramblings
Tagged fibonacci, geometry, Golden Ratio, mathematics, recreational geometry, sequence, triangles, trigonometry
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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
Posted in Heathen thought, Life
Tagged atharva veda, atharvaveda, Hindu, Hindu ritual, Indo-Aryan, Indo-European, Indo-Iranian, Iranian, religion, Rigveda, ritual, Veda, vedic, Yajurveda
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Sequences related to maps based on simple fractional functions
One of the pleasures of an unstructured youth in the pre-computer era was what we called calculator games. As our father took his prized calculator with him to work we only got a little time with it in the evenings. … Continue reading
Posted in Scientific ramblings
Tagged arithmetic, complex numbers, fibonacci, fractal, fractals, mathematics, nArAyaNa, numbers, sequence, trigonometry
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Human journeys, ascents and descents
As we headed towards the bus-stand to take our homeward conveyance, we saw an unusual stir in its vicinity. We passed a clump of young, well-to-do, white American women ambling along holding over-sized coffee or cola cups and exclaiming: “Wow!” … Continue reading
Posted in Life, Politics
Tagged American, First Americans, frontier lands, human existence, inequality
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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
Some notes on rational sector triangle triples
Rational points on a unit circle There are some events that happen in the course of ones life that might be considered historical or world-changing. One such event from our lifetime is the proving of the Last Theorem of Fermat … Continue reading
Some (geo)political talk
A political bloviation follows: We must preface this by stating we do not have any affiliation to the party currently ruling India or the RSS and actually have no specific interest at all in electoral politics in India or elsewhere. … Continue reading
The aftermath: A polynomial equation
This is merely the tailpiece to the last tale of the strange hauntings. A reader may wonder why expend so many words on a high school problem. While the ball could have fitted into the socket, it rolled away. As … Continue reading
Posted in art, Life, Scientific ramblings
Tagged mathematics, polynomial, series sum, Story
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The blue bottle and the talent show
This story itself is haunted. The deaths Seeing Vidrum intently gaze at something on his phone with an expression of near disbelief Kalakausha asked: “Vidrum, what are you looking at? We need to be leaving shortly. We have to buy … Continue reading
Posted in art, Life
Tagged Geometric construction, geometry, geometry box, recreational geometry, Story
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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
Posted in Heathen thought, History
Tagged atharvaveda, brahmA, brahmana, death, Hindu, poison, religion, Rigveda, Samaveda, Veda, vedic, Yajurveda
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Chaos, eruptions and root-convergence in one-dimensional maps based on metallic-sequence generating functions
bronze_bouncer Over the years we have observed or encountered certain natural phenomena that are characterized by rare, sudden eruptive behavior occurring against a background of very low amplitude fluctuations. We first encountered this in astronomy: most remarkably, in the constellation … Continue reading
Posted in Scientific ramblings
Tagged Bronze ratio, chaos, chaotic maps, Copper Ration, curves, fractals, geometry, Golden Ratio, mathematics, recreational geometry, recursion, sequence, Silver Ratio
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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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mAnasa-taraMgiNI 