The story of the Orissan cycle-vālā

Vidrum had been under considerable pressure. His parents had made it clear that they would auction away his new bike if he was not ranked within the top 5 in his class in the impending mid-semester exams. They had also made it clear that the goal they had set for him that year was to be in the top 3 ranks by the final semester. It had caused him considerable tension. He thought to himself: “How on earth am I going to supersede classmates like Hemling, Gomay, Tumul, Dandadipa, and Jukuta who are so diligent with the books jousting so fiercely with each other. Then we have my friend Somakhya and the unusually wise girl Lootika, both of whom even the teachers secretly fear. While they take their curricular studies very lightly, they are in the least going to be unstoppable for spots four and five. I have often wondered if their parents ever give them the kind of shit I get.” While he had risen early to study, he had instead spent the time with his geometry box neatly drawing some fascinating constructions. But that was going to hardly matter for the exams at hand. So, as the fear got to him, he looked at the sheet before him which gave the prospectus for the impending exam in chemistry.

After plying his books for some time, he felt so unmotivated that he thought it might be a better idea to study with Meghana. She direly needed his help and that would give him the right motivation to get all the correct answers for the impending questions. He ticked off the chapters that needed to be studied and collected his cheat sheets for each of them. Then his eyes fell upon a chapter titled “Naphthalene and Anthracene”. To his horror he found that he had no notes whatsoever on that. There were awful sounding terms under that heading like “preferred nitration product”, “Friedel-Crafts reaction” and the like. At the end he saw some questions based on that chapter. He felt fear deep in his stomach and wondered what to do about it. Just then it hit him that it might be best he left right away to study with Meghana and on the way head to Somakhya’s house and get the material on naphthalene and anthracene from him.

That evening after having covered quite some ground with Meghana and feeling more confident Vidrum decided to return home. But as he just got out of Meghana’s house and headed to where he had chained his bike he saw to his immense horror that the spokes of his front wheel had been smashed. With his mind numb with this disaster he slowly started walking his bike hoping that he might be able to reach the repair shop near his school and get it fixed without his parents knowing. With a down-cast face he was thus trudging along when he crossed the bylane that led to Lootika’s house. There at the corner of the street he caught sight of Lootika standing with Nikhila leaning on their bikes. He waved out them and was about to proceed along when they asked him what had gone wrong with his new bike. He told them how unbeknownst to him his spokes had been smashed when he was studying with Meghana. He then added: “You all are not studying?” Lootika: “I am 3/4ths done. So I decided to take break of an hour for the evening because it is traditional among brāhmaṇa-s not to study during this hour. Instead, since Nikhila needed some help, I was bringing her up to speed. By the way you don’t have to go all the way near school. If you go past my house and turn left in the little lane there there is a new cycle-repair chap from Odisha. He recently fixed my bike very efficiently and economically.” Vidrum: “Thanks Lootika! that’s wonderful. Let me hurry there and return home to continue with the studies. I still have to catch up with phenols.”

Thus, Vidrum headed to the repair stall and got his bike fixed. The price the repair-man quoted for his work was indeed a good one as Lootika had mentioned but then Vidrum realized that all he had was a big note with no change. The repair-man asked him to wait till he got another customer so that he could give him the change. However, Vidrum had no time for that especially on a day like this. After some wrangling he thought the repair-man sounded honest so he decided to accept his offer when he said that he would come to Vidrum’s house and deliver him the cash pretty soon if he left his address. Being in a hurry Vidrum unthinkingly gave him directions to his house and left.

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In the heat of the exams forgot about his change. Upon the conclusion of the last of the exams Vidrum was riding back home with Meghana. He was feeling slightly relaxed that they had gone quite well though he could not be sure still if he would meet his parents’ cut. Just then they came across a clump of classmates frantically discussing a problem involving Hypsicles theorem. Seeing them Meghana triumphantly announced that she had solved the killer problem correctly. They were surprised to hear that she had done so, given that she was not known for any mathematical capacity at all. Vidrum did not want to let her down by revealing that she had merely copied the solution from him. Instead, he said: “you know we had worked it out before and it came in the exam.” The rest of their classmates who had gathered there said: “Hey thus far we only knew of Hemling and also Lootika and Somakhya to have cracked it – but those two are sort of crazy – you can never guess what obscure thing they might know! How come you figured it out?” Vidrum happy to be at the cynosure of his classmates was about to spin a yarn of how he had cracked the problem when he saw a car drive by them. He noticed that it was Lootika’s mother who was driving her four daughters home from school. It reminded him that after all the solution was not his. Hemling was given to boasting about his mathematical abilities; duly, he had found this problem and brought it up to Somakhya and Lootika to proclaim his superiority over them. But not the ones to let such challenges pass, they solved it after some battle, and as Vidrum and Sharvamanyu were hanging out with them they revealed the solution to the two. Feeling somewhat ashamed at the intent to pass a patently false tale he instead discreetly told his assembled classmates that he had indeed learned some tricks regarding how to solve it while hanging out with Somakhya. It also reminded him, much to his horror, that he had not yet collected the change from the bike-repair-shop. His parents would ask him for the accounts of how he spent his pocket money in day or two and he could not let the cash go unaccounted. So he left his classmates and hurried towards the bike-man’s shack.

In the meantime Somakhya mounted his bike and feeling the relief of the exams being behind him he wended his way towards a new rocky outcrop he had discovered among the basalts. While he cursed the basalts mentally, wondering why the gods had not birthed him in a land rich in Mesozoic strata, he still was excited by the prospect of finding some geodes, which he wished to analyze for their chemistry and structure. In particular he had acquired an interest in the chemistry of zeolites that were found among these basalts. He thought to himself: “for biochemists like us the chemistry of silicon puts many things in a distinct perspective.” He wandered in solitude among the basaltic rises from the great eruptions marking the close of the Dinosaur Age collecting chabazite, mica and quartz geodes. He had lost all sense of time in his pursuits and as he climbed towards the plateau above the temple of Caṇḍikā, he spotted a circle of basalt pillows that appear to have been laid deliberately by the human hand. To investigate it further he got close to them and started looking around. After some examination he realized that the stone circle was a likely remnant of the ancient megalithic peoples streaming into the peninsular of the subcontinent. While scanning the rocky debris in side the circle he found a metal ingot with the image of the Vetāla, an agent of Rudra, stamped on to it. It was clearly from an age closer to the current time. He realized that it was likely dropped by the Vetāla-worshiping tribesmen who gathered on the adjacent hillock on certain nights for an animal sacrifice. His excitement knew no bounds at his find, which suddenly made him aware of the time, and he headed home.

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The next day school was off much to the relief of Somakhya. Lootika was to visit him for lunch and then hang on. Somakhya was in his home lab when he heard his mother intercept Lootika at the gate. Much to his embarrassment he heard her quizzing Lootika about the questions on the just concluded exams and how she had answered them. Lootika answered that she had already forgotten about them. S.M: “Lootika, but would it not be nice cosmetics if you guys actually translated your intelligence into splendid results on the exams?” Lootika: “Nice cosmetics may be, but for whom to behold? As long as we pass and go to the next class what do these exams matter? And not that we are barely scraping through.” Then Somakhya’s mother proceeded to ask Lootika in regard to some molecular biologist featured in that day’s newspaper: “Would you someday be rich and famous like him”. Somakhya was now positively concerned knowing how brusque Lootika could be. He half got up from the microscope to distract them and bring her in quickly. Thankfully, Lootika responded with a boring answer: “I am not too good with names of people so I will have to read the article to find out what he works on precisely to give you an appropriate answer.” This answer was so confusingly unexciting for Somakhya’s mother that she decided not to pursue that line questioning any further. Somakhya heaved a sigh of relief that unnecessary fires were not lit.

She ushered Lootika taking the box with some food item which Lootika had brought along asking her: “Should I have my husband drop you back home in the evening – I just saw in the news that an animated protest for the aggrandizement of the local apabhraṃśa was to take place. As you know this is often coupled with pratibrāhmaṇatvam and we could be a target. L: “So it is. A member of one of the protest-organizing committees even asked me to join saying that the brāhmaṇa-s proscribed females from using the artificial Sanskrit language. So it was natural for women to stand by those fighting for all education in the state language! In any case thank you but no worries; my father said he’ll pick me up in the evening.”

After lunch Somakhya and Lootika were engrossed in a deep discussion on silicate minerals and Somakhya was showing her the minute crystals of various minerals under his microscope even as they set aside samples for chemical analysis. Lootika produced from her bag a rock which she had found. It had a striking globular crystal growth with the surface of each globule having a smaller crystals – a bit of fractality. At base of the globular growths was another mineral with a smooth more glassy surface. L: “What is this one?” Somakhya closely examined it with a lens: “The globular crystals are a good specimen of chalcedony while the the mineral at the base is moganite. Such appear to have formed in some quantity in our local basalts during the end of the Mesozoic.”

As they they set up some acid treatments for qualitative analysis Lootika remarked: “Deep within the two of us are svābhāvika biochemists and these minerals have a bit of an alien touch! Studying their chemistry makes me even more skeptical of Silicon-based life outside of computers elsewhere in the universe.”
S: “In most part I tend to agree with one possible exception that deserves more discussion. We have been looking at a bunch of zeolite structures and as you would have noted while there is the same tetrahedral geometry there is much less tendency for lability – and tendency to prefer oxygen over hydrogen – in this indeed I would posit lies the difference between the ability to make life or not. The one exception being certain clays, which some have seen as a possible Si based form of life.”
L: “Ah! talking of clays I forgot to show you this.” She pulled out a bottle with an interestingly colored clay in it. “This one is from Sagaradurga.” Somakhya prepared a mount of the clay under the microscope and remarked: “You see those crystals are believed to be part of a templating mechanism that allows clays to be treated as a type of Si-based life.”
Having taken a close look Lootika donned her spectacles again saying: “But is such accurate templating not a general process in any crystal growth? You would recall our freezer experiment to grow snowflakes that our parents would hate us for. While every snowflake is unique, the six sectors of each snow flake are often accurate copies of each other suggesting that templating mechanism around the core starter is transmitted quite faithfully even in water. But such templating hardly gets you to life. Moreover while it might be moderately accurate across the six sectors it is too mutable between snow flakes to represent any faithful information transmission.”
S: “That’s right. The snowflake is a good example for how accurate templating can happen in crystal growth, but the clay as life hypothesis goes beyond: It posits that certain clays are more prone to attracting mineral precursors from solution or sol to their surfaces to incorporate them into the growing crystal lattice. The difference in this capacity is seen as a form of natural selection which allows certain clays to “prosper and grow” while the less-sticky ones which cannot attract mineral precursors do not grow or spread. Like with the snowflake it reproduces the initial configuration or crystal “defects” accurately in the daughter crystals but is seen as having more intrinsic stability of structure – something we can verify with the crystals we have been examining. When drying occurs and the crystal breaks into pieces, those pieces preserve the original crystal configurations. They are then seen as being dispersed widely by natural forces, like say wind. These then nucleate new clays that then grow – thus, the proponents would say there is genetic transmission. New defects are the mutations, which can then be copied by the same process too. Thus, this theory posits clay to be a system like life with capacity for replication, natural selection, mutation.”

Lootika: “Though it is not at all clear if the mutations in clay in anyway are the subject of natural selection?”
S: “Yes; that, as far as I can say, is a leap of faith in this hypothesis.”
L: “But would it have any links to life as we know it at all?”
S: “Its proponents propose something called the “genetic takeover,” where biochemicals somehow use the original replicating clays as a vehicle for their own chemistry and transmission. This is followed by they becoming independent replicators to break off on their own as life as we know it.”
L: “That indeed can be seductive idea: but it still suffers from the problem of “special nature of life” principle we have proposed. Why don’t we see such proto-life repeatedly forming on earth with the clay phenomenon still available today?”

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Suddenly Somakhya received a message from Vidrum asking if he could stop by. Somakhya was surprised – he thought Vidrum would be having a party with Meghana and friends. He showed the message to Lootika and asked: “Why would he want to come to see me? We are in the midst of interesting things what should I tell him?” L: “Yes. As I was leaving for your house I saw a knot of our classmates and heard their raucous yells and whistles even as I passed by Meghana’s house. May be just tell him we are busy with our minerals and he might get bored if he came.” Somakhya did so but Vidrum answered that if Lootika was around it was all the better since it was a matter the two of them would be most suited to give some answers for. Somakhya gave in and asked Vidrum to come over.

Even as Vidrum came in he said: “Good to see you guys; I am sure this is an issue only you might be able to provide an answer for. Now I understand why in the past our society valued brāhmaṇa-s so much.”
Somakhya: “Why dear Vidrum? You seem to be somewhat agitated by something beyond the ordinary. I have never heard you call upon our brahminical credentials for the more routine issues of education that we were supposed to be in charge of in the days of yore. Moreover, the exams just got over and I understand they went quite well for you. So what beckons you to come to us for brahminical services.”
Lootika said nearly laughing: “Hey, I caught a glimpse of you having a whale of a time with some of the classmates. It seems to have ended prematurely?”
Vidrum: “Lootika, why rub salt thus. Women are always like that! I know I am disturbing you in whatever interesting stuff you are doing but if you don’t mind please hear me out.”
Lootika: “Why? Would you have thought of us if something had not interrupted the session with your other friends? Never mind, we are all ears. Tell us what happened.”

Vidrum: “Please bear with me. It is a bit of a long and absolutely bizarre story! Lootika knows the beginning of it but I’ll fill you in Somakhya. That day before the chemistry exam after getting the needful from you I went over to study with Meghana. While at her place it seems a tempo filled with heavy iron rods dumped its cargo on the wheel of my new bike which was parked at her gate. As result some of my spokes were smashed. Thankfully, Lootika recommended me a bike-vālā near her house who repaired the damage but did not have change for the note I gave him. It was most of my pocket money. He promised to send the change over to my house as soon as possible but did not do so. I remembered this only yesterday and ran to get the change from him but his shop seemed to have shut down!”
Lootika interjected: “No wonder he did not return your change Vidrum. Tragically, he died that night!”
Vidrum: “What! That explains everything! This is certainly a matter in your domain!”
Somakhya: “What happened? Do you know how he died?”
Lootika: “That night before the chemistry test I became rather overconfident that I had nearly revised everything by evening. I started whiling away my time and helping little Varoli and Jhilleeka with their impending exams until I suddenly realized it had gotten quite late and I had not yet finished the part on anthracene with all that photodimerization and oxidation. So I decided to get up early in the morning and finish it off along with a round of last minute brush up. Even as I woke up there was some commotion going on. My father was called up by a bunch of people and he had to arrange for an ambulance all of a sudden. There are some days my father has to handle medical emergencies but they are rare these days. At breakfast Jhilli and Varoli remarked that they had heard a loud explosion. It is rather amazing that Vrishchika and I had so blissfully slept through it all. My father informed us that the car-vālā whose shop is next to the late cycle-vālā’s had a storage tank of nitrogen that was attached to the thin wall separating him from the latter’s shack. For some reason that tank of N2 exploded and propelled itself through the wall into the cycle-vālā’s shack and shot out through the roof. But the cycle-vālā who was sleeping in the shack seems to sadly have died from asphyxiation though we were not sure if he was rather hit by shrapnel from the explosion.”
Somakhya: “That’s sad indeed! But Vidrum you have not completed your story. Please continue.”

Vidrum: “Ah. In light of what Lootika has just informed us I think I’m making more sense of the bizarre events. Nevertheless, let me continue in order so that you understand my situation. Last evening with the exams behind us I went with several friends to watch a movie with that I had exhausted all the cash I had. Today we watched another movie at Meghana’s house and then our gang suggested that we go to the famous Kūrmakūpa hotel for lunch. Unfortunately, I had no cash. Our friends counted their cash to see if they could subsidize me but all they could muster was less than what would be needed for a plate. Hence, with much sorrow I decently decided to opt out. Cursing the cycle-vālā I came back home in sorrow. I grabbed a quick lunch from what my parents had left in the fridge and went to the bathroom to wash my mouth. To my shock when I spat out the water it was red as though with blood. I examined my mouth and found no cut. You won’t believe it – each time I did it the same thing happened! Unnerved by this I went to my room and sat at my desk. If this was bad, what happened next positively shook me. The fan on the ceiling suddenly started rotating on its own making a weird noise. It was like a periodic whooping noise that I seemed to have heard some years ago one night at my ancestral village. My folks told me it was the dreaded ghost Daṇḍalūma making his rounds! Then from one corner of my room I heard a girl singing in an unknown language. I looked hard but I saw no one. I have told you before that there were some strange incidents pertaining to the cemetery near my house and when I mentioned them to my aunt she wanted to take me for a psychiatric evaluation.

Now I thought I was really losing my wits as my aunt had claimed. The alluring singing continued and I looked again and I saw the faint outline of the face of a girl with straight thick hair. Then that stopped abruptly and a darkish face appeared on my wall-clock. It looked vaguely familiar. I raked my brain as to who it was. But only now, after hearing what Lootika said, I realize that it was the late Orissan cycle-vālā. He kept scowling at me from the clock and it deeply terrified me. I did not catch much of what the face kept jabbering but I did hear one phrase: “kṛtaghna-kukkuron-vālā-kula”. Now I realize he was pissed off because I cursed him so many times for not returning my change not knowing he had already died. But it just did not stop sometimes he would appear on the fan with that whooping noise in the background, and sometimes in the clock and it would swing violently. Then it would stop and the girl’s singing in that strange language would continue. Finally, I was so scared that I sent you the message and came over. I know you guys have some special means of tackling this type of entity from beyond. So tell me what can be done!”

Somakhya and Lootika: “Wow.”
Lootika: “There is precious little we can do without being there on site I believe. We could come over there in the evening.”
Vidrum: “But my folks would be back home and we can hardly do anything suspicious!”
Somakhya: “Vidrum we cannot just come over for such an adventure. We first need perform some rituals so that Śiva is on our side as we step into your spooky lair. To be frank I’ve always been a bit concerned of your place.”
Lootika: “Indeed. His place is positively haunted. May be we should do it tomorrow.”
Vidrum: “Hey. If you guys are so scared then what to say of me. What do I do? I cannot just go back and spend the night with the angry phantoms.”

Lootika: “There is something more in your case. We can see the possible reasons for the late Orissan to pursue you but that girl appears strange – could there be two ghosts here?”
Somakhya: “That’s good point! Since Vidrum’s place was always haunted, and bhūta-s like certain loci, I wonder if that girl was displaced by the Orissan’s ghost who tried to occupy the same locus?”
Lootika: “In practical terms that possibility makes it quite difficult for us to handle this thing. I was thinking that the best way for us to deal with this issue of Vidrum without us going on site to do some karman was to create a second mobile locus to draw the bhūta into which we could then collect and tranquilize. But that would need us to set up a khārkhoḍa, which would itself need some labor in the first place. But now we have two to deal with. What if the girl goes into the khārkhoḍa, while the Orissan continues to haunt Vidrum?”
Somakhya: “Ah! that can happen. Did the girl look like someone familiar?”
Vidrum: “I think she looked East Asian. Very strange, right?”
Lootika: “Indeed!”
Vidrum: “How long might it take you to set up that khārkhoḍa thingie? Can you make two?”
Lootika: “It could easily take Somakhya a day. If I ask Vrishchika’s services, we might be able get two between all of us in a few days, given that neither me nor my sister can be sure of our success in the first try. Further, remember tomorrow is a holiday but day after we are back to the drudgery of school.”

Somakhya: “While making a khārkhoḍa from scratch is some challenge. I have an unusual solution. By some luck I found this vetāla ingot of the hillmen. It can prove to be an effective as a khārkhoḍa with just 20 minutes of ritual. Vidrum we need you to go away – may be circle around on your bike and come back after half an hour. I’ll need to do this ritual in some silence and Lootika alone can be around as an uttarasādhaka.”

Vidrum duly left. Somakhya showed Lootika how the ingot could be set up as a khārkhoḍa using the Vetālabhairava mantra. When Vidrum returned he handed it over to him: “Vidrum, take this home and place it the southern corner of your room or under the wall-clock.”
Lootika: “So what do you intend to this later this evening?”
Vidrum: “The friends are going to be back from lunch soon and gathering at Gardabh’s house. I intended to join them there. Do you all have some plans?”
Lootika: “Good. We are going to play some badminton once we are done with our study of the zeolites.”
Vidrum laughed out aloud: “Lootika: do you ever get at least a point against Somakhya? He’s quite stiff even for Sharvamanyu who is apparently the best in our school.”
Lootika: “Never mind. It gives me some practice so that I can bully Abhirosha and Vrishchika later. You continue with your plans but do not eat any meat and if possible light a lamp at the Śmaśānasarasvatī shrine and whenever possible make a clicking noise slapping your tongue against the palate.”
Vidrum: “That’s strange.”
Somakhya: “Yes, but do as she says. That’s the best we can do for you now. I know this can be a difficult day for you but before doing anything deposit the khārkhoḍa and bring it with you to school day after and hand it over to me.”
Vidrum looked a bit uncertain but decided to leave them to join his other friends.

Later that evening Lootika’s father came to pick his daughter up. As he did so he reminded Somakhya’s parents that his family was conducting a caitya-yāga to Kumāra the next evening as a relative was going to visit Kārttikeyapura in the mountains. He then reminded them that his wife and he had invited them to come along with Somakhya to participate in the ritual as that way they could convey their offerings too.

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The next evening Somakhya’s family arrived at Lootika’s home for the said caitya-yāga. Lootika’s mother opened the gate to let them in. Lootika and Vrishchika came out with their mother and Somakhya immediately glimpsed a certain tension and excitement on their faces, especially that of Lootika. Lootika immediately exclaimed: “I believe it has played out to the worst of our fears. The phantom has struck at Vidrum’s place!”.
Lootika’s mother said with a stern face: “Girls go inside. Let them come in and sit down. This is not the first thing you want to tell them!”
Seeing her mother’s reaction, and their parents busy with pleasantries, to maintain social decency, Somakhya avoided any immediate conversation with the caturbhaginī, who sat in a closely knit clump on the couch eyeing each other and Somakhya with an expectant look. Lootika’s father told them that he was nearly done with the preparations of the yāga and that they could start in a few minutes.

In the mean time Lootika’s mother filled them in saying that their schedule was a was disrupted because of an emergency call that Lootika’s father had to attend to around 3:00 AM that morning: “There is this kid Vidrum who is Lootika and Somakhya’s classmate who lives some distance away near the śmaśāna.”
Somakhya’s mother: “Well I saw him visit our kids just yesterday.”
L.M: “His aunt Vaidoorya was apparently running down the stairs from her room on the upper floor in the dark when it seems her dress got caught in the railing and she tripped and fell headlong. She suffered a major head-injury and had to undergo an emergency procedure. They called my husband because that’s often the fastest way to procure care in this kind of a situation. Moreover, she was a student of mine in the course I teach at the med-school. Sadly, her situation is pretty bad.”
Lootika’s and Somakhya’s mothers quickly caught their kids visual communication. L.M: “I am sure you might have heard this from your son. Our kids like to keep saying that Vidrum’s house is haunted and, as you can imagine, with this tragedy, my girls have been spinning tales of the wildest fantasy all day and have been waiting to share those with Somakhya.”
S.M: “Are kids can be strange isn’t it? On one side they show this precociousness in several directions but almost as though the compensate for that they can spout utterly crazy fantasies that makes me feel worried sometimes.”

Their parents then admonished them to focus seriously on the ritual if they wanted any phala and stop being distracted by their fantasies. After the ritual they packed the offerings to be sent the caitya at Kārttikeyapura. Then they sat down for a feast in course of which Somakhya and Lootika could hardly talk anything about the matter that was really on their mind because of the eyes of the elders upon them. Instead, the dinner conversation revolved around a heated debate sparked by Vrishchika concerning issues of the metabolic syndrome, while at one side Jhilleeka and Somakhya’s father kept out of it having their own discourse on fractality and irrational numbers.

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With school resuming after the exams Somakhya and Lootika never got to talk about the events at Vidrum’s place in private. A whole fortnight passed thus when one day Lootika and Vrishchika had just gotten on their bikes to ride to school. They heard someone riding hard behind them to catch up; alarmed they turned around only to be relieved at the sight of Vidrum with his face blanched as a ghost itself. As Vidrum caught up with them, without much of a word he handed over the vetāla ingot to Lootika: “Found it in my aunt’s room! I couldn’t wait to get rid of it. So I’m handing it over to you rather than Somakhya who has been wondering what befell it.”
Lootika: “OK. Let me bury it outside my gate and we can retrieve it later.”
Vrishchika: “Has your aunt’s intracranial swelling subsided? How is she now?”
Vidrum: “She’s recovering slowly. Luckily, yesterday’s neurological tests were positive but it seems she will miss the year.”
Lootika: “Hopefully she recovers well. I believe my mother can some how arrange with the authorities that she doesn’t miss the whole year but only this semester. But you look very pale and wan yourself?”
Vidrum: “Today is report day. I have made it to the 6th place, but not within the first 5 so I fear I may lose my bike and will be back to the chore of walking.”
Lootika: “Ah. Yes let’s see what music we all get in front of our parents from the teacher.”

School ended early that day but they had to wait for their parents to come and collect the reports in the order of their rank. The teacher assigned to their class first handed the report to Tumul and conferred fulsome praise on him before his parents commenting about his high intelligence, courteousness to teachers, and good behavior. Puffed up he left with them exultantly looking down on the rest. When Lootika and Somakhya’s turn came the teacher unceremoniously handed their reports to their mothers: “Somakhya and Lootika have a similar temperament and are likewise tied for the 5th place. They are sometimes very aggressive in their questions to the teachers in class. Somakhya began badgering the chemistry teacher and Lootika joined him to almost bring the teacher to tears with claims that she was teaching things wrongly. Hence, we have had to cut their marks or else they would have ranked higher.” Then she turned to Lootika’s mother and remarked: “Your daughter hangs out most of the time with the boys and has learnt mischief from them like bringing a catapult and a bag full of clay balls to class. She might do better if she cut that out. The only saving grace is that she is the girl with the highest marks in maths by a huge margin given how tough this exam was.”

Then came Vidrum’s turn. Handing his report to his father, the teacher remarked: “Vidrum has been very focused on his studies this term and well-behaved. He makes excellent notes in class and has shown a major improvement since last year with a strong all-round performance to rank 6. Keep it up.” With the sheen taken off Somakhya and Lootika’s performance, Vidrum 6th place seemed to shine brighter their own tainted fifth place. That was not lost on his father and he was let to keep his bike with the relatively mild admonition of getting higher in the next exam.

With school over early for the day Vidrum, Somakhya and Lootika hopped on to their bikes and headed to see the displays at the newly reopened museum of the archaeological survey. On the way Vidrum asked his friends, somewhat triumphantly, if they got some music from their mothers. Somakhya: “Every dog has his day and today is yours. Deep within our folks know only too well that the standards we have to measure against are not these reports but those of our ancestors of yore, the Atharvan-s and the Aṅgiras-es. So beyond some words at the spur of the moment, they don’t get too caught up with such.”
Vidrum: “But what about the chemistry class incident for which you all were docked some marks?”
Lootika: “Hey. We did you all a good service by calling her out. A person who does not know the formula of Carbon disulfide should not be a teacher, let alone that of chemistry. Our parents know fully well we were doing our brahminical duty of pāṣaṇḍa-khaṇḍanam.”

As they went through the new displays in the museum Somakhya brought the attention of his friends to an unassuming set of objects in a small display. One was a metal mirror with a handle which was labeled as a toli. Beside it was a small doll-like object which was labeled an ongon. Then there was a yellow paper on which something was written in a curious script. Beside it the exhibit stated that the mysterious document was found among the possessions of Doherty, the secretary to the English tyrant Elgin, who was buried in the city cemetery. It was undecipherable until recently a lama from Mandi had translated it for the Archaeological Survey.
The first line read: “Princess Irinjinbālā”. Somakhya: “Vidrum – that is your east Asian lady!” She has recorded her tragic fate in this document. See – in the next line she quotes her ancestress, the mother of the great Khan:
‘Not misunderstanding ancient words,
Not forgetting old words.’
She records her ancestry as being from none other than illustrious Qasar and Sübedei.”
They read the translation of what she had written. She was captured by Elgin’s troops in in 1860 and this Doherty brought her against her wishes as a slave-concubine to our town and subject her to much suffering. She was foretold by her uncle, a noted lama, that she would meet a dreadful fate but die in the holy land of Jambudvipa on account of which after much suffering she would eventually attain the svarga of Indra and reside there. The same lama told her that her illustrious ancestor himself was reborn as a great paṇḍita-warrior in Jambudvipa and thus attained the realm of Kubera.”
Lootika: “I wonder if it was her suicide note?”
Vidrum: “That’s pretty remarkable if it was her! I never heard or saw anything of her after that day. What English expedition was this? To Tibet or to Mongolia.”
Somakhya: “No, it was the opium war in China, where she was evidently captured in the English raid near Beijing. Lootika, some day you would encounter and release her. She would certainly give you service in return.”
Lootika: “You talk like your ancestor Kabandha Ātharvaṇa.”
As they walked among the exhibits they stopped to take a careful look at a bow which was labeled as that of the great brāhmaṇa warrior among the marātḥā-s. Somakhya: “I had always the wondered if this great warrior was Sübedei and Qasar reborn in our midst. We seem to have obtained our confirmation today.”

After the museum trip they swung by the temple of Caṇḍikā and climbed up the hill to the circle of basaltic pillows. There, in the middle of it they buried the vetāla ingot again, put some of the remaining soil in Vidrum’s head and asked to have bath upon his return. Somakhya: “Within 4 days you will have a dream where the deceased Orissan will appear to tale his tale. Record it, however painful it might be, and send it to us.”

◊◊◊◊

The four sisters were huddled in their home-lab when Jhilleeka and Varoli asked Lootika if there had been a closure in Vidrum’s case. Lootika: “Yes, he sent us an account of his dream. It brings everything to a resolution. It so happened that after the cycle-vālā died there was no one to claim his body or cremate it. So it was chopped up in the anatomy department of the med-school. However, his brother came a few days later and honestly tried to settle any outstanding payments that were there. One of those was Vidrum’s. Hence, he went to Vidrum’s house on the last day of our exams when only Vaidoorya was around. He tried to return her Vidrum’s money by knocking at the door. She did not understand what he was saying and thought he had entered the house and stolen money. She called the police and they arrested him. In the mean time it appears our cycle-vālā had become a bhūta and he vented his ire the next day on Vidrum’s family especially Vaidoorya. That day Vidrum came to us for help upon being attacked. Somakhya prepared a khārkhoḍa that drew the Orissan’s ghost into it. However, that night Vidrum managed to get our classmates Gardabh or Mahish to let him stay at their house to evade the phantom in his. For some reason his aunt had gone to his room and seeing that pretty ingot, which was the khārkhoḍa, took it with her to her room. That was her doom.”

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Posted in Life | Tagged , , , , ,

Godhūmo vijayate

As we have noted several times before, the Ṛgveda represents a very early stage of the evolution of Indo-Aryan. Its agricultural terms relate to a major puzzle in Indo-European history. There is an unmistakable agricultural vocabulary including words such as kṛṣṭi = cultivation, deriving from the root kṛṣ to plow. The furrow sītā and also the eponymous goddess represent agricultural practice in a field often termed kṣetra. The primary grain cultivated in these fields was yava = barley, one of the oldest crops cultivated by man. Another word generally taken to mean a generic grain is dhāna. All these words have a clear Indo-European origin and are part of a small but consistent vocabulary of agricultural terms that can be traced back to a very early stage of IE if not PIE itself. Yet, the archaeological evidence for agriculture among the early Indo-Europeans is murky. This issue has been raised before by Mallory as a key problem in our understanding of early Indo-European archaeology. There is no mention of wheat, and at best 3 uncertain mentions of rice – i.e. the word odana, which could have simply meant a boiled grain.

The Yajurveda and later layers of the Atharvaveda, in contrast, present a different picture. Rice and wheat are both present and the former is already on its way to overtaking barley as the principle grain. The words for rice include vrīhi (regular rice) and nīvāra (a wild rice). The first word is found in Iranian as birinci and has cognates across the Iranian languages. The first word was also either transferred to Dravidian as arici or acquired by it parallely to Indo-Iranian. It is also found in Greek as oruza, Mongolian ür-e, Japanese uruchi. The same applies for wheat, which in Yajurveda is already seen as godhūma. It is also found in the later Avestan layers as gantuma. Dravidian shows a form similar to the Indo-Aryan word. It also occurs in Hittite as gant and in the Egyptian branch of Afro-Asiatic, and Semitic as well, it has cognates with similar sounds. Thus, these two crops most likely spread rapidly and laterally from a focus and were taken up by related and unrelated language families as they spread. This suggests that, while rice is not found in RV, the Iranians and Indo-Aryans acquired at least some knowledge of this crop even as they neared their current homelands. However, we cannot entirely rule out knowledge going back to an earlier period. The Altaic and Japanese cognates for rice suggest an eastern focus while the western cognates for wheat likewise suggest a western focus. Both of these are consistent with the ecology and genetics of the domestication of these crops.

If we look at rice and wheat production today the stamp of these foci and distinct ecology are clearly visible. In figure 1 we plot the mean annual density (tons/hectare of national land; log-log scale) over 17 years of wheat versus rice production for the 72 countries that cultivate both these crops. We find that they are entirely uncorrelated (r^2=0.034). This is notable given that wheat and rice are among the most cultivated crops in the world (wheat most, then corn, then rice).

Rice_Wheat_densityFigure 1

Now if we divide the plot into 4 quadrants based on the median values for rice and wheat cultivation we find that there is a relatively small group of 12 countries (1/6th of total set) that show a high density for both wheat and rice cultivation (Table 1)

Table 1: High density rice and wheat cultivation; Land is national area in hectares.

Country                           Land         Rice        Wheat
--------------------------  ----------  -----------  -----------
Bangladesh                    13017.00   1162382.50     58596.88
China                        932748.77   6876275.00   4541253.88
Egypt                         99545.00     76581.38    201579.00
India                        297319.00   3244250.00   2661475.00
Iran, Islamic Republic of    162855.00     85245.50    713768.25
Iraq                          43737.00     12825.00    385919.62
Italy                         29413.14     42250.00    589500.00
Nepal                         14335.00     80625.00     66600.00
Pakistan                      77088.00    239241.38   1121625.00
Portugal                       9150.00      3750.00     28000.00
Spain                         49900.00     17144.00    471508.38
Uzbekistan                    42540.00     12625.00    196625.00

It is notable that 4 of these make up bulk of the Indian subcontinent while 3 others are part of the old greater Iranian zone. These lie precisely at the junction of the eastern rice focus and the western wheat focus. Indeed, we find low wheat-high rice density zones like Bhutan, Myanmar, Japan, Korea, and Thailand around the eastern periphery of this zone and reverse on the western periphery. This also raises that possibility that combined cultivation of the two, in addition to ecology, is in part the echo of the entry of the Indo-Iranians into this zone who then stabilized both the eastern and western acquisitions across their core domains.

In figure 2 we plot the wheat versus barley production (in tons; log-log scale). A similar picture is obtained if we plot densities as above. The two, in distinct contrast to rice, show a good correlation (r^2=0.644). Further, while just 72 countries grow both rice and wheat, 96 grow both wheat and barley. This suggests that barley, which was the old IE crop, was to a degree ecologically and operationally equivalent to wheat, with steppe-land as opposed wetland preference (rice). Thus, unlike rice, barley has taken little root in non-Mediterranean Africa. Hence, it appears that as wheat was acquired, it ate into the share of barley across the steppe-land but barley still holds on as the fourth most produced crop. Its role in domesticated animal feed and probably its special role in alcoholic beverage production (already described in the Yajurveda) play an important role in its tenacity and even expansion.

Barley_WheatFigure 2.

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

A note on tales of fratricide, warfare, cannibalism and incest

The Osman conqueror of Constantinople, Mehmet-II, bothered by the civil wars his predecessors had to fight to take the throne, institutionalized the system of fratricide. In this system, the rival brothers of the sultan, who took the throne, were all imprisoned and the moment he had fathered a live son in his harem, he had his brothers strangled with a silk rope. The Mohammedan tyrant of South India, Adil Shah, is said to be one such brother who escaped execution. In the 1600s the sultan Ahmed commuted the death to and imprisonment, usually with access only sterile mates. In another Mohammedan potentate, that of the Mogols of India, the tyrant Shah Jahan fathered several sons and daughters in his harem where he cocooned himself and went on the indulge in incestuous couplings with the latter. His sons were locked in a fratricidal conflict in which Awrangzeb emerged victorious after killing his brothers and deposed Shah Jahan. It is almost a truism: “Much of what we have seen in Homo has been seen before in hymenoptera”, and things can get pretty ‘lurid’ there. That is what we shall be taking a brief look at here.

We had early discussed the case of the male competition among the chalcidoid fig wasps where the males fight unto death in the natal fig in order mate with their sisters. A similar scenario with its own complexities can be seen in another chalcidoid lineage of the Eulophidae; e.g. the parasitoid Melittobia and Anastatus wasps. The Mellitobia are tiny wasps (1-2 mm) which are unlikely to have been noticed by anyone other than those with a biological interest. They are parasitoids which lay their eggs mainly on the prepupal stages of solitary wasps and solitary bees. Popular hosts are: the organ-pipe mud-dauber wasp (Trypoxylon), which makes tubular nests from mud and provisions its larvae with spiders; certain bumblebees; leaf-cutter bees; wool-carder bees. They may also attack any other larvae that are cohabiting the nest of the said bees/wasps or other insects like blowflies. Typically, the flying female with long wings on locating a suitable host, makes its way through the host nest reach the developing host and stings it. The toxins from the sting paralyze the host and arrest its development to go no further than the pupa. Then the female uses its mandibles to suck the haemolymph of the host from the wound and thus it gains nutrients in anticipation for egg-laying.

wasp_morphsFigure 1: Mellitobia morphs from Biology of the Parasitoid Melittobia (Hymenoptera: Eulophidae) by Matthews, Gonzalez, Matthews, Deyrup.

What follows depends on the kind of host she gets. If it is a small host, then she lays as many eggs as is possible for such a host, which then develop into a small number of males and a much larger number of flying females with long wings like the mother. These females need to feed before they can lay eggs themselves and are capable to flight to a new host. If it is a big host then she might lay about <3 haploid (unfertilized) eggs that becomes males and roughly 30 or fewer diploid eggs that develop into a different kind of female. These initial larvae develop rapidly from the egg and, like their mother, feed primarily off the haemolymph of the host. The females developing from these diploid eggs have short vestigial wings and do not need to feed before laying eggs. They mate with the small-number of brothers who emerge and start laying a new round of eggs right away to amplify the egg count. These males might also mate with their mother if she is still alive and around. The new round of offspring feature larvae that are equipped for directly eating the host tissues rather than merely drinking haemolymph. Thus, they consume the host and mature into adults – this generation of females are like the foundress – they have long wings and are capable of flight. They mate with their brothers and then make their way out of the host cocoon. For this, a pioneer female stings the host cocoon at a spot and its venom itself apparently acts as a pheromone to attract other females. Then the females assemble as a circle and cooperatively chew at the wall till they break an opening and then crawl out. They move by crawling, jumping or flying in search of a new host.

There is no evidence the males ever leave their natal nest and die after mating with their sisters or on occasions their mother (see below). But the most striking aspects of the life of the male is their lethal combat with siblings and their elaborate mating ritual (dance). An interesting consequence of this lethal combat is that the females might be left as virgins if all their brothers are killed in combat before mating with them. If this were happen then the long-winged females fly away as virgins to find a new host and feed on it. Then they lay a small number of unfertilized hence haploid eggs on the host. She then carefully tends to these eggs closely guarding them and stroking them with her antennae. In roughly 2 weeks they develop into adult males and emerge from the pupal cocoon. She mates with her first son who emerges and when her eggs are fertilized she proceeds to lay a regular clutch of eggs as before.

wasp_transbergamotene

Figure 2 Alpha trans-bergamotene

For blind incestuous males the mating ritual in Melittobia is rather elaborate. Virgin females appear to be first be attracted by towards males by the male pheromone trans-bergamotene which has a “woody warm tea”-like odor. Once the two have paired the male mounts the female and perform a “dance” by fanning their wings and wagging their middle and hind legs. They stroke the females antennae and then clasp her antennae with theirs. This ritual has been described as the most complex among chalcid wasps. The females queue up behind the mating pair and once the male is done he moves on to the next female. This peculiar courtship ritual of the male is puzzling. Why invest in an elaborate courtship ritual when you have all the opportunity to mate with your sisters and they have no major alternatives to choose as mates?

wasp_fratricide

Figure 3. brother killing brother from Feeding and siblicidal cannibalism in a male parasitic wasp (Hymenoptera: Eulophidae) by Deyrup, Matthews, Deyrup

The lethal combat with their brothers is conducted primarily using their scythe-shaped mandibles and might involve decapitation and amputation of appendages. Entomologists have obtained images of decapitated males trying to incapacitate their rivals even in death by holding fast to their appendages by means of the severed head alone. Yet males even after suffering damage are quite capable of sustained copulations. Further, the males upon killing their brothers, suck their blood and feeding on their blood appears to make them live longer and mate to their fullest potential. Typically, males which are bigger emerge as winners. Males which are born first again have an advantage over their later emerging brothers whom they quickly attack and dispatch However, this propensity for violence is different among different species: In Melittobia femorata it has been reported that the male violence is muted rarely resulting in death. However, in this species the females engage in combat and inflict serious injuries on each other. Thereby they apparently establish small exclusive territories. In other species the number of violent incidents between males decrease if the number of females is more. However, in other genera like Anastatus apparently this situation accentuated male violence leading to more deaths in a winner take all struggle for mating with the sisters. While most male violence in Melittobia is directed against the brothers on rare occasions they might abruptly convert a copulatory attempt into an attack to kill the sister or mother they are mating with and feed on their haemolymph. This extreme male aggression with fratricide and cannibalistic imbibition of the blood of brothers is puzzling for inbred and hence apparently closely related males. Also puzzling is the rare but reproducibly observed violence against sisters and mothers. This does not appear like a simple mistake in recognition because the males proceed to copulate and then suddenly turn to attack their potential mate.

wasp_killing_mate

Figure 4: Male killing female from Biology of the Parasitoid Melittobia (Hymenoptera: Eulophidae) by Matthews, Gonzalez, Matthews, Deyrup.

We can draw comparisons between this violence and that seen in other hymenopterans and arthropods. First we we may look at the more generally parallels seen outside of hymenoptera: 1) The colonial fungus eating thrip, Hoplothrips karnyi, engages in lethal male combat using its weaponized forelegs and also the abdomen as a club. Thus, they take over and guard the egg-clusters at sites where female lay eggs. Here, like with the parasitoids, the bigger males win outright. But it differs in that the small non-guarding males sneak matings with females away from the egg clusters – suggesting a certain inter-male polymorphism. Further, this conflict is not exclusively between sibling males. 2) The cannibalistic redback spiders show strong male-male aggression for getting access to virgins because of a strong first male-sperm preference among females. Here too big males are favored in combat but it is rarely lethal. The females also attack the males but only when multiple males are competing. Smaller males tend to adopt the sneaky quick coitus strategy. However, their success is lowered by them being cannibalized by the female with whom they initiate a quick mating. In contrast, the victorious big males initiate a long-drawn coitus with high success of insemination.

wasp_copidosoma

Figure 5. The encyrtid wasp Copidosoma

Closer parallels are seen in other hymenopterans: 3) We have earlier discussed the comparable violence seen in certain fig wasps but here there two male morphs those that fight and tend to inbreed and those that fly away. 4) The fighting male morphs of the Cardiocondyla ants are (nearly) blind and engage in fierce fighting including killing of their still developing brothers. In different Cardiocondyla species 72-84% of the emergent queens mate with their brothers. Thus, in this hymenopteran there are many convergent similarities to Melittobia and Anastatus. However, they are different in having a distinct flying male morph like the fig-wasps that facilitates out-breeding. 5) The case of the parasitoid encyrtid wasps like the Copidosoma lineage which attack plusiine moth caterpillars features comparable conflicts in the context of the remarkable process of polyembryony. This process begins with the mother laying a single or two (one haploid and one diploid) egg in a moth egg. The egg then undergoes early divisions to give rise to a primary morula embryo, which then partitions into up to 3000 separate secondary morulae – polyembryony. These then separately develop into adults. Up to 24% of embryos develop into special larvae of the soldier caste which do not develop into adults instead dying when their reproductive siblings complete development and eat up the caterpillar. The soldier larvae engages to two types of conflict: (i) conflict against non-kin larvae which have been inserted into the same caterpillar. This in observed both in Copidosoma bakeri and C. floridanum where they recognize non-kin via their surrounding membrane. (ii) Only in C.floridanum the females soldiers additionally attack the male embryos and kill their brothers. This reduces their numbers in order to establish a highly female-biased sex-ratio at end of development resulting in a situation similar to Melittobia and Anastatus. These few surviving brothers both mate with their sisters in the natal caterpillar and also fly off to seek external copulations. Thus, here the male numbers are reduced not by male-male conflict but by the non-reproductive female soldiers that kill them.

Looking at things from the other side of the biological conflict, we find that the hosts of Mellitobia, being locked in a life-and death conflict, are not passive either. They use multiple remarkable means to defend themselves: The mud-dauber wasp Chalybion californicum secretes a poorly-studied aliphatic waxy compound from the underside of its abdomen which it rubs against the nest walls; this repels the invading Mellitobia effectively. The vespid keyhole wasp Pachodynerus nasidens appears to visually or olfactorily detect invading Mellitobia and directly bites them. The wool-carder bee, Anthidium manicatum, one of the victims of Mellitobia, collects plant hairs from the leaves and stems of certain species to make a “wool” in a form resembling cotton balls as its brood chamber. Then it uses specialized hairs on it tarsi to collect a secretion from the extrafloral trichomes of a totally different set of plants and smears them on the wool. These secretions inhibit parasitization by Mellitobia and other parasitoid wasps. Thus, this mechanism is similar that used by the bee-killing beewolf wasp that involves treatment of nests with Streptomyces bacteria. The antibiotic produced by the bacterium kills fungi which might infect the nest.

wasp_mites

Figure 6 Acarinaria from Mutualism: Wasp Keeps Watchdogs to Protect Young by Kronauer

Certain wasps like the eumenine wasp Allodynerus delphinalis and bees like the yellow-banded carpenter bee, Mesotrichia caffra, have specialized pockets on their thoracic and first/second abdominal segments, called acarinaria in which they carry symbiotic mites. In the case of the former wasp the mite is Ensliniella parasitica while in the case of the latter bee it is Dinogamasus braunsi. In the case of the Allodynerus-Ensliniella system studies have shown that the mites are transmitted to the nest from the acarinaria of the mother and they develop alongside her larvae feeding both off the provisioned caterpillar and later the wasp larvae themselves. Thus, at first sight they look like parasites, but their real use becomes apparent only when the Allodynerus wasp is attacked by the parasitoid Mellitobia. When this happens the mites launch an attack on the parasitoid biting it and it fights back by biting them. But if there are about 10 mites they are mostly sufficient to overwhelm the wasp and abort the parasitization. Acarinaria are present, in addition to eumenid wasps, in different bees of the families Apidae (carpenter bees), Halictidae (sweat bees) and Stenotritidae (Australian burrowing bees) suggesting that the mites might be a widely recruited watchdogs against Mellitobia and other parasitoids. A very curious twist of this symbiosis is seen in the mite Kennethiella trisetosa and the potter wasp Ancistrocerus antilope, which makes a mud nest in tubular cavities. Here, the mites develop with both female and male eggs, but once the females mature they kill the mites in their brood cell and emerge mite-free. However, males continue to carry them. At the time of mating they are transmitted from the male to the female acarinaria in the anal region. This makes one wonder if the mites impose some cost, which the females mitigate by killing them.

In general, the mite-hymenopteran symbiosis resemble the association of the reduced endosymbiotic bacterium Hamiltonella defensa with aphids which helps defend the latter against parasitoids. Few years ago we discovered some of the enzymatic toxins that might be used in this defense. Notably, many lizards also have mite pockets (sometimes also housing ticks) but their function remains rather unclear. However, another group of vertebrates, the rodents known as packrats, seem to house pseudoscorpions in their nest and even transport them on their fur when they disperse. These arachnids have been observed killing and eating fleas which are parasites on the packrats suggesting a comparable association to the mites of the wasps and bees. Over all the military use of mites by the wasps and bees against Melittobia is comparable to the human military dependence on the horse, elephant and to some extent the dog.

The incest- and fratricide-filled lives of these little wasps interface with many basic evolutionary questions of interest. In his initial study of this phenomenon among hymenopterans, the great biologist Hamilton, theorized that, when there is natally contained sib-mating, selection would cause biased sex ratio with greater number of females than males. This is because a female maximizes her fitness by producing only as many sons as minimally require to fertilize all her daughters. Expenditure in any further sons would be waste because they die in their natal nest with no further mating, whereas the daughters fly away to found new broods. So more the daughters, more the new offspring. This would also reduce male competition among the sons in the natal patch. Further, Hamilton noted that the hymenopterans are haplodiploid in sex-determination with the males developing from unfertilized eggs. This means that a female does not even need fertilized eggs for making males suggesting that the sex-ratio could be slightly more female-biased. Hamilton’s theory suggested that as the number of distinct females laying their eggs in the same site (number of foundresses) increases then the sex ratio would increase towards 0.5 because the males have more opportunities for matings with daughters of other foundresses and thereby increase the male-derived fitness of a given foundress. However, in practice this has not been observed in Melittobia, with the sex-ratio not responding to the number of foundresses in same site.

In the final part we will take a little detour to talk about a problem that goes back the Charles Darwin’s pioneering studies on inbreeding. In his work on this topic he stated (perhaps inspired by the deaths in his own family probably arising from his marriage with a first cousin):
“It often occurred to me that it would be advisable to try whether seedlings from cross-fertilized flowers were in any way superior to those from self-fertilized flowers.”

Accordingly, for 11 years he meticulously studied the effects of inbreeding on various plants. In course of his study he did a series of careful experiments with the plant Ipomea purpurea where he found that inbreeding resulted in a reduced height, and reduced number of fruits and seeds in the plants. However, after 6 generations of inbreeding he got a plant he named “Hero” which was unexpectedly vigorous and its descendants continued to be so. This marked the beginning of the study of a phenomenon that has occupied geneticists since. The initial loss of fitness is termed as inbreeding depression (ID) and is explained in terms of genetic load possessed by a population in the form of the deleterious recessive alleles masked by heterozygosity at those loci. These alleles get exposed by inbreeding because of selfing producing homozygosity at those loci with a consequent loss of fitness. Then when these alleles are eventually removed by purifying selection upon persistent inbreeding – termed purging – we are left with organisms like “Hero”. These show an increased vigor due to the removal of these deleterious alleles and now being a purified line with only the good alleles at those loci. Since Darwin there has been a vigorous experimental and theoretical debate on the role of purging on stabilization of long-term inbreeding in plants and animals with no universal consensus for diploid organisms. However, one intuitive prediction of this idea has been that haplodiploid organisms, like hymenopterans, would be more amenable to the development of long-term inbreeding because the deleterious recessive alleles are obligately exposed in haploid males for purging. Thus, the haplodiploid organisms are seen as been already pre-purged; hence, are thought to pass through the initial phase of persistent inbreeding without a major fall in fitness due to ID which could under some circumstances lead to extinction. This seems to be borne out by the emergence of long-term stable inbreeding in parasitoid wasps like the above chalcidoid eulophid wasps, the fig wasps, and certain mites with haplodiploidy.

However, in practice, even in hymenopterans the issue of purging remains complicated. Notably, studies have suggested that persistent inbreeding in Cardiocondyla, where queens mate with fighting males for several generations, results in ID manifesting as shortened queen life span, and higher brood mortality. Further, even in Melittobia it has been observed that multiple unrelated foundresses parasitize the same host individual. This suggests that there is potential for outbreeding, and even here, as in the fig wasps, Cardiocondyla or Copidosoma, inbreeding might not be complete. This suggests that the same danger of ID which has been reported in Cardiocondyla and some parasitoids might exist for wasps like Melittobia. This calls to question the theoretical prediction that haplodiploidy facilitates persistent inbreeding as apparently seen in the parasitoids via pre-purging in the haploid male. Given these observations we wonder if after all there is a degree of ID that does not escape purging even in the chalcidoid eulophid parasitoids. Further, we have reported effectors encoded by endosymbiotic Wolbachia bacteria that can either directly mutate DNA (deaminases) or induce breaks in DNA (restriction endonuclease fold DNases) which on being repaired results in mutations (a principle exploited in the now popular application of the Cas9 CRISPR systems). Given that Wolbachia are present in these parasitoids they could increase the genetic load by causing mutations via these effectors. We wonder if the male lethal combat, the mating dance, and even female killing, might be mechanisms by which this genetic load is reduced as these actions help purge accrued mutations.

Some literature:
-Evolution of social wasps; Hunt.
-Wasp Keeps Watchdogs to Protect Young; Kronauer
-Parasitic mites as part-time bodyguards of a host wasp; Okabe and Makino
-Biology of the Parasitoid Melittobia (Hymenoptera: Eulophidae); Matthews, Gonzalez, Matthews, Deyrup
-Feeding and siblicidal cannibalism in a male parasitic wasp (Hymenoptera: Eulophidae); Deyrup, Matthews, Deyrup
-Plant secretions prevent wasp parasitism in nests of wool-carder bees, with implications for the diversification of nesting materials in Megachilidae; Eltz, Küttner,Lunau and Tollrian
-Ecological and evolutionary significance of phoresy in the Astigmata; Houck and OConnor
-Sex determination and inbreeding depression in an ant with regular sib-mating; Schrempf and Heinze
-Symbiotic relationships between pseudoscorpions and packrats (Rodentia); Francke and Villegas-Guzmán
-A review of the biology of species in the genus Melittobia (Hymenoptera: Eulophidae) with interpretations and additions using observations on Melittobia australica; Dahms EC
-Extremely female-biased sex ratio and lethal male-male combat in a parasitoid wasp, Melittobia australica (Eulophidae) Abe, Kamimura, Kondo, Shimada
-Alternative mating tactics and fatal fighting in male fig wasps; Cook
-Wingless and fighting males in fig wasps and other insects; Hamilton
-Females reward courtship by competing males in a cannibalistic spider; Stoltz, Elias and Andrade
-Asymmetry in male lethal fight between parapatric forms of a social spider mite; Sato, Sabelis and Mochizuki
-Risks and benefits of lethal male fighting in the colonial, polygynous thrips Hoplothrips karnyi (Insecta: Thysanoptera); Crespi
-Phenotypically plastic traits regulate caste formation and soldier function in polyembryonic wasps; Smith, Milton, and Strand
-Do plant populations purge their genetic load? Effects of population size and mating history on inbreeding depression; Byers and Waller
-Inbreeding depression and haplodiploidy: experimental measures in a parasitoid and comparisons across diploid and haplodiploid insect taxa; Henter

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The Satija-Ketoja system

Satija and Ketoja discovered an interesting dynamical system in course of the study of the Schrödinger equation for one electron in a two dimensional periodic lattice on a uniform magnetic field. While this equation and its variants have several uses in physics, that is not our concern here. Rather, we shall purely focus on the neglected mathematical aspects of the Satija-Ketoja system in a form completely removed from its connections to quantum mechanics. To our knowledge, some of this has never been explicitly discussed. The Satija-Ketoja map is two dimensional map with a strikingly simple definition:

x_{n+1}=\dfrac{1}{x_n-E+2\sigma\cos(2\pi\theta_n)}

\theta_{n+1}=(\theta_n+\omega) \mod 1

Unless stated otherwise for all the experiments described here we recursively perform the above mapping for 100,000 iterations. Here, the parameter E stems from the eigenvalue of the underlying Schrödinger equation. It may be taken as 0 or for the purposes of the experiments shown here as 0.1 – it is not of much consequence for our purpose. For the first experiment (Figure 1) we set the parameter \omega=e, i.e. 2.718281828. \theta_n the angle variable of the map changes by increments of size \omega. However, since we are taking modulo 1 of the value, our \theta_n axis is bounded between 0 and 1 and effectively projects the map on the surface of a cylinder of unit circumference. The parameter \sigma is then made to vary between .1 to 2. We find that as \sigma changes the map generates an attractor, whose “core” evolves from a simple closed curve (on the said cylinder; .1, .25); to a curve with one break (.5), to one with break and a separate branch (.75), to a strange attractor at \sigma=1. For \sigma>1 attractor becomes a many branched curve with trails of points (1.25, 1.5, 1.75, 2).

Satija_01Figure 1

In our next experiment (Figure 2) with the S-K system we keep \sigma=1 and set \omega to the following values: \phi (Golden Ratio), \sqrt{2}, \sqrt{3}, \sqrt[3]{2}, e, \pi, \sqrt{10}, \tfrac{22}{7}, \tfrac{355}{113}. The first 7 are irrational while the last two are rational and the well-known 1st and 3rd convergents of the continuous fraction expressions for \pi.

Satija_02Figure 2

Another way of visualizing this attractor is in a \theta_n-independent manner by plotting x_n and x_{n+1} (Figure 3) for the same values of \sigma as above. This reveals the strange attractor structure in a rectangular hyperbolic framework. This latter framework comes from form of the definition of x_{n+1} which involves a reciprocal relation with x_n

Satija_04Figure 3

We notice that for all irrational values both these representations define complicated attractors. In the case of the x_n-\theta_n plots they are either of the form of a many branched curve with point trails or a strange attractor similar to that seen with e in our first experiment. However, the two rational \omega values produce “sparse” attractors of the form of a small number of attracting points. The closer the rational number is to the irrational number it approximates the denser is its attractor and the degree to which it recapitulates the structure of the irrational attractor (compare \tfrac{22}{7} to \tfrac{355}{113} and both to \pi). However, two relatively close irrationals (e.g. \pi and \sqrt{10}) have no particular similarity in their attractors.

While the modulo operator confines \theta_{n+1} to a cylinder of unit circumference, the hyperbolic framework for x_{n+1} in principle makes it unbounded allowing to take a value between -\infty :\infty. In the above plots we used all x_n within the range -4:4. But what is the entire range covered by x_n? To see that simply we plot all x_n values obtained for each \omega in the above experiment (Figure 4).

Satija_03Figure 4

This plot reveals a striking feature: For irrational \omega values x_n can explore a very wide range with rare values that are huge in magnitude. However, for rational values x_n remains bounded in a relatively small range. For example, using \omega=e, in our next experiment 92.7\% fall within the range -4:4. It has a mean of 0.00551 and a median of 0.0326 but a large standard deviation of 102.38 and can explore values ranging from -14899.84 to 13963.58. Figure 5 shows part of this peculiar distribution.

satija_06Figure 5: the blue curve is the below Cauchy distribution

This distribution is approximately symmetrical about 0 but has a paucity of values in the range from -0.5 : .5. Instead, it shows two peaks on either side of that zone of suppression. If we discount that central zone of suppression it shows an informal fit to a Poisson-Cauchy distribution (today simply called Cauchy) with a location of 0 and a scale-factor \gamma \approx .6. Thus, such a Cauchy distribution would be:

f(x)=\dfrac{\gamma}{\pi}\left(\dfrac{1}{\gamma^2+x^2}\right)

Indeed, certain properties of our distribution are captured quite well by this Cauchy distribution. For example, for the above run of the S-K system we compare probabilities for different values being reached with Cauchy distribution:
S-K system                             Cauchy distribution
p(|x_n|>100)=0.00253     p(|x|>100)=0.00381
p(|x_n|>500)=0.00058     p(|x|>500)=0.000763
p(|x_n|>1000)=0.00031   p(|x|>1000)=0.000381

This suggests that the S-K system x_n values appear to have a “pathological” or “fat-tailed” distribution that violates the central limit theorem.

This resemblance of the Cauchy distribution has a connection to a hidden fractal structure in the S-K system. For this experiment we continue with the above run of the S-K system with w=e. In order unveil the fractal we have to perform the following Fourier transform. We treat the successive x_n values as a time series. Thus, x_1, x_2, x_3...x_T are values happening at time t=1,2,3...T. We then define a frequency k=\tfrac{1}{12}. Then for Tth x_T we can define the Fourier transform as:

s(k,T)=\displaystyle \sum_{n=1}^T x_n e^{2\pi.k.n.i}, where i=\sqrt{-1}

Thus, for each x_n we get a complex number x+iy which can then be plotted to visualize the “walk” of the S-K system. In figure 6 we successively do it for 169, 625, 2500 and 4900 successive x_n values.

satija_05Figure 6

We observe that each of these numbers of steps captures a different scale. However, the walk has a qualitatively similar form across all scales establishing its fractality. We observe that in each case the walk has a large number of minuscule steps and a small number of huge saltations that are orders of magnitude larger than the minuscule steps and dominate the image. This pattern is indeed similar to what Benoit Mandelbrot defined as Cauchy flights, i.e. random walks where the steps follow a Cauchy distribution. This pattern is very different from what one would get from a Gaussian distribution of the steps. In the S-K system walks, if one discounts the suppression close to 0, the central events are more common and the infrequent events are extreme like in the classic Cauchy distribution.

Such distributions are what N.N. Taleb emphasizes in the context of the behaviors of financial markets. We have been attracted to them as potential analogical models (and perhaps eventually a real models) for various biological phenomena: 1) The movement of nucleic acid-binding proteins on DNA or long RNAs when measured with respect to their position along the nucleic acid polymer could display such saltations when they are transferred to distant sites by polymer looping. 2) We also believe that such saltations might capture evolutionary explorations of a certain morphospace. The morphological diversification usually is around certain fixed “types” or central tendencies but there are rare events, which are more extreme that allow entry into a highly disparate part of the morphospace. This might give the pattern biological diversity we observe: many related species with small differences but a rather large gap between one such cluster and another such cluster of related species. At the higher level this is the reason why taxonomic units like phyla of animals or families of plants look meaningful. 3) Finally, it might capture extreme consequences of certain rare events such as the origin of certain highly destructive species like Homo. This last pattern is also an analogy to understand the consequences of rare but extreme historical events.

For another such unusual distribution one look at our earlier article on the Hindu square root.

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Some simple maps specifying strange attractors

This note may be read a continuation of: Some reminiscences of our study of chaotic maps-2

While the story of the chaotic 2D attractors began with the simple-looking maps of Henon and Lozi, by the early 1990s the high-point was reached with multi-parameter maps of Sprott and some further additions of Pickover. In the process a bunch of simple maps were mostly ignored. Still we believe they are of some interest because they are excellent as simple devices to introduce a student to the concept of strange chaotic attractors. Hence, as part of recording our studies on such we present some of these. The first of these is a simple map which we discovered inspired by the basic Lozi map and has two parameters like it.

x_{n+1}=1-a|x_n|+b(y_n-x_n)\\ y_{n+1}=1-a|y_n|+b(x_n-y_n)

The evolution of this attractor for a=1.1 and b= .63 : .91 is shown below in Figure 1. Keeping with the symmetric form of the definition the map is symmetric along the x=y line.

double_abs_attractorFigure 1

From such a map we can develop a 2-parameter quadratic map where the square operator takes the place of the absolute value operator.

x_{n+1}=1-ax_n^2+b(y_n-x_n)\\ y_{n+1}=1-ay_n^2+b(x_n-y_n)

An example of the attractor specified by this map (in black) for a=0.78; b=0.406 is shown along with the basin of attraction in Figure 2. The colors represent the number of iterations needed to escape to infinity while the basin where the iterates remained trapped in the attractor is is white. We see that the attractor sits rather snugly within the basin of attraction which itself has a rather simple form.

double_quadratic_basinFigure 2

We next study its evolution as a=.78 remains unchanged while b varies from 0.25:0.406 (Figure 3). In this parameter range the we find the attractor evolving from a two-lobed bounded curve, to a 10 point convergence, to a multi-point convergence presaging the attractors, to finally a series of strange attractors.

double_quadraticFigure 3

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A rambling talk on the śaiva mantra tradition

A rambling talk we had given on the śaiva tradition. Talking is easier but less precise than writing. So please be aware of the insufficiency that goes with the domain of any talk while perusing this material.

Part 1; Introduction to mantra-s and pāśupata-s as a MP3 file: https://app.box.com/s/3wx313rfm8wijnpiv42f1q8r8z9zg2vu

Part 1, 1st addendum; early legends and iconography of Rudra: https://app.box.com/s/iqt7g7vye7c9z9tvb314swljh3um9eem

Part 1, 2nd addendum; Deployment of Rudra mantra-s in vaidika rituals; give a brief account of rājagavī-homa the animal sacrifice to rudra in the somayāga, the somārudrā ritual, the abhicāra ritual invoking rudra against enemy’s cattle, apotropaic rituals for protection again rudra’s attack (rudraḥ paśūn/prajāḥ śamāyeta), atharvavedīya mṛgāreṣṭi, and paippalāda tuṃburu-yāga: https://app.box.com/s/zg2v7zr3b36ckps4xo1i6fzavmzow8qb

Part 2; The emergence of a new mantra-śāstra: the beginnings of the tāntrika lore. Touches upon 3 key features that contributed to the emergence of the tāntrika mantra-śātra – 1) the sectarian traditions; 2) the origins of iconic and maṇḍala worship; 3) The emergence of a new mantra languages, i.e. mantra-s without semantic value, prose mantra-s with onomatopoeic elements, and mantra-s emphasizing repetitive action:
https://app.box.com/s/5l2tcpmrr07ohzh2worg2es4ml3xhmpu

Part 3; The śaiva tāntrika tradition; the 3 categories of śaiva tāntrika sādhakas: 1) the siddha-s and vidyādhara-s; 2) the sādhaka-s and ācārya-s; 3) the nīrbījadīkṣita-s and lay followers; the classification of knowledge in the śaiva tradition; the division of the śaiva śāstra into the five srotāṃsi: garuḍa, bhūta, vāma, bhairava and siddhānta; the gāruḍa tradition: Garuḍa, Śarabha and Nīlakaṇṭha; the bhūta tradition: Khaḍgarāvaṇa and his parivāra, Caṇḍāsidhara, Hayagrīva, Ardhanārīśvara and his dhyāna, Krodheśvara and Jvareśvara; the vāma tradition: Tumburu and the catur-bhaginī; the dhyāna of Tumburu in the Candradurdaṇda-maṇḍala; the transmission of vāma tantra-s and their history; special dhyāna-s of the four sisters; vāma mantra-s and yoga:
https://app.box.com/s/vd6xak6jqyuxoacv9nbesigm690de876

A very basic introduction to aspects of śaiva iconography with an emphasis on the icons depicted in saiddhāntika sthāpana tradition.
https://app.box.com/s/byb5yqght94gtqq9fnk867xbg6ca881q

continued…

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Citrabhānu’s cubes

The Hindus unlike their yavana cousins preferred algebra to geometry. Yet on occasions they could indulge in geometric games for demostrating proofs of algebraic relations. We see a bit of this in the Āryabhaṭa school and the great Bhāskara-II, but one of the masters of the self-evident geometric demonstration was Citrabhānu the nambūtiri brāhmaṇa poet, mathematician and astronomer from the cera country (1500s). His student (also that of one of India’s greatest pre-modern scientists Nīlakaṇṭha somayājin) was the ritual assistant Śaṃkara Vāriyār. In his Kriyakramakārī he records some of these self-evident proofs of his teacher. Now one such question Citrabhānu poses is to show without any algebra that:

\dfrac{a^3-b^3-(a-b)^3}{3(a-b)}=ab

Of course, this is simple 7th class algebra in our old school system. My father probably taught it to my while I was in 4th class. Yet it is some fun to show without using any algebra at all.

chitrabhanu

Citrabhānu has several such ‘wordless’ proofs that delve into figurate numbers. Of course this was not a late medieval innovation suddenly dawning on Citrabhānu. It has a long Hindu tradition going back to the Āryabhaṭa school and from there to figurate numbers of the Vedic ritual altar. Thus, it is another example of the continuity of Hindu science with the Vedic tradition of which Citrabhānu, like his coethnics, was a major practitioner. Finally, we may note that Citrabhānu seems to have had a particularly fertile abstract conception of higher dimensional space in the context of figurate numbers and what we show above is only the simplest of algebra.

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