Category Archives: Life

Cārucitrābhisambodhi

Chakkalal and Mundalal saw that Gannaram Dakiya, the owner of the little eatery, had taken a bit too much of an ethanolic beverage and had forgotten to lock the safe with his phone, cards and some cash. They broke into … Continue reading

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Some poems

Below are some poems in English by our brother. He sends us his compositions in a much more transient medium making them hard to preserve or share. Hence, we decided to anthologize those we could recover and present them here … Continue reading

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Matters of religion: the lesson by the lake

Sharvamanyu was with his preceptors Somakhya on Lootika on the shore of a lake in the midst of the mountains on a full moon night. It was the cremation ground for a lineage of Vs, who had historically specialized in … Continue reading

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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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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

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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

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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

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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

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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

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Leaves from the scrapbook-4

As described here these entries are from the scrapbook of the second of the caturbhaginī, Vrishchika. Entry 1; kāmāturā, year Siddhārthin of the first cycle: Indrasena departed for grad school last week and I am feeling a bit of loneliness … Continue reading

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Fraudulent science by Indians: some really bad news

Around 2011 we were approached by a researcher of Indian origin for a collaboration in biochemistry regarding a family of proteins whose biochemical functions we had uncovered. After more than an year of dealing with him, it became clear that … Continue reading

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Leaves from the scrapbook-3

As described here these entries are from the scrapbook of Somakhya. Entry 3; Nimlukti, year Anala of the first cycle: I was still at Turushkarajapura at a lab where I had access to a computer-network with a large number of … Continue reading

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A dinnertime conversation

A complete version of this apolog will currently not be visible to the public. Things had cooled off a bit on the political front after the assassination of the Prime Minister Pratap Simha by a massed drone attack. On the … Continue reading

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Cricket in pictures

We may say that cricket has nearly passed us by. In our youth we played and watched the game quite a bit. While in secondary school we were fairly interested in cricket statistics. The sources for statistics were not easily … Continue reading

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The second strike

PDF version Childhood Thrice a week, starting Fridays, Lootika’s mother taught her daughters mantra-siddhānta after dinner. She had covered the praxis of the secret mantra-s of the Vīṇāśikhā and had moved on to relevant sections of the Jayadratha-yāmala and the … Continue reading

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Fermat’s little theorem and the periods of the reciprocals of primes

From the genetic code to the proof of Fermat’s little theorem Nucleic acids encode the 20 amino acids found in the sequence of a protein using just 4 bases: A, G, T, C in DNA. Thus, the 4-symbol nucleic acid … Continue reading

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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

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The mathematics class

It was a dreary autumn day, the same year Lootika had joined their school. The apabhraṃśa class had just gotten over. Somakhya’s head was spinning with all the confusing genders of the vulgar apabhraṃśa that was dealt with in the … Continue reading

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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

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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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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

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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

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A day at school

It was the English class in school. The teacher, a swarthy man with somewhat liberal political leanings, strode into the class: “Today we shall be studying a poem by the white American poet Robert Frost, Fire and Ice. Dandadipa, stand … Continue reading

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Our auto-discovery of the Möbius and Mertens sequences

Recently, we were explaining to our friend the Möbius and the Mertens functions and their relationship to the prime number distribution. We also heard with some wonder from a physicist of a theoretical model where multiparticle states behave as bosons … Continue reading

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Civilizational collapse, complexity, innovation and neomania

On these pages we had provided some commentary on the work of the German thinker Oswald Spengler and his ideas of civilizational development. We had also provided other perspectives on this matter derived from analogies stemming from simple mathematical systems. … Continue reading

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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

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Of lives of men; of times of men-III

Of lives of men; of times of men-II As they were talking, they saw a sallow-complexioned youth pass by them some distance away carrying a bat on his shoulder. Vidrum waved out to him and he responded similarly and after some … Continue reading

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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

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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

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The story of the Orissan cycle-vālā

Vidrum had been under considerable pressure. His parents had made it clear that they would auction away his new bike if he was not ranked within the top 5 in his class in the impending mid-semester exams. They had also … Continue reading

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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

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The apparition of the Scottish surgeon

On a late summer evening, at the twilight hour, Somakhya accompanied by Lootika met Vidrum outside his home. Vidrum was supposed to show Somakhya something special he had found during a visit to the limestone excavations near his ancestral village. … Continue reading

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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

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Some personal reflections on Carl Gauss, Bernhard Riemann and associated matters

The biochemist Albert Szent-Györgyi had famously remarked that as he successively, journeyed for a better understanding of life from cell biology, to physiology, to pharmacology, to bacteriology, to biochemistry, to physical chemistry to quantum mechanics he lost life between his … Continue reading

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A superficial look at national population density and some life history features

Over the years we have repeatedly checked out various collections of data pertaining to the human condition in the same manner as we attempted to apprehend scientific data. We have wondered whether to write on them in any detail. We … Continue reading

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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

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A prefatory narrative

Jhilleeka and Prachetas were visiting Lootika and Somakhya. Prithika, the daughter of the latter two was much excited as she resembled and was to resemble her youngest aunt in more than one way – they seemed to have a some … Continue reading

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The great faceless man

In the late Yajurvaidika upaniṣat, the Śvetāśvatara, which is the foundational text of the śaiva-śāsana, the god Rudra is described thus: na tasya pratimā asti yasya nāma mahad yaśaḥ। There is no one who his equal, whose name [itself] is … Continue reading

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“Like the vidyādhara’s sword”

In old Hindu tradition a man who attained siddhi in his mantra practice was believed to become a vidyādhara whose might was manifest in the form his beautiful female partner who flew beside him embodying the power of fertility and … Continue reading

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Some reminiscences of our study of chaotic maps-2

Continued from part-1 The second two dimensional map we studied in our early days was that of Lozi: where and are constants. It becomes immediately evident that this map is conceptually similar to the Henon map, using the absolute value … Continue reading

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Some elementary lessons from iterative fractal maps

The famous Sierpinski gasket was one of the first fractals we wrote code for when we got access to a computer. It impressed us enormously that an intricate object with self-similarity over all scales could be generated by a rather … Continue reading

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Paper folding, Sundara Rao and geometrical constructions

Paper folding, which we shall hereinafter refer to as origami without further discussion on the correctness of the usage, is believed to have had a long history in Japan. Some believe that some primitive form of origami might have been … Continue reading

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The professor’s war

It was the end of his work week. Vidrum came to the office of Vrishchika of long tresses; she had just started her lab at the medical school. Vrishchika put on her gloves and handed Vidrum a box: “Here is … Continue reading

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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

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Ramanujan’s second construction for the approximate squaring of a circle

To experience the greatness of great men one has to relive or redo some acts of theirs to the best of ones ability. In ones youth such enactments might inspire one to make a bid for greatness. Whether this happens … Continue reading

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Leaves from the scrapbook

There were extensive memoirs in the form of electronic scrapbooks of Somakhya, Lootika and some members of their circle. Those in the know read the available excerpts due to matters of considerable interest being recorded in them. Other parts were … Continue reading

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śūlapuruṣasya vicāraḥ

Somakhya’s cousin Babhru and his family was visiting him during the vacation before they were to join university. After lunch he convinced Vidrum and Sharvamanyu to come over to his house when they got the chance for he thought more … Continue reading

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In the gray zone

Among the thinkers of the modern Occident one may take note of the Englishman John Gray. He is firmly an insider of the Anglosphere not just by origin but also by worldview: he is quick to spot the barbarisms in … Continue reading

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nakṣatra-darśanam

Varoli had just completed the synthesis of the xanthine coupled with hydroxymethyluracil and diaminotriazine to test an interesting hypothesis of Somakhya regarding a particular class of DNA-binding proteins. She was putting in considerable effort to finish it off by the … Continue reading

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Nālika-s

The first week of college had ended. Vidrum was returning from an eatery with his new friend Manjukeshi after an early supper. The two of them were rather surprised by the ferocious competitiveness of their classmates. Some refused to discuss … Continue reading

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The first three squareable Lunes

For the sake of some readers we shall first define a lune: A lune is a concave closed region bounded by two circular arcs respectively with radii and and distance between their centers as , where . This region looks … Continue reading

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The salinon

The yavana Archimedes or some later commentator of his among the Neo-Platonists of Harran described a figure they called the salinon, which was supposed to mean a “salt-cellar”. This material was acquired by the Mohammedans from those Neo-Platonists from whom … Continue reading

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van Aubel’s theorem

The van Aubel’s theorem is a simple theorem which is comparable to the theorem attributed to the French conqueror Napoleon Bonaparte regarding triangles. It is easy to prove once you know the upāya, even as the yogin-s would say ānanda … Continue reading

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Ovals, drops, tops, eights, pears and the like

Ovals, drops, tops, eights, pears and the like This piece may be seen as a continuation of the earlier one on our journey through the world of ovals. As it needed a lot of figures and some mathematical notation it … Continue reading

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svabhāṣāyāṃ śāstrīyā śikṣā

As PDF navame varṣe lūtikā tasyāḥ pañca-varṣīyāyai anujāyai varolyai dravyaśāstram aśikṣayat | lūtikā ‘vadat : “priye varoli dhyānena kārṇārpaṇaṃ kuru | atha vakṣyāmy amla-kṣāra-siddhāntaṃ ca lavaṇīkaraṇasya prayogaṃ ca | purve kāle svastyātreyeṇa+asmadīyena dravyavidā+amla-kṣāra-siddhāntaḥ proktaḥ | kāle ‘smin amla-kṣāra-siddhānto arrheniyas ca … Continue reading

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The giants among the lilliputs

For long, despite protestations and assertions to the contrary, people have known that men are all not born equal. There are few men who tower over the rest in one or more of the axes of distinction. For over a … Continue reading

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The astroid, the deltoid and the fish within the fish

As this article needed a lot of figures with some mathematical notation it is being presented as a PDF file: The astroid, the deltoid and the fish within the fish

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A biographical journey from conics to ovals

As this article needed a lot of figures with some mathematical notation it is being presented as a PDF file: A biographical journey from conics to ovals This may be read a continuation of earlier notes such as: Ovals, drops, tops … Continue reading

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The cardioid and the arbelos: the scimitar and the axe

The arbelos of Archimedes, an object most wondrous; it brought pleasure to us, when stalked by enemies, as the old yavana by Romans, who ended for good his days. What is the mystery of the scimitar and the axe which … Continue reading

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Der singende Knochen: śūlapuruṣāṇāṃ śūletyādi

That afternoon Vidrum was returning with a bunch of other friends whom he had taken through a tough course of climbing at a hilly locale. As they neared a certain road, he, Sharvamanyu, Somakhya and Lootika bade good bye to … Continue reading

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The ghosts of Tulagiri

Vrishchika was taking a few days off to visit her parents’ town before proceeding with her fellowship. Lootika had nearly completed moving her lab to Somakhya’s institute. She was happy that they could finally be together for good again and … Continue reading

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śūlajana-kāvya: Das Riesenspielzeug

Somakhya’s and Lootika’s families were returning from a ritual at the less-known temple of the goddess Bhuvaneśvarī. They were there to worship a mysterious yantra, which is one of the rare examples of the depiction of a curve known as … Continue reading

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Matters of religion-1

Indrasena had arrived at the house of Somakhya and Lootika for learning mysterious matters of religion. Entering their fire-room he saw Somakhya seated beside the square altar on a mat of bovine skin and Lootika seated beside the circular altar … Continue reading

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Lūtikā-Somākhyoḥ pravādaḥ

It was probably one weekend after the tumultuous incidents concerning the gifts of Vidrum. Somakhya’s cousin Saumanasa and her husband Matidhvaja had visited him and Lootika. Saumanasa had spent a good deal of the time with Lootika in the kitchen … Continue reading

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A geopolitical round up: last week of Nov 2015

Many turns of the sun ago, when we were still a kid in school, we had some classmates who had an unbridled admiration and enthusiasm for the Anglosphere and a rather deep-seated self-identification with it. While their English had little … Continue reading

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