An Autumnal Reverie
Some things that have been on my mind over the past few months.
Writing to me is a lot like enzyme kinetics: my thoughts are the catalyst and my writing speed is of course the rate. As my thoughts become more concrete, I write faster until my maximum throughput is reached. There’s an initial activation energy barrier to surpass, which maps to me starting my writing. Consistently this has been the hardest part of any writing I’ve done, whether it be a mundane email response, an assignment for a class, or something fun like writing a blog post. As pseudo-intellectual as it may seem to compare writing to chemical reactions (although I suppose this is true at the basal level of brain operation), I find that I need some sort of minor thought to latch onto before I can actually start writing what I want to write.1
The last few months have been like a whirlwind, where I was getting dragged along for a ride. A lot of fundamental questions have come up and I’ve spent a while thinking about them. I’ve made some good progress on my usual set of “subjects,” but the character of progression feels markedly different than it usually is.
There’s a lot of stuff I wanted to cover, so I’ve split things into different sections (with the dividers) to demarcate that. But keeping true with the name of this blog, it’s like one giant ramble anyways :)
I started my last post talking about math, and quite a few things have happened since my summer research ended. First of all, our manuscript is now available on ArXiv! You can find it here, and I hope all of you will take a look. It was fun to watch our rather jumbled manuscript get refined and polished into a presentable paper. Speaking of presentations, I was able to present my work on many different occasions, and I think talking about math with others is such a rewarding experience2 because it strengthens my own knowledge of the subject. I had a very different view on this previously, but I realized that I do enjoy explaining new concepts to others when they’re genuinely invested in learning. It was also fun to use what scattering pieces of biochemistry I still remember to try and ask insightful questions about my friend’s projects, since it’s really nice to see and learn about what other people work on too!
To build off of areas that I touched on in my work over the summer, I’m taking the graduate sequences in Algebraic Topology and Lie Groups (of which their representations have to do with generalizations of Khovanov homology theories). I’m not sure what I expected from these classes before going in, but I was pleasantly surprised to be thrown right into a heavily category-theoretic presentation of topology3 and a strongly geometric presentation of Lie groups. Particularly with regards to geometry, since differentiable manifolds was a subject that I’d been wanting to teach myself for a while. I tried to learn some in May, but I was quickly lost in notation (some like to say smooth manifolds are “the study of invariance under change of notation…”) and the sheer number of definitions. But because Lie groups are an example of well-behaved manifolds, they provided the perfect environment for me to get lost in geometry and find some path forward. The homework assignments were incredibly enjoyable once I started to figure out the manifold theory needed to answer these questions about Lie groups (for example, you can show a space is a sub-Lie group by differentiating the equation that defines its membership, like the special linear group). I still don’t have any interest in the physical applications of the subject, but I’m sure I’d understand them a bit more now. Applying geometry (as a general framework) to other subjects is also very rewarding, as I’ve already seen with quantum computing, but I’ve also been lightly looking at manifold learning and topological data analysis, and they’re quite appealing as well. Topology seems like a good balance of pure mathematics and rich potential applications to computer science, which is why I’m thinking that it’s an area I’d like to focus on for the next few years in earnest. Fitting that the first math class I took in freshman year has managed to captivate my interest this long!
I’m also taking quantum computing, which has been interesting from the perspective of the philosophy behind the mathematical and modal formulation of its computation: the idea that you can’t observe directly the concerned particles (here, qubits) leads to this probabilistic superposition, and through the clever use of quantum gates (consisting of unitary matrices, which happen to form a Lie group!) you start to see brilliant quantum speed-ups like the ever-so-famous Shor’s algorithm for factoring. I’m interested in exploring more areas of quantum computing that can be translated into pure mathematical work (for effectively, my summer research could have been titled “invariance of homological weight in Khovanov homology theories” and it would make an equally fitting title) and more applications of topology to “hot” areas of computer science like machine learning4 to see some more concrete benefits as well. I also decided to take complexity theory just to round out my knowledge of algorithmic thinking, it’s also been pretty fun so far. There are also many industry applications of having a background like this, so I think in general it’s just beneficial for me to explore what I genuinely enjoy.
In a similar vein, I’ve found that (I’m not sure if I’ve remarked on this earlier or not) my enjoyment of music has deepened in a way that just a year ago, I would have never been able to imagine. From my involvement in Columbia Raaga (you should see our new website by the way, here!) as co-president to just spending so much time with the same close friends that I’ve made through Carnatic music, my perspectives and horizons have broadened in such a wonderful way. I can genuinely appreciate music from multiple perspectives: of course, the musical one, but also the lyrical one5 and also from the perspective of the lyrical content: sthalapurāṇa, references to metaphysical concepts, and just what we call the rich bhāva of the compositions themselves. From a more global perspective6 music has changed from something I just did for the sake of it to a classical art form that I genuinely appreciate for all it has given me and continues to give me each passing day.
Over the past few months, building on how Carnatic music lies at the intersection of many important interests of mine, I’ve started to compose my own kr̥ti-s. And of many musical I’ve done, this has been extremely enjoyable. One needs to consider aspects of alaṅkāraśāstra (literary criticism and aesthetic), such as yati and prāsa (particularly the dvitīyākṣaraprāsa, which is one of the compositional features distinguishing the kr̥ti form pioneered by the trinity from the earlier kīrtana form employed by bhakti saints such as bhadrācala rāmadāsu and annamācārya). And seeing as we’ve moved to reading mahākāvya works in Sanskrit this year, it was a perfect opportunity for me to learn about these ideas. Syllable placement in relation to tāḷa is a great way to practice with and figure out intricacies of the tāḷa and rhythm in general (the confluence of percussive musical feeling with the apt choice of words to imitate and enhance said feeling with the meaning of the sāhitya to craft emotive passages) and the bhāva of sāhitya expressed as a journey through a rāga provides a wonderful complete experience of what makes Carnatic music what it is. Of course, it’s also fun to find ways to weave your own mudra (seal) into the sāhitya as well! Like the great pūrvācārya-s of the past, it’s also nice to drop little personal hints and rāga mudra-s into the compositions as well. For example, the madhyamakāla from one kr̥ti of mine on subrahmaṇya in the rāga ṣaṇmukhapriya,
ṣaṇmukhapriyanakṣatrajātaveṅkaṭapraṇavapālakāya
which we can roughly take as “[to the] protector of the one born under the stars beloved by the one of six faces, Venkata Pranav.” Other than involving the rāga mudra of ṣaṇmukhapriya, it also includes a small bit of personal information, that I was born under the kr̥ttika (Pleiades) star7. It’s fun to come up with various ways to encode all of these small ideas while also exploring musically. Expressing a love for music through the act of composition and the composition itself is also satisfying, such as the caraṇa (and pallavi!) of this kr̥ti in the rāga bilahari:
vedaśāstru lĕṟuga vārulaku dĕliyu / ī veṅkaṭapraṇavukūda talacuvāḍu...
nādopasanamu jesevārula sukhamu kanna / melaina galadā o manasā
which we can take roughly as “those who know the essence of the Veda-s and Śāstra-s know [it], and this Venkata Pranav knows it too… [that] does there exist a greater happiness than that of those who perform nādopāsana8, O mind!” This feeling was inspired by the numerous kr̥ti-s of tyāgaraju expounding similar ideas (such as nādaloluḍai brahmānandamŏndave in kaḷyāṇavasanta, saṅgīta jñānamu in dhanyāsi, saṅgītaśāstra jñānamu in mukhāri, nādopāsanace in begaḍa, sītāvara saṅgīta jñānamu in devagāndhāri, there’s enough variety to perform an entire kacceri with of these!).
At some point I’ll try and record all of these compositions properly, since of course the most significant dimension (the music) is impossible to convey over text. There is also the added benefit of being able to express genuine messages in your mother tongue, and for me to practice my Sanskrit as well. There’s just so much to unpack and enjoy here!
I’ve made inroads in other areas of Sanskrit use too. I got a copy of MacDonell’s Vedic grammar for students to start learning the Vedic Sanskrit grammar forms, and I also got a Telugu commentary (pratipadārthamu ṭīkamuto) with a Sanskrit commetary of kāḷidāsa's kumārasaṁbhavaṁ by vāviḷḷa press, who were (and still are) noted for their incredible scholarship and great publications. It helps that the commentary is written in grānthika (literary) Telugu since it’s a way to practice that too. I also got a copy of the pāraskaragr̥hyasūtra, my ancestral sūtra text that is shared by both recensions of the śuklayajurveda (the kāṇva-s and mādhyāndina-s) along with 5(!) medieval-era commentaries included with many pariśiṣṭasūtra-s (accessory texts) appended in the back. With the amount of commentary on what’s already an important text (among other things, all household rites and life ceremonies, as well as the details of performing the aupāsanahoma, darśapūrṇamāsa sthālīpāka yajña-s, and gr̥hya versions of rites such as the adiśrāvaṇa, that have their parallels in the śrauta tradition9) I’m hoping that it’ll be a good introduction on handling sūtra literature in general since it’s a very tough area of Sanskrit literature (and pretty impossible to read without a commentator) with a lot of unique vocabulary. While reading the table of contents the other day, I found a very interesting “sandhyābrahmayajñasūtra” listed at the very back, and read it (thankfully, it wasn’t too difficult to understand) and was pleasantly surprised to see that the sandhyā rites, including the non-mantrasaṁhita portions as practiced today in the kāṇva school are still the same! This text is one of the three kāṇḍa-s of the aptly named kātyāyana trikāṇḍika sūtra, which I couldn’t find much information about other than the body of the text itself with commentary (by a medieval śrauta ritualist Harihara10) and that, given the title, it’s traditionally attributed to kātyāyana, the author of the śrautasūtra associated with this Vedic school. It was very interesting to see the level of detail given to how (from the point of view of this text) a person should shower and eat (the nityasnānasūtra and bhojanavidhi). Since I’ve found that I have copies of a lot of these pariśiṣṭasūtra-s, I’ll revisit the valuable book I have on the śuklayajurvedapariśiṣta-s (from the 1950-1980s intense scholarship of śrauta and smārta ritual using traditional input from living practitioners of these rites by those in the Pune Sanskrit viśvavidyālaya) to see if there’s any more information about these texts and their commentaries.
The text also gave a hint at the sūrya-affinity of the śuklayajurvedin-s with its injunction of chanting post sandhyā (in this order) the vibhrāḷiti anuvāka (also known as the śuklayajurvedīya saura sūkta, vibhrāḍbr̥hat pibatu somyaṁ madhu...), the puruṣa sūkta (sahasra śīrṣaḥ puruṣaḥ...), śivasaṅkalpa sūkta (yajjāgrato dūram udaiti devam...), and the maṇḍalabrāhmaṇaṁ. The latter is a saura passage from the śatapatha brāhmaṇa (the śukla yajurveda's voluminous brāhmaṇa text in 18 “books”), beginning with “yadetanmaṇḍalaṁ tapati tanmahadukthaṁ…” and being a pretty decently sized brāhmaṇa (prose) passage. In particular, the identification of the Cosmic Man (the subject of the puruṣa sūkta, which is usually read for viṣṇu) with sūrya hints at the strong saura affinity of this Vedic school, which when considering the mythology of its origin (the progenitor ācārya yājñavalkya is said to have learned the śuklayajurveda from the sun god himself) adds an interesting extra dimension to that picture. Fittingly, the copy of the sūtra I have ends with the dvādaśanāma-s of Yājñāvalkya that are traditionally chanted before any rite using the śukla yajurveda (proceeded by the more common “gaṇanāṁ tvā gaṇapatiṁ havāmahe...").
I was also finally taught a few months ago the nitya samidādhāna rite (by my relatives, who maintain the ancestral job of being smārta śuklayajurveda priests), or what is also called agnikāryamu in Telugu. The original daily rite, this is a twice-daily homa that can be performed by an unmarried individual, in which the offerings consist of Peepal sticks (or one of six other kinds of trees, or darbha grass, they’re all termed samidha11 in the taittirīyasaṁhita) before the ash from their burning is placed in a black dot on the forehead, on top of the previously applied three stripes of ash (in the smārta tradition). The mantra-s (all of which are from the kāṇvasaṁhita) are quite cool in their imagery, so I’d like to share a few (with my personal translations):
yathā tvam agne devānāṁ yajñasya nidhipā asi
evam ahaṁ manyṣyāṇāṁ vedasya nidhipo bhūyāsam
We can take this as “Like you, Agni, are the protector of the treasure of the Yajña of the Deva-s, let me thus be the guardian of the Veda (of humankind)!” Like Agni is called the dūta or the havyavāhana, taking the offerings to the Deva-s, the student who learns the Veda passes it on and ensures it’s continued recitation and respect. The symbolism is quite nice.
agnaye samidham ahārṣaṁ br̥haspate jātavedase
yathā tvam agne samidhā samidhyāse
evam aham āyuṣā medhayā varcasā [...] brahmavarcasena samindhe
One may also see “… br̥hate jātavedase”, but the identification of Agni with Br̥haspati here (instead of the term br̥hant, which means lofty or great) adds an extra dimension to the meaning. This substitution seems to be a local pāṭhabheda (recensional difference). Anyways, we can translate this as follows: “O Brhaspati! For you, Agni, the one who knows all births, I have brought this samidha. Like you, Agni, are fueled by the samidha, thus I am fueled by health, intelligence, luster, and being eminent in the Veda.” Notice the vocative case br̥haspate (identifying Agni with Br̥haspati, the guru of the Deva-s) and the ātmanepada aorist form (mostly extinct in classical Sanskrit, but very common in Vedic!) ahārṣam (from hr̥, to carry, bring, or offer). The rest of the mantra goes on to ask for these very things, ending with the svāhā call (when you place the Peepal stick in the fire). Once again the duality between Agni and the offerer is emphasized, as like the offerer gives the samidha to Agni, Agni carries all of the offerings (in a regular rite) to the other Deva-s.
There are more, such as “āyurdā agne'syayur me dehi” (you, Agni, are the giver of health, give me health!) and a rather interesting rite of warming the hands with the heat of the fire before chanting the tryāyuṣa mantra upon which the ash from the offerings is placed on the forehead.
The symbolism of this rite is quite interesting, and it’s also fun to do (Peepal sticks are also very nicely fragrant when burned with ghee!).
I’ve found myself thinking a lot about how my notion of idealism and approach to life in general has changed over the past few months. I’ve thought of myself as a decently flexible person in terms of being open minded, but I watched as over the past few months I’ve internally changed a lot of my stronger opinions on things. In particular, with regards to realizing that we are always given a romanized view of the past, and that the human condition (to parrot my LitHum professor…) has not changed in the past five thousand years of productive civilization. That is to say, we’re given rules as guidelines, and that carrying forward “tradition” is left up to those who actually live in the current day rather than our fossilized and romanticized memory of a hypothetical past. In some sense, I’ve realized that humans are not infallible: people are people. While of course this is a slippery slope in terms of abandoning all common sense, and maybe this shift hasn’t really been noticeable externally, it’s more about my internal ruminations and approach to things that has just, changed. In a way that I see as a good way.
Speaking of new things, I’d officially call myself a tea addict now. I’ve tried so many new teas and varieties of tea (learning some amount of Chinese in the process) that it’s definitely become an almost daily part of my life now. I’ve found my taste has settled on Pu’erh and Taiwanese Oolong teas, and collecting cups! Check out this stained Rǔyaò glaze cup (of which I have 3, for drinking with 2 friends) that has cracks that will stain as you drink more and more tea in them:
It’s a fun way to enjoy something with a lot of depth and explore while stringing your friends along for a ride (also, the thrill of finding new places and sources to get tea from and seeing if they’re nice, randomly getting offered a tea session by people, and many more such situations!).
I’ve also started to pick back up archery, which I used to do a long time ago. I got an asiatic style bow12 that is an absolute joy to shoot and I’m trying to improve my aim (it’s a lot less consistent with the thumb draw, but this is probably because I’m used to shooting western style with 3 fingers). As a bonus, it looks pretty cool hung up on my wall. I also got a Kindle again after six years, and just like it was all those years ago, such a good purchase. I read a lot more now that I can just pull my Kindle out wherever and whenever I want to instead of having to bring physical books everywhere. I still think there’s some charm to having a physical book to read, but at the end of the day, it’s whatever gets me to read more that actually matters. I had fun finally getting to read the Avatar novels (Kyoshi and Yangchen: the former are a great coming of age and realizing your direction story and the latter are a really fun adventure in political espionage), and finally starting to whittle away at my “to-read” list of all sorts of fantasy novels, sci-fi novels, and interesting monographs.
I had the pleasure of attending a Shakuhachi workshop by Araki Kodo VI, the current head of the Araki style of Kinko-ryu shakuhachi playing. We were taught the honkyoku piece Yoshiya Reibo, and it was my first real exposure to another school (instead of the Chikumeisha guild style of Kinko-ryu we’ve inherited from Yamaguchi Goro) and the ways that the common phrases that form the grammar of Kinko-ryu playing are handled by the various schools. All of these lineages ultimately descend from Araki Kodo II and Kurosawa Kinko, but the use of techniques such as suri (for my Carnatically trained readers, these are jāṟu gamaka-s kind of) and atari (sphurita gamaka-s that begin a phrase, ataru means to hit or attack in Japanese) are different in mechanically subtle ways but drastically change the small local characters of these building block phrases. The piece itself is one of the mid-level advanced honkyoku pieces (in short, much above my level) but I was glad to have been able to learn it from such a wonderful teacher and person.
I had a nice discussion with him about the similarities between the more “organic” and melodically oriented styles of music where you can actually draw analogies between these sorts of concepts in playing (for example, we talked about the situation between disciples and their subsequent lineages having various different pieces by the original teacher, and the “speciation” of techniques and such being common to both Shakuhachi playing and the śiṣyaparaṁpara-s of Carnatic music) and how for these melodically oriented music systems, you really just have to learn by osmosis and listening. It was very fun. He also touched upon how these pieces emphasize a Buddhist ideal of “yearning for the bell [of enlightenment]” and how similarly one should strive for the sound of their flute playing to be like a resonant, ringing bell. And this is a motif that I myself had realized and pondered over for a long time but wasn’t able to express properly (or maybe no one understood what I was talking about) but I was elated to hear that when he brought it up. Although fundamentally I don’t agree with the concept that the ringing of the bell symbolizes emptiness: instead, I always think of the famous verse “pūrṇamadaḥ pūrṇamidaṁ pūrṇāt pūrṇamudacyate / pūrṇasya pūrṇamādāya pūrṇamevavaśiṣyate”13 and imagine the resonant, full sound of the bell instead. Or at least, that’s what I think to myself every time I play Shakuhachi.
But after what has been a hectic and mixed past few months, I’m excited for the rest of the year.
Without falling into my usual “it’s been a long time since I last posted on here…,” which is also true this time but I wanted to try something different.
Regardless of their background level. Of course, there’s not much you can do when people have absolutely no mathematical background, but if (for this specific case) they know some linear algebra, there’s a lot of interesting things you can talk about in a non-rigorous manner. I also appreciated when some of my friends asked good questions despite not having all the background information needed: a passion for wanting to understand is always nice to see and share with others.
Although, I expected this one, because without algebraic topology we’d have no impetus to develop category theory in the first place (although in the usual mathematical consideration you could say that the concept of a category is natural and would have been developed anyways, since they “already existed” beforehand).
After all, I’d say it’s been long enough for me to have not bit the bullet and done some machine or deep learning work (I’m going to pretend like my high-school research doesn’t exist for this comment).
I hit the critical point with Telugu to be able to comfortably understand many compositions, and same with Sanskrit. This forms the bulk of the Carnatic musical repertoire. I’ve been getting “exposure therapy” to Tamil for the past 5 months or so, and it’s slowly working so soon I hope to understand those compositions as well!
Which I find very important to stop and think about every once in a while. Working locally is important for figuring out your next steps, but it’s easy to lose sight and fall risk to tunnel-vision. Pausing and looking at what you’ve accomplished from a global perspective makes it easy to not fall into such traps.
From where the epithet kārttikeya is derived (a kr̥t-pratyaya formulation from kr̥ttikāḥ), a name of subrahmaṇya.
Literally nāda-upāsana, or adoration through music.
In fact, one begins with the gr̥hya rites as a gr̥hastha (householder) and then upon the agnyādhāna rite, the upgrading of the gr̥hyāgni into the gārhapātya (literally from gr̥hapati, lord of the house) and the other 2 śrauta fires, the darśapūrṇasthālīpāka is upgraded into the darśapūrṇamāseṣṭi rite associated with the twice-daily agnihotra.
Although, it was even more difficult to find any information about the commentary authors themselves. We have their names, such as gangādhara, vāsudeva dīkṣita, agnihotri harihara, etc., all of which strongly suggest their participation in and knowledge of śrauta ritualism, but dates are incredibly difficult to find with my current knowledge of Sanskrit textual and temporal strata. From what I could find, the date ranges stretch from the latter half of the medieval period, so around 1600-1820. It’s interesting to think about how these texts were still being commentated upon and the continuity of this traditional scheme in general while European colonialism was happening contemporaneously. It messes with your sense of time perception quite a bit.
Kindling stick!
At some point, archery was passed down in a hereditary manner in my family, with some distant relatives still having Andhra Pradesh state government cultural archery recognition titles and such. I chose asiatic archery since it’s probably the best documented form of thumb archery, which would be similar to what was done historically in India too.
Which is also from the śatapatha brāhmaṇa, and is traditionally chanted before chanting of the ātmasūkta, or the īśāvāsya upaniṣad (one of the two upaniṣad-s of the śukla yajurveda school, the other being the mighty br̥hadāraṇyaka).