Packing constants for polygonal fractal maps

Among the very first programs which we wrote in our childhood was one to generate the famous Sierpinski triangle as an attractor using the “Chaos Game” algorithm of Barnsley. A couple of years later we returned to it generalize it as a map in the complex plane. Consider the polynomial equation,

z^m+1=0, where integer m=3,4,5...

The roots of this equation, z_j: z_1, z_2... z_m, define the vertices of a m-sided polygon in the complex plan. For example, if m=3, we get an equilateral triangle defined by the roots z_1= \tfrac{1}{2}+\tfrac{\sqrt{3}i}{2}, z_2= -1, z_3= \tfrac{1}{2}-\tfrac{\sqrt{3}i}{2}.

With this in place the Chaos Game map is defined for a given m as:

z_{n+1}=r(z_n+z_j),

where z_j is one of the m roots chosen randomly with equal probability as the others in each iteration of the map and 0<r\le 1. If r=1 for any m we get a random-walk structure (Figure 1).

chg06_1Figure 1

For other m, r we get chaotic maps and for particular values of m, r we get attractors with a fractal structure. Thus, the Sierpinski triangle is obtained with m=3, r=\tfrac{1}{2}. This fills the triangle defined by z_1, z_2, z_3

chg03Figure 2

For m=4, r=\tfrac{1}{1+\sqrt{2}} we get the fractal street block (Figure 3).

chg04Figure 3

We currently revisited this map because of a curious problem that emerges when we continue this operation as below for further polygons. For m=5, r=1-\tfrac{1}{\phi} (where \phi=\tfrac{1+\sqrt{5}}{2}, the Golden Ratio) we get the fractal pentagons surrounding the interior penta-flake (Figure 4).

chg05Figure 4

For m=6, r=\tfrac{1}{3} we get the fractal hexagons surrounding the interior Koch’s snowflake (Figure 5).

chg06Figure 5

For m=7, r=\tfrac{1}{S} (where S=2+2\cos\left(\tfrac{2\pi}{7}\right), the Silver constant. The Silver constant is an algebraic number which is the real root of the cubic x^3-5x^2+6x-1) we get the fractal heptagon necklace surrounding the interior hepta-flake (Figure 6).

chg07Figure 6

For m=8, r=\tfrac{1}{2+\sqrt{2}} we get the fractal octagon necklace (Figure 7).

chg08Figure 7

For m=9, r=\tfrac{1}{2+2\cos\left(\pi/9\right)} we get the fractal nonagon necklace (Figure 8).

chg09Figure 8

For m=10, r=\tfrac{1}{1+2\phi} we get the fractal decagon necklace (Figure 9).

chg10Figure 9

For m=11, r\approx 0.2209 we get the fractal hendecagon necklace (Figure 10).

chg11Figure 10

For m=12, r=\tfrac{1}{3+\sqrt{3}} we get the fractal dodecagon necklace (Figure 11).

chg12Figure 11

Given that these attractors are fractal, they have an infinite perimeter but occupy a finite area. Thus, one can define a common feature for the above attractors namely “tangency” of the fractal elements, i.e., each polygonal unit is distinct from its neighbor with the same scale-factor but at same time makes a contact with it like a tangent. While for the triangle and the square this definition is a bit murky, it is clearly visible from the pentagon onward. It can be contrasted with other fractal attractors obtained by this method where the elements overlap or are shared. For instance for m=12, r=\tfrac{1}{2+2\cos\left(\pi/6\right)}, we have the expected dodecad structure but two dodecad sub-elements are shared by each of the adjacent elements (Figure 12).

chg_12_wheel_timeFigure 12

In the above examples (Figure 2-11) we have determined for each polygon the value of r which results in a tangent attractor:

m=3, r=\tfrac{1}{2}; m=4, r=\tfrac{1}{1+\sqrt{2}}; m=5, r=1-\tfrac{1}{\phi}; m=6, r=\tfrac{1}{3};\\   m=7, r=\tfrac{1}{S}; m=8, r=\tfrac{1}{2+\sqrt{2}}; m=9, r=\tfrac{1}{2+2\cos\left(\pi/9\right)}; \\  m=10, r=\tfrac{1}{1+2\phi}, ; m=11,  r\approx 0.2209; m=12, r=\tfrac{1}{3+\sqrt{3}}

For m=5..8 it is the reciprocal of 2+2\cos\left(\tfrac{2\pi}{m}\right)=4\cos^2\left(\tfrac{\pi}{m}\right), which are known as Beraha constants ( B_n) that appear in graph-coloring theory. However, for m=9..12 this principle clearly breaks down: e.g. for m=12, we see that \tfrac{1}{B_{12}} yields the overlapping attractor (Figure 12). We have been able to obtain closed forms for the r that yield tangent attractors for all m except 11, where we report an empirically determined approximate value. What is the closed form expression for it? This leads to the question of whether there is a general formula to obtain our r that results in tangency? To our knowledge these have not been answered.

Posted in art, Scientific ramblings | Tagged , , , , , , , ,

Cows, horses, sheep and goats

It goes without saying that humans are what they are today because of cows, horses, sheep and goats. Hindu civilization in particular is in the very least the product for the first two, while remaining two contributed to it from “behind the scenes”. The major civilizational transitions in human history were built atop the bones of these four animals: the Neolithic developments in West Asia, the urban Nilotic civilization in Egypt, the rise of the Indo-Europeans on the Eurasian steppes, the rise of the Turco-Mongolic peoples on the same steppes but at their eastern end, and the expansions of the African pastoralists. We were curious if the present distribution of these animals has any notable features or relationship to their history. Accordingly, we used the UN Food and Agriculture Organization data on these animals to visualize their distribution across different countries and continents. Table 1 shows their total population (here the term “cows” stands for what is provided in the FAOSTAT database as cattle).

Table 1. The latest UN FAOSTAT population data
\begin{tabular}{lr} \hline Animal & Population \\ \hline Cows & 1491687240 \\ Sheep & 1202430935 \\ Goats & 1034406504 \\ Horses & 60566601 \\ \hline \end{tabular}

We first plot the populations of each pair of these four animals for all countries that possess both of them using the \log_{10} (Figure 1) and tabulate the correlations between them in Table 2.

Livestock_correlationsFigure 1

Table 2. The Pearson correlations between life stock on the \log_{10} scale
\begin{tabular}{rrrrr} \hline & Cows & Horses & Goats & Sheep \\ \hline Cows & 1.00 & & & \\ Horses & 0.85 & 1.00 & & \\ Goats & 0.81 & 0.66 & 1.00 & \\ Sheep & 0.80 & 0.72 & 0.83 & 1.00 \\ \hline \end{tabular}

The populations of the horses and cows are the most correlated pairs. The sheep and goats are the next most correlated. Thus, animals of comparable size tend to be more correlated in their populations. The horse-cow pair is also the primary pair of the old Indo-European pastoralism. It is possible there is a historical echo of the Indo-European conquests that made this pair a widely adopted unit.

Livestock_ratiosFigure 2

We then looked at the distributions of the ratios for these six pairs (Figure 2). In each plot we mark the following: the mean(red), India (blue), Mongolia (green), Kazakhstan (gray), Kyrgyzstan (cyan). We can see that the plot for the cow:horse plot is the least skewed and is approximately normal. India presents a large country that is heavily skewed in the favor of the cow over the horse. The horse evidently did not do very well over larger swaths of India unlike the cow. On one hand this had its consequences for the Indians in course of their conflict with horse-borne invaders. On the other it made India the land of cows. In contrast, Mongolia, Kazakhstan and Kyrgyzstan show the reverse trend, being horse-heavy pastoralist nations. Kazakhstan was one of the first sites of horse-domestication in horse-centric pastoralist Botai culture. This form of pastoralism persisted on the eastern steppes among the Altaic type of peoples long after the Botai people became extinct after colliding with our Indo-Iranian ancestors . Mongolia still retains this state in its most drastic form.

Mongolia is also unusual in favoring both goats and sheep over cows. Notably it also has a comparable number of sheep and goats. The sheep:goat ratio shows multimodality with some countries investing heavily in favor of sheep over goats. This is where the two steppe nations Kazakhstan, Kyrgyzstan differ from Mongolia. India in contrast weighted in favor of goats over sheep, again reflecting the environmental conditions favoring goats. Further, goat pastoralism might have come early to India along with the Iranian farmers who played a major role in the foundation of the Harappan civilization. Nevertheless, sheep pastoralism eventually spread deep into peninsular India with the use of sheep milk and a memory of it is preserved in the origin myths of the Reḍḍi-s of Andhra. The goat:horse ratio is also notably multimodal suggesting that originally goats and horses defined very different pastoralist niches. The effects of this ancient niche distinct appears to persist to this date.

Livestock_Pop_changeFigure 3. India (blue), Mongolia (green), world (black)

The above are based on the latest population statistics but one can also ask about their dynamics. In this regard the FAOSTAT database has data for many countries and the world for about 57 years. One simple way to look at population change in this period is fraction of population change with respect to the start and end of this period. This can be assessed using the formula:

f_{pc}=\dfrac{2(p_f-p_i)}{p_f+p_i}

Here f_{pc} is the fraction of population change, p_i the initial population and p_f the final population. The distribution of f_{pc} for the four animals is plotted in Figure 3. Except for horses which have shown a slight decline, the populations of the other animals have shown growth world-wide. One sees that, except for sheep, the f_{pc} for India is lower than for the world for the remaining animals. In contrast, for Mongolia it is higher than for the world define a truly pastoralist nation. The Indian horse populations have shown a notable decline in this period.

Livestock_dynamicsFigure 4. y-axis in \log_{10} scale.

This measure only gives a coarse view of the population change. Hence, we looked at the absolute population change for 3 nations (Mongolia, India, USA) in Figure 4 over a 57 year period for which data exists. The dynamics of the precipitous decline of the horse in India is apparent. As noted above, much of India is not suited for the horse and in the absence of the old military and royal-display derived pressure to keep the horse numbers high it has mostly had a free fall. USA shows almost the reverse trend with respect horses and cows. We are not sure if this trend for cows relates to the decline in beef consumption among the Americans. The India cattle situation two booms followed by busts. The turning points for these busts seem to correspond to El Niño-related droughts and it needs to be see if they were indeed the triggering factors for the declines in Indian cattle. In Mongolia there seem to be generally similar trends for both cattle and horses. The marked rise in productivity after the fall of the Soviet Empire suggests the release from Soviet collectivism allowed the Mongols to recover their traditional pastoralist lifestyle. The Mongolian situation also shows the strongest evidence for climate effects, given that after the Soviet collapse the Mongolian cattle and horse populations have shown similar busts and booms. These seem to correspond to the aftermath of the severe Mongolian winters known as the jud-s that take a heavy toll on the animals and the pastoralists. However, the warming in northern latitudes might be allowing a rapid bounce back from the juds.

Posted in History, Scientific ramblings | Tagged , , , , , , , , ,

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 his research practices were questionable. Based on information from a whistle-blower we then reached the conclusion that he was involved in outright scientific fraud. This prompted us to investigate his work a little more and we found at least 15 published papers of his with fraudulent data. This brought to our mind one of the earliest cases of fraud in molecular biology by an Indian postdoc from Mumbai working with Jim Watson. A broader investigation revealed that the person whom we were dealing with was merely one of at least five researchers of Indian background all with professorial positions in the United States of America and India who were involved in a very similar pattern of fraud. This concerned us for it brings a bad name to researchers of Indian origin. However, simultaneously we also observed several examples of similar fraud by people of European, Jewish, Chinese and Japanese ethnicity. Indeed, very recently we had another case to deal with involving comparable, painful fraud by Chinese collaborators. Hence, we thought this is a universal problem with no special predilection for such fraud among Indians.

However, as the days went by since our original encounter with fraud, we seemed to accumulate more and more cases of Indians engaging in such fraud. Recently, we uncovered yet another case of fraud involving a family of proteins whose evolution and biochemistry we had helped characterize in the first decade of the 2000s. This again involved an Indian lead author giving us the gnawing doubt that things were not right among our people. This prompted a colleague and me to look at federal registry of scientific misconduct issued by The Office of Research Integrity (ORI) of the Department of Health and Human Services (DHHS), USA to see if some of the cases we had detected were in it. This register records cases in which fraudulent research performed using public money in form of grants given by the DHHS were reported to the ORI for examination. While the federal register released by ORI does not cover all cases of fraud performed using public funds, it has at least 60 confirmed cases along with the details of the case and the punishment recommended by ORI. These 60 cases were in period from 2011 to 2019 CE. The majority of them were biochemistry/molecular biology fraud of the kind we had encountered in our starting investigation: 1) manipulation of gel image; 2) creation of fake images of biological material; 3) Some cases of simple plagirism; 4) Out right creation of fake numerical data.

We realized that these 60 cases could provide a means of examining if Indians were particularly prone to fraud or not. Notably, the cases released in the register allowed the names to be classified quite unambiguously into 6 ethnic groups (Table 1). Among West Asians there are representatives from each of the 3 Abrahamistic religions of the region.

Table 1
\begin{tabular}{lrrrr}  \hline  Origin & Count & Percentage & Cheaters/million & Cheaters/1000 \\  \hline  European & 27 & 45.00 & 0.14 & 0.67 \\  Indian & 20 & 33.30 & 6.29 & 4.72 \\  Chinese & 7 & 11.70 & 1.85 & 0.57 \\  West Asian & 4 & 6.70 & 0.38 & 2.32 \\  Korean & 1 & 1.70 & 0.59 & 0.25 \\  Japanese & 1 & 1.70 & 0.77 & 0.33 \\  \hline  \end{tabular}

Indians constitute 33\% of the fraud cases in the federal register. This itself is quite striking because it is rather clear that they do not make up that high a fraction of the biomedical research workforce, which is being probed here. Now, the simplest normalization for the counts is by the representation of these ethnic groups in the USA. This population data can be assembled quite easily by an internet search for the period under consideration. Normalization by this population share is shown in column 4 of table 1 as the number of cheaters per million of the population. By this reckoning and Indian would be nearly 46 times as likely to be involved in fraud as a person of European descent.

One could object that the US population share of the ethnic groups is not a valid normalization for it does not accurately reflect their representation in the biomedical work force. While the latter part of the statement might be true it is amply clear to anyone in the business that Indians do not constitute a fraction greater than Chinese in this workforce, making this objection quite facile. Yet, one would want to perform a more objective normalization based on the proportions of these groups in the workforce. This data is much harder to get in a clean form. However, an article published in the Nature magazine “The new face of US science” by Misty L. Heggeness, Kearney T. W. Gunsalus, José Pacas and Gary McDowell (03 January 2017) allows us to get approximate figures needed for such a normalization. This article informs us that in 2014 (which is in the time range of the data under consideration and also given that a typical graduate student/postdoctoral career in about 4-5 years) that there were about 69000 biomedical researchers in the US. Of these about 40020 were of European descent (excluding Hispanics) and 23500 with ancestry in various Asian countries. That primarily includes Indians, Chinese, Koreans and Japanese. To obtain the breakdown we can use two methods: 1) Sample a random set of 100 biomedical research publications and see what proportion of these Asians are found in them; 2) Use the proportions of graduate students from these nations in American biomedical research programs to get a sense of the breakdown. Based on this we can estimate the approximate maximum number of biomedical researchers of these ethnicities to be: 4236 Indians, 12236 Chinese, 3928 Koreans and 3059 Japanese. For West Asians it is harder to get an estimate but based on the biggest contributing group of these the Israelis from a publication in the Jewish newspaper Haaretz we an infer this number to be \approx 1725. This allows a more specific normalization, which is shown in column 5 of Table 1 as the number of fraudsters per 1000 researchers.

The Indians continue to remain the most prone to fraud even after this more realistic normalization. If the 60 fraudsters were evenly distributed among the 69000 biomedical researchers then the probability of finding a fraudster at random would be 0.00087. Given this and their numbers in the biomedical workforce, the probability that at least 20 Indians are frauds in the federal register by chance alone is 4.44 \times 10^{-10} or they are \sim 8 times more likely than other populations to commit biomedical research fraud. From the names of the Indian fraudsters in the federal registry we can infer that in all likelihood all of them come from the “forward castes”. Up to 1/3 of them are likely of brāhmaṇa descent. This means they are drawn from the Indian elite. As can be seen in Table 2 they are drawn from all over India with a particular over-representation of individuals from South Indian states.

Table 2
\begin{tabular}{lr}  \hline  Region & Count \\  \hline  Tamil Nad/Kerala & 7 \\  Telugu states & 4 \\  Bengal & 2\\  Sindh/Panjab & 2 \\  ``Hindi belt'' & 3 \\  Maharashtra & 1 \\  Karnataka & 1 \\  \hline  \end{tabular}

Further, since entry into the US biomedical work force typically involves an IQ test (administered either for admission to an American graduate school or to an Indian institute), we are dealing with people most likely with IQ \ge 123. Thus, what we are seeing is not per say a problem of cognitive capacity but a problem of “ethics” or “corruption” in the Indian cognitive elite.

One could point out that there is some bias against Hindus in the US academia; hence, they might be specially picking on the Indians as opposed to the European origin majority or other foreigners, though all commit fraud to a similar degree. Undoubtedly there is bias — powerful fraudsters of European or Jewish descent are more often “rehabilitated” or overlooked than those of Indian descent. Nevertheless, that is unlikely to have been the primary cause for at least the cases in the federal register. Several of the Indian cases in the register were considered “golden boys” by the American institutions or had vanity articles about their fraudulent research in American outlets. Thus, it does not appear that at least in these cases they were being specially targeted. Thus, we posit that there is a real problem.

A part of this problem is a general one. The Euro-American biomedical research (which sets the trend in most of the world except to a degree in Japan) is beset with several serious problems:
* There is very little attention paid in biology education to the theoretical foundations of the science. We would go as far as to say that less than 50 \% of the practitioners in biomedical research have good grasp of the foundations of biology. To give an analogy of how bad this is, imagine more than half the physicists and real engineers plying their trade without knowing classical mechanics in any serious sense (e.g. having not much of a clue of how to set up a Hamiltonian or a Lagrangian of a system). As a result poor hypotheses abound, which in turn spawn a glut of bad ideas.

* The Euro-American scientific system has an unhealthy model of competition and the fetish of peer-review, which favor both an urge to cheat to get an article published as well as rich dividends for nuanced plagiarism -i.e. plagiarism of ideas without citation rather than outright copying of text. To put it bluntly we have seen some form a plagiarism of our work with total impunity almost every other month in the past few years. Plagiarism also contributes to confirmation bias and fake reproduction of bad ideas. A part of this competition is fostered by big labs in several Euro-American institutions, where powerful principal investigators run the show like industrial sweat shops. These environments also do not allow for proper oversight — I am aware of cases where the graduate student or postdoc did not see the PI for more than a month at a stretch. Further, most interaction was limited to sanitized presentations in lab meeting rather than direct oversight by the PI at the bench.

* The magazine culture: Euro-American biomedical research assessement and funding agencies place enormous emphasis on publication in the two famous British and American science tabloids or the journal Cell, their many offspring and upstarts like eLife, PLOS Biology etc. In some of these venues, especially the tabloids and Cell articles are subject to insane review processes with time lags of 6-12 months from submission to acceptance for publication. These venues are thus high stakes venues that increase the urge for plagiarism and chicanery.

These are general causes that affect both Indians and others. However, as the scientific system in India increasingly emulates these practices in some form, it increases the incentive for Indians in India to commit fraud rather than do good science. Now let us consider some factors that might predispose Indian origin researchers to commit fraud more often than others:
* Some of the fraudsters who are in the federal register come from labs run but Indian origin PIs in American institutions. Their labs are reported as having an unhealthy environment — high pressure to produce results at short notice without adequate mentoring or oversight. We have evidence that this was the case even in the fraud cases which are not in the register. As noted above this is a major recipe for malpractice. Thus, it appears that there is some tendency for Indian origin PIs to be less than professional in managing their labs.

* Indians face major immigration constraints in the US. This can be used as an anvil both by American and Indian origin PIs to pressurize their students, who typically have no other avenues for escape or alternative employment due to sword of deportation hanging above their necks. Hence, science takes a back seat to survival and the incentives are slanted towards getting ahead by means of malpractice.

* Training in Indian schools and colleges does not emphasize aspects of honest scientific practice. Students often manipulate laboratory experiments to get results that their instructor expects. Little training is given in the statistics of variation and experimental error in school and college. For example, in my first semester in college I vividly remember the instructor conducting physics lab demanding that we exactly get g=9.8\tfrac{m}{s^2} in single trial experiment!

* Importantly, most students in the science stream in India have no real interest in science per say but merely see it as a means for obtaining a seat in engineering or medical school. Those who do not make it typically enter the sciences and gradually drift their way through a B.Sc. and then a M.Sc. to finally reach a graduate program. Most of them are not from the cream of the educational system and are often not suited for cutting-edge science. Thus, when they make it to graduate school in the US they come ill-equipped for science and when subject to pressure might have some incentive to “game the system” just as they gamed the exams in India to get ahead.

* After the near-death encounters with Islam and Christianity, Hindu civilization is a shadow of its former self. There is serious decline of the internal system known as dharma. The decline of dharma shows up in the form of loss of discernment regarding the pursuit of knowledge and the pursuit of gain. In the past when a person committed himself to the pursuit of knowledge, there was a strong demand on him to observe certain ethics. These were enforced by the gate-keepers of the system and quacks would be punished. Indeed, father Manu the law-giver has a long list of criminals engaging in fraud like palmistry or future-prognostication, quacks, scams, and fellows claiming qualifications which they do not possess. He recommends that such be caught by the Rājan using investigators sent to keep an eye on such and if their crimes are proven to fine them. However, multiple repeat offenders could be put to death. Similar the legal tradition of Yājñavalkya has various provisions for the punishment of the quack physician.

In conclusion, we do not find any pleasure in presenting this. It personally only affects us in a negative way given that it has brought a bad name for Indian researchers, which is not going to go away in the near future. That is why I tell people that it is better to be a small man doing some low key but real science rather than professor Big who appears in the newspapers but does fake science. The approach of fake it till you make needs to be adopted with greatest care and does not apply to every aspect of human activity. These observations might have much deeper, unpleasant implications. It is relatively clear that the Hindus have not performed too well for being an old nation with clearly visible past achievements after they saw off the English tyrants more than 70 years ago. There are many reasons offered like the effects of the medieval Mohammedan incubus, the English tyranny, and Gandhi and Nehru. The former factors certainly have had their effect. But the past 70 odd years since independence have seen no major revival of scientific pursuit. There have been no major successors to many of the exemplary solitary Hindu researchers from the pre-Independence or early post-Independence era. We suspect that one cause for this is a terrible culture of knowledge generation among Indians in recent times. An offshoot of this is this tendency of dishonesty that we are seeing among Indian biomedical researchers. It shows in terms of tangible technology too: despite having an big need for the aeronautical engine or a proper assault rifle, Indians have had considerable difficulty in successfully mastering these technologies. Facets of this are also seen in other areas of Indian creative expression, e.g. journalism and cinema. I do not watch cinema but I am reliably informed by someone who does that there is some tendency for plagiarism from the occident. As with science, this tendency in journalism along with unthinking adoption of occidental memes are damaging for the nation. In journalism the idea is merely to produce uncritical stuff that the pay-master (e.g. the mleccha) likes. Hence, we feel that this data should be presented so that our people make take deep look at their problems and consider their science policy implementations accordingly.

See also:
Big man’s story
The fake scientist

Posted in Life, Politics, Scientific ramblings | Tagged , , , , , , , , , ,

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 nodes that I needed for my analysis. It also gave me some opportunity to talk to several researchers in my general field of inquiry. I was to leave the coming weekend to Kshayadrajanagara to take an exam. It was also an opportunity for me to spend some time with my friend Indrasena and catch up with his studies and other more rarefied matters. I had gone earlier in the evening to meet a member of my extended family for dinner. Also at dinner was a noted mantravādin known to him. We had a lively debate with him about the correct practice of various mantra-s and the incorrectness of the māhāpāduka-dīkṣā relative to the krama-dīkṣā. We essentially tried to impress on him that none of the mantra-s would have fully efficacy and in cases could even be harmful if not performed as per the authoritative tantra-s of the kaula-mārga duly adjusted for a brāhmaṇa: indeed for a brāhmaṇa, the śruti is a higher authority at a basic level than any tantra. Then our host remarked to us that he had a friend, a coethnic of ours, whose daughter also needed to travel to Kshayadrajanagara for an internship at the same university as where Indrasena’s brother was an intern. He told me that I should perform the role of a minder to her on the train journey to the city. I had to agree for it was an elder’s command but was reluctant about it for it meant I had to be responsible for a woman’s safety especially in cities where evil marūnmatta-s and dasyu-s were known to be on the prowl looking for women.

Entry 4; Āgantu, year Anala of the first cycle: I was at station to board the train to Kshayadrajanagara. My extended clansman’s wife got the young lady who I had accompany. She seemed like a quiet and shy person who said nothing beyond her name which was Shallaki. While remarkably unusual like that of the caturbhaginī, it still sounded vaguely familiar though I could not place it. Since I am no conversationalist myself I did not say anything beyond my name and just helped her a bit with her luggage. She seemed to be in the age range as the two younger caturbhaginī but something again struck me as unusual beyond her name: she had some lakṣaṇa-s similar to them unlike no other women, which are only visible to the insiders of the gaṇacakra. I again quietly remarked to myself that it was a strange thing. While some ruffianly dāḍhīvāle got into the train with us, thankfully, they passed ahead and the two other travelers in the compartment seemed innocuous. One was a soldier and the other was a pious vaiṣṇava woman. As the train got moving I spent my time looking out of the window as the vast expanses of Bhārata had always fascinated me. Occasionally an interesting temple and on other occasions a cemetery would pass by. When the latter would come in sight I would quietly utter the first verse of the Nīlarudra. Sometimes a strange-looking granite mountain would pass by. By examining its rock closely, I realized that these were the Archean granites — some of the oldest rocks on the Earth. As the train coursed ahead I caught sight of some sedimentary rocks likely from the Proterozoic and remarked to myself that someday I should perhaps journey there to see if I could collect some of that rock.

The reddish dusk soon gave way to the inky darkness of night and I could catch sight of the great star \alpha Cygni giving me a good indication of the precise direction in which we were traveling. In clear air away from the cities I could catch sight of the Milky Way sprawling in the midst of the summer triangle. My fellow-traveler Shallaki then opened a large packet my extended clanswoman had provided her and asked if I might want to have dinner. I acquiesced and she quietly gave me a share while telling me that I could take more if I wished. She also courteously offered the food to the other two passengers who had, however, purchased their own fare. I received a message from Lootika who was also journeying back home to take the same exam but at a different center. Like me she too was unhappy about the break it was causing to the flow of our work. She also had some other sense of unease, which she stated arose from an encounter with a bhūta that Vrishchika had told her about. But the exchange grew more lively when she said that she had collected several specimens of microthelyphonid whip-scorpions in course of her field work that had been totally ignored since the English naturalists had found them in the days when their tyrants were lording it over our land. We exchanged messages regarding the peculiar bristles on their second limb wondered what their function might be. Thinking about this I seem to have fallen asleep.

The next morning when I arose the rest of the passengers in the compartment were already awake. The elderly vaiṣṇava woman was reading some devotional material and asked me if a certain station had passed since I was the only one who kept gazing out of the window. I replied in the negative. She was happy as she said that she wanted to get some surasā and uttered it with a Dravidian accent. I was a bit puzzled and did not get what she said. Shallaki pointed to me that she meant surasā as in tulasī. A little while later the train stopped for at that station and I darted out and got bunches of basil for the vaiṣṇava woman. Since she said she was proceeding to a shrine of Nṛsiṃha where she wanted to offer them I got some extra bunches so that she might offer some on our behalf too. She was very thankful that I had obtained the basil given that she might have not been fast enough with her aging limbs to get back into the train. She insisted on getting me and Shallaki dośaka-s in the next stop despite our strong protestations. Invoking Rudra that his darts might not harm me in the form of food I consumed the dośaka in order not offend the elderly woman.

When Shallaki told me that the lady meant tulasī by surasā, I made a remark that it gives some hint about the obscure etymology of the plant’s name. Till that point in the journey Shallaki and I had exchanged just a couple of sentences but her eyes suddenly lit up at that comment of mine and we had a interesting discussion on the etymology of the Indian words for the basil and wandered off into a discursive chat on the substrate in Indo-Aryan. It was in course of that conversation that I learned that she was interested in the evolution of languages and that it was the object of her study. The conversation also convinced me that the crossing of our paths had some deeper significance but I still did not known what it was.

Entry 5; Cakram, year Anala of the first cycle: Finally, we arrived at Kshayadrajanagara and upon getting off the train I saw Indrasena and his brother Pinakasena who had come to pick me up. I introduced them to Shallaki. The brothers stole a quick glance at each other with utter and unbelievable surprise but did not say anything. Suddenly, I realized that a prophesy from a few years back by might be playing out. We boarded the bus to go to Indrasena’s home. While my mother had wanted that I stay with my uncle during this visit, I instead had made up my mind to stay with Indrasena’s family. My cousin Saumanasa was also writing the same exam and I thought I could meet her briefly after the exam and convey my familial sentiments.

As the bus labored through the crowded roads of Kshayadrajanagara we saw many a dirty sight — a consequence of a roguish political party Congress-S which ruled the state and paid little heed to cleanliness. Coming from a small town Shallaki was more startled by the sights than the rest of us. Suddenly the bus came to a standstill and showed no signs of even inching forward. Despite craning my neck, I could not see much but Pinakasena clarified that the city was being visited by an important CEO of a mleccha multinational, a person of Indian origin, Pachchaisundari by name. Her convoy was passing by and had held up all the traffic. She was recently in the news for the supreme court had green-lighted her plan of online-social credit which she had established in collaboration with another CEO Lundberg. It works thus: If you say publicly made a statement on social media like ”Mohammad was perhaps the greatest man who ever walked on the earth” or ”Mahmud Ghaznavi employed Hindus and Moslems alike based on their merit and service credentials” then you got a positive credit. On the other hand if you made a statement like ”Baboor demolished a famous temple of the Hindus at Ayodhya” then you got a negative credit. Building negative credit could eventually lead to such a score that your email on Pachchaisundari’s platform could be locked up for a week or you could not post on social media and so on. But if you built positive credit you could cash it for discounts on online purchases, subsidized tickets for online movies and serials and the like. It was being touted as a great tool to aid the building of secular democracies although it was model pioneered first the neo-Han empire of Xi in China.

After nearly a half hour wait, we finally got moving and reached Indrasena’s house. We let Pinakasena to lead Shallaki to the apartment she was to stay in with two other women. After I had refreshed myself with a bath, I went to Indrasena’s room and he mentioned the prognosis of the Vīrabhadra-nartaka. I nodded and said that everything was falling in place indeed and confirmed to him that till the moment I saw him and his brother I did not precisely realize what was playing out. Indrasena asked me if had heard anything from Lootika and before I could answer told me of Vrishchika’s encounter with the bhūta. I remarked that Lootika was rather worried of the same and that the alignments of the prophesies were rather striking and even quite unexpected to me.

Entry 6; Luki, year Anala of the first cycle: After the exam was over I briefly dropped by at my uncle’s workplace to wish him and then went to his house to meet my cousins and aunt. Then I ambled back to Indrasena’s home for the evening. Pinakasena had sought the permission of his parents to have Shallaki over over for dinner. Thus, when I came in the three of them were lost in a discussion on certain intricacies of the upāsanā of Guhyakālī. The prophesy was now confirmed in my mind beyond any smidgen of doubt. Leaving the other two to continue their discussion, for it was after all their kula, Indra and I went over to his room. He asked me a bit about the exam since he was to write the same the following year. I then offered worship to his idols and pictures of Vaiśravaṇa. He told me of a strange dream he had witnessed the prior night — he seemed think there was something to it. He had dreamt of a man being killed by a centrifuge rotor exploding out of its spin-drive and striking him. The four of us then went up to the terrace to ply the planchette as we all felt a strong premonition of encountering at least one bhūta. Surely enough, we had steady stream of phantoms animating our device one after the other. The first bhūta startled Indrasena greatly. It was a ghost of a young man who said that he had been killed in a centrifuge blast at Turushkarajapura. Indrasena wanted to engage him a bit more but I sensed danger in letting him hang around. So I signaled to Indra to dismiss him right away. Before leaving he tried to seize Shallaki but she repulsed him with a mantra that neither I nor Indra knew but was apparently known to Pinakasena. I knew, however, that it was not the last that our gang was going to see of this phantom.

The next bhūta was that of a young woman who narrated the following biographical details: While she was born in a dīkṣita family, she had degenerated to being a puṃścalī. Indra remarked that it was a case of regression to the mean but it could have been something worse — a memetic infection triggered by familial degeneration. She began practicing her puṃścalī-vṛtti while she was enrolled in college. There were exams at the end of the semester. Previously, for the physics exam students could only use log tables or slide-rules. However, that year there was an announcement that the state might allow the use of electronic calculators. Being flush with money for a college student due to her puṃścalī-vṛtti she had bought herself two calculators an ordinary one and a scientific one and took them with her in the hope that the state might allow calculators on the morning of the physics exam. Indeed, they permitted the use of calculators that day. There was a brāhmaṇa boy in her exam hall who had only brought log tables. He was on only one in the class who had no calculator and at a clear disadvantage of finishing in time. He asked the supervisor if he could share the calculator of his neighbor. The puṃścalī stood up and told the supervisor that she could lend the brāhmaṇa her spare ordinary calculator. The supervisor acquiesced. With that and the log tables he was able to smash the exam and finished it well ahead of time. However, puṃścalī having spent her time elsewhere during the semester found the going tough. So she looked at the brāhmaṇa who sat a few benches away. He realized she was in trouble and placed his answer sheet such that she could copy some of his stuff. Thus, she somehow passed and obtained a degree. She had subsequently become a high-level veśyā and grown close to a certain Habib Raqib. He sliced her throat one day as she refused him her services for free that day. She wondered if she had any puṇya left from her service to the brāhmaṇa. We dismissed her by directing her at the marūnmatta who had killed her.

The next ghost was also that of a young woman of the vaiśya-varṇa. She declared herself to be a roadside maker of fast-food like bhṛjika-s and śṛṅgāṭaka-s. She was originally from a barely middle-class family hailing from a sector of Mathura where an old temple of Kumāra had stood. All members of her immediate family had been killed by socialists when they were journeying on a vacation to see some relatives in Magadha. She was take for dead in the attack but survived as the body of her brother had taken all the bullets shielding her. A distant relative had given her some money and with that she journeyed to Kshayadrajanagara along with a vagabond friend and two set themselves up there on a street there as fast-food makers. Her vagabond friend was killed shortly thereafter in an accident but she labored on. Her snacks were so popular that she was soon demolishing the businesses of her rivals on the street. Her rivals harassed her in several ways and had her cart confiscated. However, is so happened that the inspector of the local police-station had become a big fan of her snacks; so, he restored her cart and utensils and let her continue her trade. He even went as far as to help her from harassment by the rivals. One evening her stove suddenly switched of by itself and she saw the image of her own face in its dying flame. The next day she found her skin darkening, felt a tingling sensation in her extremities and a racing heart. It kept getting worse and eventually she expired. Her corpse was handed over to the local hospital. The physician named Jayasena who performed the autopsy on her corpse had declared that she had been poisoned by the ”scorpion-killer”. She said it was slipped into her food by the rival vendors and she was searching for them.

The next phantom that possessed our device was that of a brāhmaṇa man. He was clearly aggressive and apparently a learned V1, which made us curious about his fate. But he did not answer our questions and instead posed questions to us. He asked us: ”In which saṃhitā are the Rudra-s called Sadāśiva-s?” We thought it was joke. But he said he would not leave like Vikrama’s vetāla unless one of us answered. Taking hold of the planchette I told him that it was that it was in the AV. He asked me then to spell out the mantra. I recited the ṛk and he said by way of the device ”svasti”. He then spewed a string of what looked like nonsense words and paused but we knew he was still there. Indra and I realized after a bit that he had communicated a protein sequence. We asked him back ”What?” He responded: ”What is its structure and function”. I said it was a helix-turn-helix domain and that it would bind DNA and was a likely transcription factor. He declared that we had passed the test and asked us we knew of some proteins that he named. Indra and I answered in the positive. Then he gave us a bit of his biography. He said that he was the one who had discovered them and elucidated their origins and function. Even though he had published several works on them, he said that his discoveries were appropriated by some barbarous mleccha-s who became renowned for that. He then said that he had wished to strike back at them but he was struck by a dart of Paśupati and was unable to do so. He said that was because even though he was nearly a sarvaśāstravit his yoga had failed him like the astra-s failing the sūtaputra. He had then faded away into oblivion like the Italian Majorana. He then said something rather troublesome to me: ”If the spider remains with you, you will be greater than me. In the previous round the plant was crushed below the eyes of Skanda. But it this round the spider could crushed below the eyes of Skanda and you will die soon after her.” He then uttered a howl and left saying: ”If you help me avenge my defeats I would come to your aid as Vetālabhaṭṭa”. Indra and I looked at each other knowing that what we had heard from the previous two ghosts was not a joke. I remarked to him:”The last two are not unrelated. This will be of the order of the killing of the fierce Bharadvāja on the Kuru field.” Indra said to me: ”The only astra we can take recourse to is that of Atharvāṅgirasa incantations. The yāga should be performed but what if it is disrupted like that of Viśvāmitra?”

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Mongolica: The Tangut empire

In the early 1100s of the CE Rtsa-mi lotsawa Sangs-rgyas grags-pa was in Nālandā, India, to study and transmit the latest that the tāntrika strain of Bauddha-mata had to offer. Within a century both his world and that of his Indian hosts was to come crashing down. It was almost as if the prophetic section of the nāstika Kālacakra-tantram that he was there to study and take to his lands would play out unerringly as the yuga-cakra turned with the irruption of the demons of makkhaviṣaya and the mlecchendra-duṣṭa-s. Sometime close to the beginning of the 1200s a marauding band of Mohammedans led by the Moslem Turk Ghazi Ikhtiyar al-Din Muhammad Bakhtiyar Khalji razed to ground this famed mahāvihāra of Nālandā. Rtsa-mi lotsawa Sangs-rgyas grags-pa was a Tangut from their kingdom known as Xi Xia in inner Asia. In 1205 CE the Tanguts supported the fleeing rivals of Chingiz Khan and were subject to a swift punitive assault by the Mongols from the western corridor. The Mongols followed it up by further invasions in the Tangut territory in 1207-8, 1209-10 and 1215 CE, in each case punishing them, seizing bits of their kingdom and forcing them to vassalage. In 1217 CE the great Khan sent an emissary asking the Tangut kingdom to join the Mongols in the great assault on the Mohammedans of Khwarazm. The Tangut king arrogantly responded: “If you have no strength [to fight on your own] there is no reason to be a Khan.” The Tanguts were pay dearly for this: they became the target of the final campaign of Chingiz Khan. By 1227 CE the Mongols had erased the Tangut kingdom off the face of the earth.

What was the origin of this Tangut Kingdom and what was its story? This remained somewhat mysterious given that it had been annihilated by the Mongols. However, their language survived that event and continued to be used by the remaining Tanguts until it was finally exterminated by the Ching. They would have remained a mystery had they not produced an enormous volume of written literature, a library of which was discovered by the Russian explorer PK Kozlov in 1908 in the Tangut fort of Qara Khoto. This library has formed the bed rock of Tangutology, which has since then has had a small but vigorous set of practitioners. It is rather unfortunate that there has been no Indian interest or participation in Tangutology especially given the religious links they had to India and the importance they attached to knowledge of the Sanskrit language and production of translations from it. Further, after the destruction of their kingdom the surviving members of the ruling clan became notable in the Indian state of Sikkim. The Tangut language was itself written in a very complex system where basic logograms are successively put together to make a new array of logograms that represent further new words. They superficially resemble Chinese but are mostly unrelated to it. This complex Tangut script was almost designed like a secret code so that none of their competitors and neighbors like the Tibetans, the Uighurs, the Khitan or the Han could read their documents. It was also designed with the view that its structure encoded a certain innate “mantraic power” — ultimately a Hindu concept acquired from the bauddha tradition (It is conceivable that the mysterious Khitan script also was designed with such ideas in mind). This script was in place by at least 1036 CE. The Tangut language written in this script found in the books discovered by Kozlov was deciphered by the great Russian Japanologist NA Nevsky, who was murdered by Stalin’s henchmen before he could publish it. This decipherment has formed the foundation of the Tangut studies that followed and suggest that it was member of the Tibeto-Burman family of languages. These texts give us a picture of the heydays of a rather interesting state, the Tangut Kingdom.

Tangut_manuscript

A Tangut document showing their script and artwork

From the Chinese evidence we observe that their predecessors or at least that of the ruling Ngvemi clan of the Tanguts might have originally had links to the Tabgach (Chinese: Tuoba) people with Altaic affinities: they were either early Turks or Mongols or a distinct extinct branch of the Altaic family. Consistent with this, the Mohammedan Qarakhanid Turk, Mahmud Kashghari, who wrote a Turkic-Arabic lexicon mentions the contemporary Tanguts as being one of the more sedentary of the 20 tribes of Turks that he lists. A Chinese Song record also claims that they were a clan of Turks. A memory of the pastoralist origin of the ruling clan, consistent with Altaic roots, appears to have been preserved in the poem of one of their ancestors that reflects the simple concerns of such herders:

They fixed the livestock enclosure, a wolf cannot get it,
They dug a well in the thicket, the livestock will not suffer from thirst.

If the courageous and wise do not sit [there], the meeting will not be successful,
If there is no bull with high horns in the herd, the herd is empty.

If you cannot ride the rounds on a horse, it is no good for riding.
If the livestock are beyond count, the owner deals only with livestock.

If you know the saying poorly, you will not be able to have a conversation,
If you have a few horses and yaks, you will not eat your fill.

There are no better close ones than [one’s] father and mother,
there is no meat tastier than the meat on the bones.

He who has livestock is not rich,
He who has a [good] mind is rich.

-translated from the original Tangut by the famous Tangutologist Kychanov.

In their own mysterious verse on their ancestry, they claim that their ruling Ngvemi clan stemmed from their ancestral mother ‘A-mbah (the etymology of this name is unknown to me but of interest!):

Our mother ‘A-mbah, source of families and clans,
silver-wombed and golden breasted,
the valiant tribe did not die out and
carries the name of Ngvemi.

-translated by Kychanov

In this regard it is notable that the Mongol sources in China mention a Tangut ethnonym as Yü-mi, which is believed to be derived from the name of trans-Himalayan goddess Umai who is mentioned as consort of Möngke Tengri in Turko-Mongol sources. In the Indo-Aryan world this goddess was incorporated as an ectype of Rudrāṇī i.e. Umā. It is hence conceivable that her other name Ambā has a relationship to the ancestral mother of the Tanguts mentioned in the above verse.

However, in their own writings the Tangut also mention that they as a people, the Tibetans and the Han Chinese have a common origin: was this some kind of early recognition of the monophyly of their Tibeto-Burman languages? In their earliest days going back to the 300-400 CE they appear to have had marriage relationships with the para-Mongolic Tuyuhun (Tuguhun) Khaganate and played a role in the formation of this state in between the Tibetans and the Chinese. It was in this period they appear to have associated with the speakers of the Tibeto-Burman language that became the dominant language of the Tanguts. Other Tabgach people appear to have sinicized early and adopted Chinese in the more eastern regions. As the Tibetans started expanding their empire in the 600s and eating into the Tuyuhun Khaganate and marching towards Tang China the proto-Tangut fled North-East and submitted to the Tang empire in return for protection of their identity against the Tibetan advance. Thus, having survived the Tibetan assault and the proto-Tangut developed a close client relationship with the Tang Chinese empire. However, this did not help them when they came under attack again, this time from a more determined foe — the Blue Turks (Gök Türks) of Mongolia. Blue Turk ruler Qapaghan Khagan had charted out a comprehensive plan to attack the Tang empire and punish the Chinese severely. He first aimed to capture the Chinese towns of Paoting and Chengting and for this decided to perform a flank-clearing operation by neutralizing those who might come to the aid to the Tang. Thus, in 700 CE he sent his 17 year old nephew the rising star of the Turks and their future Khagan, Tengrida Bilge, against the Tangut. This is the first time we hear of them under that name. The results of the devastating Turkic attack on them is summarized in the Orkhon inscriptions thus: “When I was 17 years old I went on a campaign against the Tangut. I put the Tangut to rout; there I took their wives and children, horses and possession” [Translation: Talat Tekin from the Bilge Khagan inscription in Mongolia].

Having barely survived this assault they got a chance to enhance their profile when the Blue Turks and the Uighurs were gone or had declined and Tang empire was wracked by natural calamities in the late 800s. The Tang excesses in their wake triggered the rebellion of farmers under Wang Xianzhi. At the same time a Chinese smuggler Huang Chao was taking advantage of salt shortages to run a salt trafficking operation. Having amassed a force of fighters he made an initial alliance with Wang Xianzhi and then broke up with him to lead his own rebellion, which in many ways paralleled that of the Chinese brother of Jesus Christ closer to our times. At the height of his rebellion Huang Chao took Guangzhou and then the Tang capital of Chang’an. The Tang emperor fleeing from these attacks called upon the proto-Tangut lord Tuoba Ssu-Kung (880-884 CE) to come to his aid. The Tangut crushed the Huang Chao rebellion in the west between and were rewarded the regions of Inner Mongolia by the Tang and title of “Prince Pacifier of the West”. The Tangut lords then welded together a multi-ethnic state which other than themselves contained Chinese, Tibetans and the remnants of the Tuyuhun Khanganate (Some of whom later joined Chingiz Khan; e.g. the lord Alaqush-digit-quri).

Subsequently, with the decline of the competing Central Asian powers operating in the region the Tangut were able to solidify their power. In the 900s when the Tang collapsed the Tangut established themselves as an independent state. While the Song tried to reconquer the old Chinese territory in 960 CE they could not subjugate the Tangut who continued to grow in power. In northern China the Khitan of para-Mongolic origin had established the Liao dynasty, which was also poised for potential conflict with the Tangut. However, negotiating their hold through these times they consolidated their kingdom as the Xi Xia, which was what Chingiz Khan eventually destroyed. It came to include what is today the Western and Central part of China’s Gansu province, Northern Ordos in Inner Mongolia and Ningxia Hui.

By around 1000 CE it appears that the Tangut queen Lady Wang had become a practicing bauddha with special attachment to the deity Mañjuśrī. At her death in 1007 CE the Tangut requested that the Song allow offerings to be sent to Mañjuśrī at his holy mountain Wutai in the name of the late queen. The Song allowed these offerings to proceed but had reasons to be vary of the Tangut. The Tangut prince Li Yuanhao, who also had an affinity to Mañjuśrī, was a noted warrior and began a series of conquests of Chinese and Uighur lands starting in the 1020s. He took Hexi and then in 1028 advanced against the Uighurs. The Tanguts defeated them after a bloody battle which is recorded by Mahmud Kasghari with some glee because that relieved the Uighur pressure on the Qarakhanid Mohammedans. Thus, the Tanguts seized Ganzhou and moving on in 1031-31 Li Yuanhao captured Liangzhou and finally took Dunhuang. This brought him in possession of various bauddha domains strengthening his association with the religion. Sometime after 1035 CE an Indian śramaṇa, evidently fleeing from the assault of the Mohammedans led by Mahmud and Masud of Ghazni on Gandhara and the Panjab, reached the Tangut kingdom. He presented Li Yuanhao with what he claimed were 150 relics from the cremation of the Buddha. These were supposed to include an ungual and a cranial fragment (likely from Gandhara). Filled with piety Yuanhao had an elaborate coffin made for them with a stone inner chamber in which they were placed in a silk wrap with gems. This in turn was placed in an iron box which was then placed inside a golden casket which in turn was placed in a silver outer coffin. The coffin was then placed above an underground spring. On top of the coffin he had an image of Kubera installed and the yakṣarāṭ was invoked to protect the king and state and provide overflowing granaries. In this period Yuanhao (1035 CE) also bartered several horses that they were good at breeding as pastoralists for bauddha texts in Chinese translation from the Song. He obtained another batch from the Khitan for a similar barter of horses. He then commissioned translation of all of these into the Tangut language by a panel of scholars — this illustrates the esteem in which he held the direct textual study of bauddha knowledge.

Thereafter, around 1038 CE Yuanhao declared himself to be cakravartin, superior to all the Han emperors of the past, and his kingdom to be a dharmarājya. Despite claims of being an embodiment of humaneness as per the bauddha-mata Yuanhao’s coronation rituals as cakravartin had elements that were clearly aimed at a display of military power. It remains unclear where these elements of the rituals came from — the pre-bauddha Tangut religion or from some Altaic adaptation of the bauddha-mata. We hear that:

“[Yuanhao] together with his braves smeared blood on their lips and took an oath first to attack Fuyan, desiring to enter [Song territory] simultaneously from three routes out of Dejing, Saimen fort, and Chicheng. Then [he] built an altar, received appointment, and assumed the imperial position (ji huangdi wei). At that time [he] was thirty sui.” – translation from noted Tangutologist Ruth Dunnell.

Hence, when in 1038 CE when Li Yuanhao, now king of the Tanguts, wanted to send offerings to Wutai the Song blocked them claiming that he was using it as ploy to spy on the defenses of Shanxi, which they felt he might raid next. Enraged Li Yuanhao commissioned the construction of this own mountain-shrine of Mañjuśrī for worship according the tantra known as the Mañjuśrīya-mūlakalpa. This was set up in the Helan mountains west of modern Yinchuan oriented in the holy Northeast axis of Mañjuśrī with respect to India.

By this time the Tangut state came into its own as a well-oiled military machine. Their law stipulated that every able-bodied man from age 15 to 70 was to enlist to serve in the army. Failure to enlist was punished right away with death. Every boy at age 15 was subject to a special medical checkup by state doctors and if found fit was registered in the army. Half were assigned to the reserves and half were placed in the current fighting register. Based on their abilities the men were either placed in the fighting force or in service and logistics or in military engineering. The latter included military manufacture, which produced iron and fashioned cavalry swords (= talvār-s) on a large scale that were reported as being among the best in the world by the contemporary Chinese. The recruits were classified based on the household income: the men from lower income families had to join the army with either one horse or one camel; those with higher income had to join with two horses or two camels. The main fighting force of the Tanguts was a formidable cavalry with each unit placed under a unit commander who was to be protected by his men to death. The best men were drawn into elite forces units known as the “Iron hawks” who conducted special operations and deployed special weapons. They also had a special weapons camel-division, which comprised of mobile stone-throwing machines with a rotating base mounted on camel backs which allowed all-round bombardment. On the theoretical front the Tangut made a close study of the military theories of other civilizations. They made several translations of the Chinese military works like the “The General’s Garden” and the “Art of War”, both of which they appear to have adapted to their needs. The Chinese record the terror of the movement of the Tangut army which they mention as “moving like a tornado this way and that…” This martial background of the Tanguts provides a measure of the military achievement of Chingiz Khan and his men when they smashed the Tangut armies one after another.

With a strong military system in place in Li Yuanhao eyed further hostilities with this neighbors even as he had vowed during his coronation as cakravartin. In 1038 he faced the possibility of enmity the with the Khitans as his wife who was a Khitan died under mysterious circumstances and the Khitans suspected that he might have eliminated her. Having for the time being pacified the Khitan ambassador sent to his court Li Yuanhao marched against the Qingtang Tibetan state and crushed them. Then in 1039 he opened the big war with the Han Chinese of the Song empire. This war lasted 5 years and towards its end the Khitan also joined it against the Tanguts. However, the cakravartin proved his name and emerged victorious on both fronts solidifying the Tangut state and perhaps now justifying the the term empire applied to it due to his conquests. In 1046 Yuanhao faced a second Khitan invasion which ended inconclusively on the battlefield but the Tangut ended up retaining their territory. A couple of years later Yuanhao and his eldest son with whose mother he had a conflict had an armed duel and he was killed as a result.

In the interim period where a tribal council was ruling them the Tanguts faced a defeat at the hands of the Khitan (1051) and a few years later they negotiated peace with the Khitans who, however, refused to have any marriage with them from then on. In this period they were ruled by a queen who was assassinated in 1056 CE. In 1067 for the first time in a while the Song were able to retaliate for the successive defeats they had been facing at the hands of the Tangut and defeat them even as their cakravartin Liangzuo, bastard son of Yuanhao born of incest died. The Han Chinese followed this up with successive victories against the Tanguts and in 1081 taking advantage of their internal strife launched an invasion of their empire. Finally, in 1084 after heavy losses the Tanguts repulsed the Chinese. They faced a Tibetan invasion shortly thereafter but managed to negotiate a settlement without territorial loss. In 1096 the Song attacked the Tanguts again in attempt to destroy them but they repeatedly asked the Khitan for help and finally in 1099 managed to repel the Chinese attack albeit with loss of some territory. The Chinese then took advantage of the turmoil in Tibet and tried to invade it. The Tangut quickly formed an alliance with the Tibetans against the Song and established a marriage alliance with the Kokonor Tibetan ruler to face the Chinese in 1102. They then negotiated with the Khitan to aid them to win back their territory lost to the Song. They appear to have partially succeeded in this with Khitan help by 1106. In 1114 the Chinese resumed their war with the Tanguts and a few years later they lost their Khitan allies, whose empire in China was dramatically overthrown by the Tungusic Jurchen invasion (proto-Manchu). Taking advantage of the chaos that followed the Tanguts led by their emperor Li Qianshun recovered all their lost territory and also seized Qingtang from the Tibetans.

This was followed by a phase of sinophilia among the Tanguts where they established the cult of Confucius and appointed a Chinese commander Ren Dejing who surrendered to them as a high official. With his internal Chinese faction he staged a coup to nearly precipitate a civil war after they threatened to take over the state. He and his Chinese faction were all killed in 1170 and the Tangut empire’s unity was restored. At that point with their army at the peak of its size and performance it looked as thought the Tanguts were unconquerable. Indeed, in 1193 the Jurchen tried to invade them at multiple points along the border but were forced to retreat. But in 1205 CE they faced a challenge of the kind they had never faced in their whole existence: Temüjin, who was soon to be Chingiz Khan. Those who they thought might be a weaker version of their para-Mongolic cousins the Khitan proved to be something else — within 5 years from first defeat at the hands of the Mongols the mighty Tangut empire was reduced to vassalage followed by its total destruction.

A notable point about the Tanguts was how they ran a state based on the bauddha-mata. First, they did not let let come in the way of their lifestyle, which still had a major pastoralist component. Despite being bauddha-s the Tanguts permitted eating the meat of dead animals and also had animal sacrifices in May of each year. However, outside of this there could be a stiff sentence of hard manual labor for killing a cow, horse or camel for meat and a lower sentence for killing a donkey or a mule. Second, as we noted above they did not let it come in the way of developing a highly militarized state, which was the need of the day in Central Asia when flanked by all manner of aggressive neighbors. Importantly, as a counter-religion the bauddha-mata is not very well-suited for state-forming. In India the rulers with bauddha orientation could always draw from the bedrock of Hindu institutions and theory of statecraft for running their kingdoms. The same model worked where Indians directly transmitted their religion — they also transmitted their apparatus of Hindu administrative theory, which was operationally rather effective across different kinds of people. However, this advantage was not afforded by people who received their dose of Indian tradition indirectly via intermediates who did not have the rest of the “package”. This was the initial situation with the Tanguts. Like their Tibetan neighbors they too gravitated towards Vajrayāṇa, which of all the bauddha schools had an apparatus closest to a genuine religion rather than a counter-religion. However, they did considerably value older bauddha traditions, like drawing just the right amount of inspiration from the life of the old Maurya emperor Aśoka. What the Tanguts did was to incorporate the bauddha-mata they had received within a unique system of statecraft of their own. A part of this Tangut system was definitely influenced by the Chinese traditions of legalism and Confucianism. It was from legalism that they likely acquired their centralizing tendencies: for example, creation of their own distinct script and the adoption of a unique national hairstyle for all males. This allowed them to develop a distinctive national identity despite being a multi-ethnic state with Turkic, Chinese, and Tibetan peoples in addition to Tanguts proper, themselves with a potentially composite origin. They were generally quite meritocratic and allowed an individual of any of these nationalities to occupy high office based on merit. Indeed, many bauddha Uighurs rose to high positions in their midst. Only if there were competing individuals of same caliber for a given rank they gave the first preference to the Tanguts. It was in this context of dealing with the multiple ethnicities that they used the bauddha-mata as a religious glue. They, like their contemporary and earlier Tibetans, also had an interest in incorporating various branches of secular knowledge into their system. The Tibetans acquired several of these from the Indians and at to some extant the Tanguts also did so in terms of medicine. We saw above that they used secular Chinese knowledge for military strategy. It also appears they developed their own systematic veterinary medicine with specialists for horses, cows, camels and ovicaprids. These were called to investigate epidemics of these animals such that orders to could be issued to prevent consumption of their meat in these periods. These veterinarians would study wells, pastures and the carcasses of dead animals to identify the sources of epidemics and remedy them. Just as in military technology they also innovated in secular technology developing advanced book-printing techniques including a version of the movable type.

As a bauddha cakravartin-s, the Tangut emperors starting from Li Yuanhao showed keen interest in directly studying the bauddha-mata. He initially took the help of Uighur scholars from the Uighur lands he had just conquered to produce printed Tangut-language editions of important mahāyāna texts. Later in his career and during that of the subsequent emperors they got to directly interact with Indian teachers whom they patronized at their court. They created an office known as the Saṃgha office to which they appointed Jayānanda the Indian paṇḍita from Kashmir as the director. They also sent several students to the Pāla and Sena schools to study directly with reputed Indian teachers. These introduced the cult of Mahākāla which started to grow in popularity among the Tanguts. In the Tangut texts we also have the biography of an Indian brāhmaṇa teacher known as Akṣobhyavajra, who is said to have studied both the Veda and the Vajrayāṇa doctrines and completely internalized the bauddha doctrine. He then came to the Tangut kingdom (likely in the 1100s) and stayed at the Huguo temple where he did translation work and taught the nāstika Yoga tantra-s. He instituted a ritual of food-charity among the Tanguts. He is described as a great mantravādin. Another Tangut text on the sādhana of Bhaiṣajyaguru also mentions “a great Indian paṇḍita” as its teacher and the Tanguts following his teaching made several paintings of this deity. Another of fragment of a Tangut text collected by the Russians is a Chinese translation of the medical teachings an Indian physician.

The Tangut emperors’ self-perception with regard to their place in the bauddha hierarchy grew with time: starting as cakravartin-s, they soon conceived themselves as bodhisattva-s, which culminated in them considering themselves the Buddha of the age just before their destruction by Chingiz Khan. As self-conscious dharma-pāla-s running a dharmarājya, they sought to protect the mata in their realm from vandalism. We get a number of details in this regard from a legal document discovered among the Tangut texts and studied by Kychanov. It states that: “Nobody is allowed to steal, spoil or damage Buddha’s images, temples, images of religious champions, canvases with Confucius’ image or images of gods [i.e. Hindu deva-s and yakṣa-s transmitted as a part of the bauddha system].” Who were these potential vandals against whom this law was laid down? Evidently it was the Mohammedan vandals from the neighboring Qarakhanid kingdom, which was carrying out mass forced conversions of bauddha and shamanistic Turks and sending out missionaries to their neighboring countries. It was also probably a defense against iconoclastic Nestorian Christians who were known to be active in the region. Thus, the Tanguts did probably play some role in keeping the evils of Mohammedanism from spreading east in Asia at that time. In this regard the Khitans, however, played a much bigger role actively crushing mullahs who tried to operate in those regions. It was perhaps this self-perception as dharmapāla-s that made them acutely conscious of the mata being a counter-religion at its heart and the need to prevent competing claimants in the bauddha hierarchy. Already in the days of Li Yuanhao, he made a strong ideological attack on the Tibetans claiming to be bauddha-cakravartin-s. Subsequently, they introduced strict laws to control the propagation of the bauddha-mata in their realm. Among the laws found in the Tangut legal document are those that: 1. prosecute a preacher for teaching anything that might distort the mata or mislead people or create social unrest. Thus, all preachers of the bauddha-mata had to register with the court and obtain clearance for their sermons before preaching. Failing to do so would result in 3 years of hard physical labor. 2. In a move against the very natural rise of bābāistic tendencies among the nāstika-s, any quack claiming to prognosticate the future or making claims like seeing a divine light from the Buddha was punished similarly. If he did make people follow him and pay him for such claims he was put to death. Other socially disruptive teachings of a lower order received a labor sentence of an year. The state also regulated who became śramaṇa-s and punished misbehaving śramaṇa-s who may engage in unauthorized sexual activities with their female counterparts [We know from bhaṭṭa Jayanta that this was the case in India]. Only those women who were widowed or had no man showing interest in marrying could register to become a bhikṣuṇī. Thus, the religion was not allowed to develop parasitic or depraved tendencies in the Tangut state.

In conclusion, one may infer that the Tangut state was a rather brilliant nāstika state in East-Central Asia. While it was destroyed by the Mongols, evidently several of its innovations were taken up by them. Some Tangut survivors who surrendered to the Mongols were given various posts: for example Tolui appointed a Tangut woman as nurse for his children. The bauddha establishment was mostly spared by the Mongols and played a role in the transmission of the nāstika religion among the Mongols.

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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 in other traditions but not in their own saṃhitā or brāhmaṇa. Additionally, they also include some mantra-s which are unique to these mantra-pāṭha-s. For example the famous Yajurvedic version of the Śrīsūkta is found in the mantra-pāṭha of Bodhāyana. However, most practitioners in South India do not correctly use the accents of this sūkta and seem to be unaware that the KYV version of this sūkta occurs in this text. The mantra-paṭha-s of the Āpastamba, Bodhāyana, Vaikhānasa and Hiraṇyakeśin sub-schools have come down to us. The mantra-s in them are typically deployed in gṛhya rituals directed by instructions from their gṛhyasūtra-s. However, the Vaikhānasa-mantra-pāṭha is distinctive in having a late terminal part that is used in the iconic worship of Viṣṇu by the Vaikhānasa-s. The Hiraṇyakeśī-mantra-pāṭha has a ṛk-saṃhitā as part of it and is used by the Hiraṇyakeśīn-s of Maharashtra and Tamil Nadu in their rituals to this date. In someways this is reminiscent of the hautra-pariśiṣṭha of the Āpastamba-s that is used by Yajurvedin-s to supplement the role normally performed by the Ṛgvedin hotṛ.

Other than these mantra-pāṭha-s of the KYV, we also have comparable supplementary mantra-collections among the Sāmavedin-s in their Mantrabrāhmaṇa and the famous khila of the RV. Further, beyond the Taittirīya school, the Kaṭha school, which was once widespread in the northern parts of the subcontinent like Kashmir and the Panjab, had it own mantra-paṭha that went along with their gṛhyasūtra, namely that of Laugākṣi. While the original form of this mantra-paṭha does not survive to my knowledge, a version of it with accretions of tāntrika and paurānika material used in smārta practice by the brāhmaṇa-s of Kashmir and some of their counterparts in Himachal Pradesh has come down to us. This text was published by the Kashmirian brāhmaṇa-s Keśava Bhaṭṭa and Kāśīnātha-śarman in the first half of the 1900s. I had earlier examined a defective version of this text but thanks to the massive text-scanning effort of the eGangotri Trust of the texts at the Kashmir Research Institute, Srinagar we can now examine a better version of this text.

The melding of tāntrika and vaidika tradition found in this Kashmirian text has a long history in Hindu tradition. Indeed, as we have pointed out before[footnote 1], a small mantra-saṃhitā comparable to the mantra-pāṭha-s is found preserved in the śākta-purāṇa, the Devī-purāṇa, which might preserve a distinct vaidika tradition. Similarly, the Āṅgirasakalpa of the Paippalāda school of the Atharvaveda preserves a combined mantra-deployment of Paippalāda AV mantra-s along with tāntrika-vidyā-s. With regard to the AV tradition one may also point to the Tripurārṇava-tantra, an authoritative mūla-tantra of the Śrīkula tradition. The 20^{th} taraṃga of this text preserves a combined tāntrika-vaidika mantra-deployment for the Indramahotsva (the great festival of Indra) which associates itself the AV. This association is likely genuine for the AV is the one vaidika tradition that has clear injunctions for the Indramahotsva in its pariśiṣṭha-s. This section of the Tripurārṇava-tantra specifies several vaidika mantra-s that are to be used in the worship of Indra and other deva-s, which are combined with the worship of the Bhairava of the Śrīkula tradition under the tāntrika scheme.

Our Kashmirian text associated with the Kaṭha school, like other mantra-paṭha-s, has some unique Vedic material. One such is the Bhadrasūkta which is the topic of this note. This sūkta of 22 ṛk-s is to our knowledge not found in any other saṃhitā. It is mostly comprised of regular jagati-s (12-12-12-12), with the last ṛk being a triṣṭubh (11-11-11-11). There may be some hypermetrical verses like ṛk-17 (12-12-12-13). The sūkta has a form rather similar to the RV7.35 of Vasiṣṭha Maitrāvaruṇi. Like that one it is a vaiśvadeva-sūkta, which invokes the entire pantheon for luck or felicity. In RV7.35 the word for luck or felicity is the indeclinable śam. In our sūkta the word bhadra is used instead. It is used as an adjective that declines as the deity being invoked with the dative pronoun naḥ (“for us”) being used just like in RV7.35. Hence, in this sūkta we translate bhadra as auspicious (or can be taken in the sense of the deity being luck-granting). This word bhadra is also found in multiple ṛk-s of another famous vaiśvadeva-sūkta, RV1.89 of Gotama Rāhūgaṇa, in an equivalent sense (ā no bhadrāḥ; devānām bhadrā sumatir ṛjūyatāṃ; bhadraṃ karṇebhiḥ śṛṇuyāma devā bhadram paśyemākṣabhir yajatrāḥ). More generally, the pattern of the repetitions of bhadra is seen on multiple occasions in the RV albeit not in vaiśvadeva-sūkta-s (e.g. RV8.62 of Pragātha Kāṇva) and also in the AV saṃhitā-s. A ṛk of Sobhari Kāṇva (RV8.19.19) also uses the word bhadra repeated in a sense similar to this sūkta:
bhadro no agnir āhuto bhadrā rātiḥ subhaga bhadro adhvaraḥ | bhadrā uta praśastayaḥ ||
For us auspicious Agni when he is made an offering, the auspicious gift, the auspicious ritual, you the giver of good luck, [for us] auspicious hymns of praise.
Another comparable word is svasti (“well-being”) used in a similar sense by the Atri-s in their vaiśvadeva-sūkta, RV5.51.11-15 and also by Gotama Rāhūgaṇa in RV1.89. Indeed, in the Kashmirian tradition the Bhadrasūkta is used on conjunction with RV1.89 and RV5.51.11-15. This style continues into the epic period where we observe Kausalyā confer a blessing on Rāma using a comparable incantation with svasti ( in R2.25).

The pantheon of the Bhadrasūkta is entirely Vedic with no paurāṇika features. This squarely places the sūkta within the classic vaidika tradition and it was perhaps even originally attached to some now lost saṃhitā. However, in ṛk-2 we encounter the god Prajāpati. He is not found in the comparable RV7.35 or other core RV vaiśvadeva-sūkta-s. He appears to have entered the Vedic tradition relatively late from a para-Vedic tradition [footnote 2]. His position in the sūkta suggests that he has not superseded the old aindra system as it happened in the even later Vedic layers. In this regard his position is comparable to that found the camaka-praśna of the Yajurveda tradition. This suggests that the sūkta indeed belongs to a comparable relative temporal layer and was a relatively late composition with the Vedic tradition, perhaps consciously mirroring the RV7.35 and RV1.89. The final ṛk has the refrain: “tanno mitro varuṇo mā mahantām aditiḥ sindhuḥ pṛthivī uta dyauḥ” (Mitra and Varuṇa, Aditi, the river, the Earth and also Heaven should grant this to us), which is characteristic of the Kutsa-s of the RV (e.g. RV1.94). Kutsa also has a certain predilection for composing low complexity sūkta-s, which is also seen rather plainly in this one. Importantly, his two vaiśvadeva-sūkta-s, RV1.105 and RV1.106, have characteristic low-complexity style with repetition. Notably, his sūkta to the Sun (RV1.115) uses the word bhadra repeatedly as in this sūkta. Together, these indicate that the composer of the Bhadrasūkta was a member of the Kautsa clan.

Some notable features of the Bhadrasūkta are:

1. Venas is implored to be ever-desirous (uśan…sadā) of the worshiper. This furnishes a link between Venas and the later name of Venus in Sanskrit tradition, Uśanas. Thus, it further strengthens the identification of Venas with Venus and suggests an early IE origin for this planetary name.

2. Mātariśvan is explicitly identified with Vāyu in this sūkta. In the RV Mātariśvan is often mentioned as bringing Agni to the Bhārgava-s and humans at large (evidently from Vivasvat). In RV3.29.11 Viśvāmitra clarifies this identification by stating: “mātariśvā yad amimīta mātari vātasya sargo abhavat sarīmaṇi ||”: [He is called] Mātariśvan when he measures out [the space] in his mother; he became the rush of the wind in flowing out. Thus, we translate Mātariśvan as “he who grows in his mother” meaning “he who grows in the world-womb.

3. In ṛk-10 we seen an invocation of various physiological processes. This is unique for a vaiśvadeva-sūkta and not seen in RV sūkta-s of this type. In this regard it has a flavor more typical of the AV.

4. In ṛk-s 12-14 we encounter a great diversity of devatā-dvandva-s, which is unprecedented in any other vaiśvadeva-sūkta elsewhere in the śruti.

The emended text of the sūkta is presented below with an approximate translation.

Bhadrasūkta: text
bhadro no agniḥ suhavo vibhāvasur bhadra indraḥ puruhūtaḥ puruṣṭutaḥ |
bhadraḥ sūrya urucakṣā uruvyacā bhadraś candramāḥ samitheṣu jāgṛviḥ ||1||
For us the auspicious Agni, well-invoked and abounding in light, the auspicious Indra much-invoked and much-hymned; the auspicious Sun, wide-seeing and wide-ranging, the auspicious Moon keeping an eye [on us] in the battle.

bhadraḥ prajā ajanayannaḥ prajāpatir bhadraḥ somaḥ pavamano vṛṣā hariḥ |
bhadras tvaṣṭā vidadhad rūpāṇy adbhuto bhadro no dhātā varivasyatu prajāḥ ||2||
For us the auspicious Prajāpati [who] progeny-generated, the auspicious Soma, the purified one [Footnote 3] and the manly yellow one; the auspicious Tvasṭṛ giving wondrous forms [to things]. May the auspicious Dhātṛ show favor to [our] progeny.

bhadras tārkṣyaḥ suprajastvāya no mahām̐ ariṣṭanemiḥ pṛtanā yudhā jayan |
bhadro vāyur mātariśvā niyutpatir veno gayasphāna uśan sadā ‘stu naḥ ||3||
For us the auspicious Tārkṣya Ariṣṭanemi for the sake of good progeny and for conquering the hostile army by means of battle; the auspicious Vāyu, expanding within the world-womb [footnote 4], the lord of the team of horses. May Venus, the wealth-increaser, be always desirous of us.

bhadro mitro varuṇo rudra id vṛdhā bhadro ‘hirbudhnyo bhuvanasya rakṣitā |
bhadro no vāstoṣpatir astv amīvahā bhadraḥ kṣetrasya patir vicarṣaṇiḥ ||4||
For us the auspicious Mitra and Varuṇa, and Rudra verily with augmentation, and Ahirbudhnya the protector of the universe; the auspicious guardian of the homestead: may he be the destroyer of illness and the auspicious guardian of the field, ever-full of activity.

bhadro vibhur viśvakarmā bṛhaspatir bhadro dviṣastapano brahmaṇaspatiḥ |
bhadraḥ suparṇo aruṇo marut-sakhā bhadro no vāto abhivātu bheṣajī ||5||
For us the mighty, all-maker Bṛhaspati, the auspicious foe-scorcher and lord of the ritual; the auspicious falcon, reddish-brown and the friend of the Marut-s [footnote 5]. May the auspicious Vāta [footnote 6] blow medicines towards us.

bhadro dadhikrā vṛṣabhaḥ kanikradad bhadraḥ parjanyo bahudhā virājati |
bhadrā sarasvām̐ uta naḥ sarasvatī bhadro vaśī bhadra indraḥ purūravaḥ ||6||
For us the auspicious [horse] Dadhikra, the neighing stallion, the auspicious Parjanya [who] manifoldly shines forth; the auspicious Sarasvat and also Sarasvatī, the auspicious cow and the auspicious Indra, the loud-roarer.

bhadro naḥ pūṣā savitā yamo bhago bhadro ‘graja ekapād aryamā manuḥ |
bhadro viṣṇur urugāyo vṛṣā harir bhadro vivasvām̐ abhivātu nastmanā ||7||
For us the auspicious Pūṣaṇ, Savitṛ, Yama and Bhaga, and the auspicious first-born Ekapāt, Aryaman and Manu; the auspicious Viṣṇu, the wide-strider and the manly lion. May indeed the auspicious Vivasvat blow towards us.

bhadrā gāyatrī kakub uṣṇihā virāḍ bhadrānuṣṭup bṛhatī paṅktir astu naḥ |
bhadrā nas triṣṭub jagatī purupriyā bhadrāticchāndā bahudhā vibhūvarī ||8||
For us the auspicious Gāyatrī, Kakubh, Uṣṇihā [Footnote 7] and Virāṭ. May Anuṣṭubh, Bṛhatī, Paṅkti each be auspicious to us. For us the auspicious Triṣṭubh, the much-loved Jagati [footnote 8] and the auspicious long meters manifold and of many treasures.

bhadrā no rākānumatiḥ kuhūḥ suhṛd bhadrā sinīvāly aditir mahī dhruvā |
bhadrā no dyaur antarikṣaṃ mayaskaraṃ bhadro ‘śvo dakṣastanayāya nas tuje ||9||
For us the the auspicious Rākā, Anumati and friendly Kuhū, auspicious Sinivālī, Aditi, and the firm Earth goddess. For us the auspicious Heaven goddess, the atmosphere giving pleasure, the auspicious horse, and Dakṣa for extending for us [our] lineage.

bhadro naḥ prāṇaḥ sumanāḥ suvāgasad bhadro apānaḥ satanuḥ sahātmanā |
bhadraṃ cakṣur bhadram icchotram astu no bhadraṃ na āyuḥ śarado asacchatām ||10||
For us the auspicious life-process with a good mind and good speech unmanifest, the auspicious excretory process with the body and the consciousness; indeed may the vision be auspicious and hearing be auspicious for us. For us the auspicious life with autumns, a 100 yet to manifest.

bhadrendrāgnī no bhavatām ṛtāvṛdhā bhadrā no mitrāvaruṇā dhṛtavratā |
bhadrāśvinā no bhavatāṃ navedasā bhadrā dyāvā-pṛthivī viśva-śaṃbhuvā ||11||
For us the auspicious Indra and Agni fostering the Law; for us the auspicious Mitra and Varuṇa maintaining the Laws. May the two auspicious Aśvin-s be cognizant [of us]. For us the auspicious Heaven and Earth benevolent to all.

bhadrā na indrāvaruṇā riśādasā bhadrā na indrā bhavatāṃ bṛhaspatī |
bhadrendrāviṣṇū savaneṣu yāvṛdhā bhadrendrāsomā yudhi dasyu-hantamā ||12||
For us the auspicious Indra and Varuṇa, devourers of foes. May Indra and Bṛhaspati be auspicious to us. [For us] auspicious Indra and Viṣṇu who augment [us] during the soma libations. May the auspicious Indra and Soma slay the dasyu in battle.

bhadrāgnāviṣṇū vidadhasya prasādhanā bhadrā no ‘gnīndrā vṛṣabhā-divaspatī |
bhadrā no agnīvaruṇā pracetasā bhadrāgnīṣomā bhavatāṃ navedasā ||13||
For us the auspicious Agni and Viṣṇu, the ornaments of the gift-distribution. For us the auspicious Agni and Indra, the bulls, the lords of heaven. For us the auspicious Agni and Varuṇa, the ever-mindful ones. May the auspicious Agni and Soma be cognizant of us.

bhadrā sūryā-candramasā kavikratū bhadrā somā bhavatāṃ pūṣaṇā naḥ |
bhadrendrāvāyū pṛtanāsu-sāsahī bhadrā sūryāgnī ajitā dhanañjayā ||14||
For us the auspicious Sun and Moon, the two full of insight. May Soma and Pūṣaṇ be auspicious. [For us] the auspicious Indra and Vayu conquering in battle and the auspicious Sūrya and Agni unconquered and winning wealth.

bhadrā naḥ santu vasavo vasuprajā bhadrā rudrā vṛtrahaṇā purandharā |
bhadrā ādityāḥ supasaḥ sunītayo bhadrā rājāno maruto virapśinaḥ ||15||
May the auspicious Vasu-s be wealth and progeny [giving]. For us the auspicious Rudra-s who slay Vṛtra and smash the [hostile] forts and the auspicious Āditya-s, well-seeing and well-guiding, and the auspicious kings, the Marut-s, the exuberant ones [footnote 9].

bhadrā na ūmā suhavāḥ śataśriyo viśvedevā manavaś carṣaṇīdhṛtaḥ |
bhadrāḥ sādhyā abhibhavaḥ sūracakṣaso bhadrā naḥ santv ṛbhavo ratna-dhātamāḥ ||16||
For us the auspicious helper-[gods], well-invoked and with a 100 riches, all the gods and the Manu-s, supporters of the folks. For us the auspicious Sādhya-s, the overpowerers, radiant as the Sun. May the auspicious Ṛbhu-s be gem-givers for us.

bhadrāḥ sarve vājino vājasātayo bhadrā ṛṣayaḥ pitaro gabhastayaḥ |
bhadrā bhṛgavo ‘ṅgirasaḥ sudānavo bhadrā gandharvāpsarasaḥ sudaṃsasaḥ ||17||
Auspicious the racers, winners of booty; auspicious the sages, [our] ancestors, the sun-beams. Auspicious the Bhṛgu-s and Aṅgiras-es, the liberal givers; auspicious the Gandharva-s and Apsaras-es, the powerful ones[footnote 10].

bhadrā āpaḥ śucayo viśvabhṛttamā bhadrāḥ śivā yakṣmanudo na oṣadhīḥ |
bhadrā gāvaḥ surabhayo vayovṛdho bhadrā yoṣā uśatīr devapatnyaḥ ||18||
For us the auspicious waters, pure and the foremost supporters of all, the auspicious, benign, disease-repulsing herbs; the auspicious cows, charming and invigorating, the auspicious nymphs and loving wives of the gods.

bhadrāṇi sāmāni sadā bhavantu no bhadrā atharvāṇa ṛco yajūṃṣi naḥ |
bhadrā nakṣatrāṇi śivāni viśvā bhadrā āśā ahrutāḥ santu no hṛdi ||19||
May the Saman-s forever be auspicious to us. For us the Atharvaṇ spells, the ṛk-s and the yajuṣ-es. May the auspicious asterisms [be] all benign and [may the] directions, the coordinate lines be auspicious at their conjunction.

saṃvatsarā na ṛtavo mayobhuvo yo vā āyuvāḥ susarāṇy uta kṣapāḥ |
muhūrtāḥ kāṣṭāḥ pradiśo diśaś ca sadā bhadrā santu dvipade śaṃ catuṣpade ||20||
The years [of the 5 year cycle] and the seasons be gladdening to us, be they productive, easy-going or drought-ridden. May the muhūrta (=48 minutes)-s and kaṣṭa (=3.2 seconds)-s, the directions and the inter-directions be ever-auspicious and [may there be] welfare for the bipeds and quadrupeds.

bhadraṃ paśyema pracarema bhadraṃ bhadraṃ vadema śṛṇuyāma bhadram |
tanno mitro varuṇo mā mahantām aditiḥ sindhuḥ pṛthivī uta dyauḥ ||21||
May we see auspiciousness. May we perform auspiciousness. May we speak auspiciousness. May we hear auspiciousness. Mitra and Varuṇa, Aditi, the river, the Earth and also Heaven should grant this to us.


Footnotes
1. https://manasataramgini.wordpress.com/2010/06/25/the-mantra-samhita-of-the-devi-purana/
2. Note the presence of a comparable deity among the Greeks in the form of Phanes or Protogonos
3. Emended pāvamāna to pavamāna
4. Mātariśvan: literally growing within the mother: the mother implies the world-womb or the world-hemisphere
5. Later tradition clarifies him to be the charioteer of the Sun
6. The wind deity
7. Another form of Uṣṇih meter
8. The composer seems to indicate his love for the Jagati, the meter in which he has composed most of the sūkta
9. Emended virapsin to virapśin keeping with the form found in the RV
10. Emended sudamśas to sudamsas

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Liṅga-kāmādi-sūtrāṇi

Devanagari PDF version

.. Sūtrapāṭhaḥ ..

atha liṅga-kāmādi-sūtrāṇi vyākhyāsyāmaḥ . jīvasūtrāṇunām anukrameṣu parimeyā vikārā jīvā-paramparāyā+avaśyam . jantvoḥ saṃgrāmas tasya paramaṃ kāraṇam . tasmād ajāyata jīvasūtrāṇunāṃ vyūḍhīkaraṇam . RecA-nāma jīvakāryāṇu-kulaṃ jīvasūtrāṇunāṃ vyūḍhīkaraṇaṃ karoti . mukhyaśo ‘nagnijīvasūtrāṇunām . anagnijīvasūtrāṇu-mithunayor maithunāt . idam eva jantūnāṃ maithunasya rahasyam ..

anābhikānām pranābhikānāṃ ca+ anagnijīvasūtrāṇunām maithunaṃ naimittikā prakriyā . nābhikānām maithunaṃ nirūpitā prakriyā . vyūḍhīkaraṇa-dvirbhāvāt . tasmād ajāyanta liṅgāni . nābhikeṣu bahuśo liṅge dve . kecid bahuliṅgāni pradarśayanti . kyākūni yukta-kāmarūpiṇa romakoṣṭhakāś cety udāharaṇāni . eteṣu liṅga-koṣṭhānām parimāṇa-bhedo bahuśo nāsti . dviliṅgasthitau liṅga-koṣṭhyor parimāṇa-bhedaḥ sadaivodeti (sadaiva udeti) . mahattaro liṅga-koṣṭhaḥ strīti (strī+iti) . sā bahuśas tiṣṭhati . kanīyaḥ pumān iti . sa bahuśo gacchati . liṅgakoṣṭhānāṃ nirmāṇasya dattāṃśa-bhedāj jāyate liṅgayoḥ saṃgrāmaḥ . kiṃ tu paramparā-santatyai viparītayor liṅga-koṣṭhayor ākarṣaṇaḥ saṃgamanaṃ saṃyogaś ca+avaśyam . etaddhi mūla-kāraṇaṃ kāmasya . dattāṃśa-saṃgrāmo ‘karṣaṇaś ca dvayoḥ pratidhrājyoḥ sammelanād dvayor ekaḥ pūrṇaṃ vijayaṃ nāpanoti . tasmāj jāyate ‘nantā spardhā liṅgayoḥ ..

bahukoṣṭha-jantuṣu liṅgakoṣṭhā anyebhyaḥ koṣṭhebhyo bhinnāḥ saṃvṛtāḥ . tasmād viviktā upasthāḥ . udāharaṇāny oṣadhīṣu paśuṣu ca . teṣu viparītānāṃ liṅgakoṣṭhānāṃ sammelanāya vividhā upastha-lakṣaṇāny avartanta . śepo yoniḥ puṣpañ cety udāharaṇāni . paśuṣu trividhā maithuna-vyavasthā . dhṛṣṭa-vratam bahupatnī-vratam ekapatnī-vratam vā . bahupatnī-vratam dvividham . krameṇa bahupatnayaḥ sadyo bahupatnayo vā . pṛṣṭhadaṇḍa-paśuṣu prāyeṇa 25 jīvasūcanāḥ prabhavanty ekapatnī-vratam . Gibbons, orangutans, gorillas, chimpanzees and bonobos te sarve nṛbandhavaḥ . alpa-nṛbandhuṣv ekapatnīvratam bahuśaḥ prakṛtimat . anyeṣu nṛbandhuṣu bahupatnī-vrataṃ ca dhṛṣṭa-vrataṃ ca sāmānyam . mānaveṣu ca . prāyeṇeyaṃ nṛbandhunām mūla-sthitiḥ . strī-balātkāro rakta-nṛbandhunām eko maithunopāyaḥ . rakta-nṛbandhunāṃ vṛṣa-jātir dvividhā . nemivantaś ca+anemivantaḥ . nemivanta ugrā dhunimantaś ca parasparaṃ yudhyante ca . anemivantaḥ śāntāḥ pracchanam maithunaṃ kurvanti ca . bhūriretāḥ pumān nityam bahūn maithunāvakāśān mṛgayate . svāṇḍānāṃ niṣekāya strī su-jīvasūcanā-dhāriṇam puruṣam pratīcchaty anyān nirākaroti ca . tasmād bahuvidhāḥ spardhāś ca pradarśanāni ca ..

manuṣyāṇām prāyeṇa sahajā vyavasthā dhṛṣṭa-vrataṃ ca krameṇa bahupatnī-vrataṃ ca sadyo bahupatnī-vrataṃ ca . lubdhaka-vanagocarāvasthāyāṃ te sarve ‘vartanta . kiṃ tu manuṣyānām upavāsitāyāṃ sthiteḥ prabhūtyās te sarve vaighnakā abhavan . kāsmat? strībhyaḥ parasparam puruṣāṇāṃ naiṣṭhikāt saṃgrāmāt . idaṃ kāraṇaṃ ekapatnī-vratasya+āvaśyakatā dhruvāyopavāsita-jīvanāya . kiṃ tu mānavānāṃ netṛtvam pratibhā sāhasaṃ ca nṛdravyād udiyanti . ataḥ strīniyāna-bhedo nṛṇāṃ svābhāvikaḥ . tasya virodhāt upadravam pravartituṃ śaknoti . paraṃ tu śāntyai dhruvāyopavāsita-jīvanāya ca sarvebhyo puruṣebhyo nyūnātinyūnam eka-patnyā saha vivāham avaśyam . strīṣu vyābhicāriṇī-vratam bhrūṇahatyā +adhipuruṣānudhāvanaṃ cetyādi pravṛttīnāṃ codanāt puruṣa-viṣādo’pi vardhate . ādhunikatā nūtana-kṛtrima-mānava-samājasya nirmāṇaṃ vā tāni sarvāṇi codanti . ataḥ prāyeṇa + ādhunikatāḥ paura-saṃskṛteḥ pratiṣṭhām pratirundhate . yadīdam tatvaṃ tarhi manuṣyāṇām ādhunika-paura-saṃskṛtiś cirāyur nāsti ..

namaḥ somārudrābhyāṃ namaḥ prajāpataye ..

.. Nighaṇṭhuḥ ..
jīvasūtrāṇuḥ : nucleic acid molecule
anagnijīvasūtrāṇuḥ : DNA
jīvakāryāṇuḥ : protein
vyūḍhīkaraṇam : recombination
vyūḍhīkaraṇa-dvirbhāva : meiosis
anābhikaḥ : bacteria
pranābhikaḥ : archaea
nābhikaḥ : eukaryotes
kyāku : fungus
yukta-kāmarūpin : plasmodial slime mold
kāmarūpin : amoebozoan
romakoṣṭhakaḥ : ciliate
liṅgakoṣṭhaḥ : gamete
dattāmṣaḥ : investment
bahu-koṣṭha-jantuḥ : multicellular organism
jīvasūcanā : gene
nṛbandhuḥ : ape
alpa-nṛbandhuḥ : gibbon
rakta-nṛbandhuḥ : orangutan
nṛdravyam : testosterone

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