Some novel observations concerning quadratic roots and fractal sequences
Disclaimer: To our knowledge we have not found the material presented here laid out here presented in completeness elsewhere. However, we should state that we do not follow the mathematical literature...
View ArticlePattern formation in coupled map lattices with the circle map, tanh map, and...
The coupled map lattices (CMLs), first defined by Kunihiko Kaneko around the same time Wolfram was beginning to explore cellular automata, combine features of cellular automata with chaotic maps. The...
View ArticleOf 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...
View ArticleFrustrations 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...
View ArticleAstronomical experiments: a preliminary look at globular clusters
While Alexander von Humboldt was exploring South America he observed a fuzzy object in the constellation of Centaurus and thought that it was a new comet. However, it turned out that it was the...
View ArticleCivilizational 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...
View ArticleMongolica: Knowledge preservation and generation, Bolad Aqa and the like
We had earlier written an essay on the preservation and production of synthetic knowledge by the Chingizid Mongols. Here we discuss a few additional points in that regard. It is clear that throughout...
View ArticleOur 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...
View ArticleCounting primes, arithmetic functions, Ramanujan and the like
We originally wished to have a tail-piece for our previous note that would describe more precisely the relationship between the Möbius function and the distribution of prime numbers. However, since...
View ArticleThe quotient triangle, the parabola-hyperbola sequence, the remainder...
The quotient triangle Consider a positive integer . Then for all do the floor operation . Say , we get , a sequence of quotients of the division . If we do this for all we get the quotient triangular …...
View ArticleMongolica: Qubilai Khan’s campaign to destroy the Southern Song
The final act in Mongol conquest of China shows the military capability of Qubilai and why his grandfather, the great Khan had singled him out as the one who someday would adorn his throne. We shall...
View ArticleA 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...
View ArticleThe remarkable behavior of a map displaying derived from a simple model for a...
One of the simplest yet profound mathematical models for biological growth emerged sometime in the middle of the 1800s due to the work of Verhulst. It describes population growth thus: let be the...
View ArticleA brief note on some new developments regarding the genomics of Indians
When we wrote a previous article on this matter we had stated that new data will alter the details of our understanding of picture discussed therein. Indeed, two new manuscripts which were deposited in...
View ArticleA 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...
View ArticleConvergence to a palindrome
This is a brief account of a sequence we constructed inspired by Dattatreya Ramachandra Kaprekar. It is not known to us if he had discovered it in one of his obscure publications from a small town in...
View ArticleA sequence related to prime counting
The current note arose as an exploration branching off from the matter discussed in these earlier notes: this one and this one. As we saw before, Carl Gauss, while still in his teens, produced his...
View ArticleSītā 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...
View ArticleThe 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...
View ArticleA note on āṃreḍita-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...
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