Pearls at Random Strung

Just a place to jot down my musings.

Friday, January 31, 2014

A meditation on mathematics as meditation

Following the previous posts on bhāvanā, bringing-into-being, and its role in meditation, literature, and human creative activity in general, I couldn’t help but relate some of those ideas to mathematics.

Many (pure) mathematicians are content to take the mathematical structures they explore as givens, which they can figure out or manipulate in interesting and sometimes profoundly beautiful ways. This is a naïve version of Platonic realism, which grants to mathematical structures an objective existential status that lies beyond human beings. (This also means that sentient alien species should have exactly the same mathematical ideas as we do, that the Vulcans would accept that Euclid’s axioms generate the same results as us, and so on.)

Philosophers of mathematics who are formalists of various stripes hold instead that mathematics comes down to playing games with symbols: pushing arrows and boxes and Greek and Hebrew characters around based on well-defined rules. (Cue Wittgenstein.) They reject the idea that mathematicians “discover” mathematical structures; rather, they formulate new rules and new symbols and manipulate them.

While it may certainly seem from the outside that this is all mathematicians do, and while Western models of logic separate formal syntax and formal semantics in a way that seems to encourage this line of thought, it does not gel with my personal experience of actually doing proofs. Seldom can a real proof be hit upon simply by pushing symbols around on a piece of paper. At least for me, thinking about a hard mathematical problem involved trying very hard to “see” what was going on behind the symbols: symbols barely came into it. Strangely enough, the harder the proof, the more I thought I was seeing something that was already there! And even in those cases when one does merely shuffle things around, there is a crucial psychological difference between staring at a bunch of symbols on a page and hitting the Eureka moment. The proof is complete, I would argue, only with the latter. (This is not a “proof” that formalism is wrong, but merely an observation that it doesn’t fit with the phenomenology of at least some mathematicians.)

So where does bhāvanā come into the picture here? I would like to suggest (without proof, hehe) that what makes a proof a proof is precisely the fact that when(ever) it is understood correctly, it reliably and unfailingly brings into being in our minds a mathematical truth, in a manner that is at least intersubjectively valid, if not objectively. A proof is the means by which a particular mathematical end (a fact, a theorem, a lemma, or whatever) is attained. 

I have been vaguely inclined towards this manner of thinking ever since I read one of the greatest math books written in recent times in my opinion, Tristan Needham’s Visual Complex Analysis. Needham takes perhaps the most aesthetically remarkable branch of modern mathematics and offers a fabulous tour of its key features and structures in a manner that emphasizes visual and geometric thinking over the algebraic. (That is, he encourages you to prove things not by pushing symbols on paper but by visualizing, rotating, and dilating mathematical structures.) Given my prior bias towards visualizing mathematical structures, this book has been particularly enjoyable to read. (Perhaps my favorite exercise in visualization is the one in which I had to “see” the complex logarithm multifunction twisting and lifting the complex plane into an infinite helix.)

This process of visualizing a mathematical object is both deeply personal and yet objectively available. Two people who visualize a mathematical object will both agree on its key characteristics and its relevant properties, and may yet visualize it in ways that differ quite dramatically (and yet inexpressibly) from each other. To me, this situation bears a thought-provoking resemblance to Hindu/Buddhist meditative exercises in which devotees are asked to bring-into-being a particular deity in their minds, and are usually given elaborate visual descriptions of the deity’s characteristics to aid them in the process. Two different devotees may thus both bring-into-being very different versions of the same deity in their own minds, while yet agreeing fully on all of the key features possessed by this deity. The former half allows them to “take ownership” of the deity, in a sense; the latter half lets them participate in a shared conversation with others about the deity. Of course, by comparing meditative exercises with mathematical proofs, I intend to make neither religious claims about mathematical entities nor mathematical claims about religious entities!

Sunday, January 5, 2014

On goals, systems, and bhāvanā

An article by James Clear called “Forget About Setting Goals. Focus on This Instead” [Oh Upworthy, how I truly hate thee!] has been doing the rounds recently. It has received a lot of attention, but when I finally sat to read it a couple of weeks ago, I found myself deeply bothered by something I couldn’t quite get a handle on. It is only just now that I’ve realized what the problem was, and the answer came to me from Mīmāṃsā.

What on earth does a nearly 3,000-year-old Hindu tradition of ritual hermeneutics have to do with any of this? As it turns out, a lot! Mīmāṃsā’s primary intellectual concern has been with the Vedic sacrifice: how it works, how its descriptions in various ritual texts cohere, how it is organized, and so on. To do so, it has developed a formidable arsenal of techniques and frameworks. One of these, the concept of bhāvanā, was widely used and taken up in disciplines far outside Vedic ritual exegesis, including literary theory and imagination / meditation. (See my prior post on imagination for some other uses of the concept of bhāvanā in South Asia.) The time has now come to apply bhāvanā to yet another problem: motivating people to stay on track with difficult projects!

What is bhāvanā?

To massively oversimplify things, and with apologies to Andrew Ollet’s excellent article, a bhāvanā, a bringing-into-being, is a particular action (or a set of actions) designed to create something, undertaken by an agent. Every such bhāvanā has three essential components to it:
  1. The desired end which the agent is trying to bring into being through this operation
  2. The instrument using which the agent is carrying out the operation
  3. The procedure which the agent is following with the instrument to bring about the desired end
These three are respectively called the kim (the “what”), the kena (the “by what”), and the katham (the “how”). These three things are very different from each other. Confusing them can be fatal to understanding how things are actually supposed to work.

The standard introductory Mīmāṃsā handbooks usually explain bhāvanā with an example from Vedic sacrifice. Here’s a rather different, much more quotidian scenario where the three components are nevertheless clearly distinguishable.
After a long, grueling day at work, you come home utterly famished. You don’t want to go out to get dinner, so you decide to make yourself a quick dinner. You have a microwaveable mac & cheese sitting in the freezer, so you take it out, read the instructions on the packet (you don’t really ever cook), stick it in the microwave, and a few minutes later, satiate your hunger with some piping hot coagulated carbs and fats.
In this scenario, it’s pretty clear that something new was created: the state of the world, and more importantly your own state, was transformed in this scenario. In not-so-technical Mīmāṃsā non-jargon, some sort of bhāvanā thingie occurred here. So what were the components of this bhāvanā? What was created?

It is tempting to think of the mac & cheese dinner as being what is created: after all, before you cooked it, it was just a frozen lump of carbs and dairy and preservatives, and it was your cooking it that transformed it into an (arguably) edible mush. However, this would be a major mistake, according to Mīmāṃsā: the mac & cheese was not the desired end of your actions. It wasn’t why you undertook all these steps. Instead:
  1. the real end, the kim, must be the resolution of your hunger. 
  2. the mac & cheese is the means, the kena, by which your hunger is resolved. 
  3. the way you resolve your hunger, the katham, is by following the procedure outlined on the packet to cook and serve the mac & cheese.

Goals and Systems

If my quick overview of bhāvanā didn’t foreshadow it clearly enough, it should be clear what my beef with Clear’s piece is: he conflates kims and kenas when talking about goals, and therefore overemphasizes the importance of systems (which are not quite kathams). To see how he does this, let’s look at the section where he distinguishes between goals and systems:
What’s the difference between goals and systems?
  • If you’re a coach, your goal is to win a championship. Your system is what your team does at practice each day.
  • If you’re a writer, your goal is to write a book. Your system is the writing schedule that you follow each week.
  • If you’re a runner, your goal is to run a marathon. Your system is your training schedule for the month.
  • If you’re an entrepreneur, your goal is to build a million dollar business. Your system is your sales and marketing process.
Look carefully at the four things he describes as goals: winning a championship, writing a book, running a marathon, and building a million-dollar business. And look carefully at the four types of people he describes as having these goals: the coach, the writer, the runner, and the entrepreneur. Now, many of us would agree with these things as being described as “goals” (which to me only reinforces the fact that we live in a deeply instrumentalist society). But are they really goals? Are they more like the mac & cheese or like satiating the hunger for a hungry person?
  • For a coach who is hungry for a win, winning a championship will certainly satiate his hunger. But it is not obvious to me that people become coaches in order to win championships. It can be argued that the real purpose of being a coach is to, well, coach a bunch of players to the best of their abilities, so that they can perform superlatively on the field. If the team can do that consistently, then they may very well end up winning a championship. It seems to me that winning the championship is really just a means (a kena) to the real end (kim): the joy that comes from watching people do their best on the field. (It is possible to win a championship and yet be dissatisfied, because perhaps your opponent defaulted; it is possible to lose a championship and yet be pleased, because you did your absolute best and fulfilled your “duties”, so to speak.)
  • Writers don’t write in order to create books; they write books in order to do something else: tell a story, persuade their readers to act, create emotional states in their readers, convey some valuable information, or even simply feed their families. The book is clearly just a kena. The kim is whatever motivates the writer to write.
  • As with the example of the coach, it may well be that running a marathon is a real kim for some people. However, it is again quite likely that there are other satisfactions here: enjoying the endorphin rush, raising money for a valuable cause, staying in shape, or whathaveyou. In all of those cases, the marathon is just a kena that is subordinated to the more significant kim.
  • Again, it certainly is the case that some entrepreneurs are just in it for the money. In that simplest of cases, the business is the kena to their real kim: making a boatload of money. But as Guy Kawasaki has said many a time: “make meaning, not money” is the heart of entrepreneurship. Whether your business is worth a billion dollars or a hundred, the real purpose should be to do something that creates meaning for you and for the people you engage with. In such a view, the mere instrumentality of the business is even more strongly pronounced.
None of the four examples of goals here is clearly and precisely a kim: an end that people strive for and desire. Some of these could possibly be treated as kims, but Mīmāṃsā argues (and Clear would agree with this, as he himself writes) that to do so would be to fundamentally misunderstand the nature of each of these sets of actions.

Clear has correctly identified one problem: the so-called “actionable goals” he describes are notoriously bad at actually getting achieved. The real reason for that is because they aren’t in fact goals: they are means to other ends. These other ends are the real goals we should keep in mind. In the absence of those real goals, people wouldn’t act at all!

The problem isn’t with goals at all; it is with the fact that Clear is using two terms (“goal” and “system”) to describe three distinct pieces (the [real] goal, the means to the goal, and the procedure; to use a different metaphor, the destination, the means of transport, and the particular path you navigate). Because of this conceptual blurring, he emphasizes “systems” more than they can bear: what he calls systems are just glorified procedures. 

The real system is the the whole triplet that Mīmāṃsā describes, and this systems needs all three pieces to succeed: a real goal to motivate us to act, a means by which this goal can be achieved, and a procedure that can be followed (with all the useful tips that Clear provides).  


One of the subheadings in Clear’s piece gives the game away to the reader who is keyed into Mīmāṃsā: He describes one of the faults of the goal-based approach as being the fact that “Goals reduce your current happiness.” This is exactly what sets kim apart from kena in Mīmāṃsā! Take the typical injunction that Mīmāṃsā analyzes: yajeta svarga-kāmaḥ, “The heaven-seeker should perform a sacrifice.” Lots of Hindus have desired to perform sacrifices, and still do to this day. But Mīmāṃsā argues that the real end here, the real kim, here has to be heaven. The sacrifice itself is only the means by which this end is brought about. And one of the arguments is this: a sacrifice is a difficult, expensive, resource-intensive, and physically taxing undertaking. No rational (pleasure-maximizing, pain-minimizing) human would perform a sacrifice for its own sake. Therefore, a sacrifice must be the means to some other end: the promised result. To follow Clear’s line of reasoning, you would focus on the individual actions of a sacrifice (its procedure) but ignore the coherence of the sacrifice itself as an instrument, and altogether forget about the real goal, the heaven that is the result of the sacrifice!

Saturday, December 21, 2013

The beloved who is near and hidden

It’s been far too long since I translated any Persian, so here’s a poem by the master of masters, Mawlana Rumi, in the simple but beautiful rajaz muthamman meter:

ay bā man-o penhān cho del, az del salām-at mīkonam.

ای با من و پنهان چو دل از دل سلامت می کنم
تو کعبه‌ای هر جا روم قصد مقامت می کنم

Hey you, who’re with me and are yet hidden, like my heart—
my heartfelt greetings to you!
You’re the Ka‘bah: wherever I go, I head straight for your place.

هر جا که هستی حاضری از دور در ما ناظری
شب خانه روشن می شود چون یاد نامت می کنم

Wherever you are, you’re present, as the supervisor within us from afar;
The bed-chamber is flooded with light when I remember your name.

گه همچو باز آشنا بر دست تو پر می زنم
گه چون کبوتر پرزنان آهنگ بامت می کنم

Sometimes I briefly alight, like a friendly falcon, upon your arm;
Sometimes I head for your roof, like a pigeon fluttering its wings.

گر غایبی هر دم چرا آسیب بر دل می‌زنی
ور حاضری پس من چرا در سینه دامت می کنم

If you’re absent at every moment, then why do you injure my heart?
And if you’re present, then why do I try to ensnare you in my bosom?

دوری به تن لیک از دلم اندر دل تو روزنیست
زان روزن دزدیده من چون مه پیامت می کنم

You’re far from me physically, but there’s a window from my heart onto yours;
From that stolen window, I send you a message, like the moon.

ای آفتاب از دور تو بر ما فرستی نور تو
ای جان هر مهجور تو جان را غلامت می کنم

O sun, from afar do you shine your light upon me;
O you, who are life to all abandoned by you, I serve you as a slave.

من آینه دل را ز تو این جا صقالی می دهم
من گوش خود را دفتر لطف کلامت می کنم

I give to the mirror of my heart your lustre;
I make my ears a record for your delicate words!

در گوش تو در هوش تو و اندر دل پرجوش تو
این‌ها چه باشد تو منی وین وصف عامت می کنم

In your ear, in your mind, in your exuberant heart
Whatever may be, you’re mine—
thus do I generally describe you.

Friday, December 20, 2013

On imagination, meditation, and bringing-into-being

In this fascinating interview, Tanya Luhrmann addresses the tremendous importance of imagination in religious traditions such as American evangelism. The idea that religion is “belief”, the affirmation of the truth-value of some proposition, is a particularly Western, Protestant, understanding of religion, and is profoundly different from the religious experiences of people from, say, the dharmic traditions. (Or for that matter, from the experiences of Orthodox Christians.) Luhrmann says about kataphatic prayer:
It makes what is imagined in the mind more real. In kataphatic prayer you are saying that certain of your mental images are significant, and you are making these images more sensorially rich, you are allowing yourself to imagine them more vividly. The demand of religion is to teach you that the world as you know it is not the world as it is—and to teach you the capacity to see the world as it is, as something good. So you’ve got to make what is imagined real, and you’ve got to make it good.
The obvious response of the outsider to something like this is to describe it as clearly false, or “merely” imagined. And in a certain sense, the outsider is right: it is the believer who has imagined a particular religious experience into being, for which there is most likely no objective correlate. But Luhrmann argues that this attitude misses the heart of the experience as the insider experiences it: as something real, indeed as something more than real—because they create a new reality for the insider. It makes the insider more likely to feel loved, and thus to become more loving. Luhrmann thinks that something like this may even help reverse the erosion of social ties that people complain about today.

A number of Luhrmann's ideas squarely fit in with late medieval South Indian Hindu thought as is described in More than Real: A History of the Imagination in South India by David D. Shulman.

Shulman focuses on the importance given in medieval South India to the force of imagination: to the fact that human being are at their core imaginative creatures, who shape reality by imagining it together. 
  • Sometimes this imagination is internal to the person: Shulman tells the story of an impoverished devotee of Śiva who constructs in his mind a temple so beautiful that Śiva prefers to dwell there instead of in the vast granite temple that a king has built for him (said to be the Kailāsanātha temple of Kanchipuram). 
  • At other times, this imagination is intersubjective: Shulman describes in great detail a performance from the Kūḍiyāṭṭam dance-drama tradition of Kerala, in which a solitary skilled dancer transforms an empty, prop-less stage into a story-universe through the combination of his gestures and through the shared imaginations of the entire audience. 
Worship is imagined in the same way—by imagining our iṣṭa-devatās in our minds and by that very act bringing them into being. The word used for bringing-into-being is bhāvanā, a word borrowed from Mīmāṃsā ritual hermeneutics that refers to the power of a sacrifice to bring into being its fruit.[*]

Shulman points out that the philosophical and theological systems in which these systems developed in South India were staunch defenders of ontological realism, but of course not of physicalist, materialist reductionism. (Paradoxically, it was Advaita Vedānta that was fairly skeptical of the positive power of imagination.) He writes, comparing 16th-century India and Europe:
In Europe, the ancient dichotomy of mind and matter hardened into a fully desubjectified theory, or evolving set of theories, about the status of objects within an external, natural world. In India, the dichotomy is itself questionable, and the metaphysics of inner and outer took another course. Broadly speaking, in one conceptual system the imagination became increasingly associated with pathology, while in the other it tended to be understood as therapeutic. (p. 278)
Suspension of disbelief is the wrong way to think about what's going on here (at least in the Indian context; it may well hold for Luhrmann's evangelicals). We don’t lie to ourselves about something being there when it isn’t; we construct it with our mental acts—and by doing so, we make it real.

And towards the end of the book, Shulman also touches very briefly upon Ibn ‘Arabī, in whose vast work khayāl, “imagination”, is profoundly related to the structure of the universe and to the relationship between man and God.

[*] This explains the use of words like bhāvayāmi in much devotional Carnatic music. The singer-devotee is trying to actualize the deity in the minds of all those present at the performance. 

Tuesday, May 21, 2013

And the winner of the mostest ugliestest word goes to …

… “winningest”!

Seriously, who on Earth (or in America, to be precise, since to my knowledge nobody outside the US actually uses this linguistic abomination) thought that this word makes any sense? Did its coiner pause to reflect, even for a moment, about whether the structure of the word hung together in any coherent way? Or whether the meaning the word was intended to have (a) needed a single word to express it, and (b) was in fact expressed in some sensible way by this word?

And now, the New York Times, of all places, uses it. Admittedly, it’s only its Magazine section, but why oh why would someone use this horrid, cumbersome word at all?

If there was an annual competition for “hideousest word of the year”, “winningest” would be the winningest word.

Wednesday, May 15, 2013

Grammar and God

One of the most famous verses in Sanskrit is the opening verse of Kālidāsa’s Raghuvaṃśa:

vāg-arthāv iva sampṛktau vāg-artha-pratipattaye |
jagataḥ pitarau vande pārvatīparameśvarau ||

Here, Śiva and Pārvatī are seen to be inextricably intertwined like a word and its meaning.

Another verse I came across today expresses a similar relation, but between different pairs of upamānas and upameyas:

rāsa-vilāsa-vilolaṃ smarata murārer mano-haraṃ rūpam |
prakṛtiṣu yat pratyayavat praty-ekaṃ gopikāsu sammilitam ||

May you remember that enchanting form of Mura’s Conqueror,
        dancing around playfully in the Rāsa-līlā,
        united individually with all of the milkmaids,
                like a suffix with flexional bases.

As may be imagined, this is the opening verse of a grammatical text: the Prakriyā-sarvasva of Mēlpattūr Nārāyaṇa Bhaṭṭatiri, who is most famous for his composition of the Nārāyaṇīyam addressed to Kṛṣṇa. As to why Kṛṣṇa should be seen as a suffix (which, in English at least, sounds like it’s subordinate somehow to the word to which it’s added), it’s because the Pāṇinian tradition of grammar sees the suffix’s meaning as dominating the word’s meaning. Moreover, a suffix can be added to far more words than a word can take suffixes, and so it has greater “freedom of union” in that sense. Finally, and conveniently, the word for suffix, pratyaya, takes masculine gender, while the word for flexional base, prakṛti, takes the feminine gender.

Monday, April 29, 2013

Looking back in space and time

The 17th-century Syrian poet Fatḥ Allāh Ibn al-Naḥḥās (فتح الله ابن النحاس) was regarded as one of the two best poets of his time. Although this particular period of Arabic literature has been ignored and disregarded as an age of decadence, prolixity, and baroque ornamentation (the so-called ‘aṣr al-inḥiṭāṭ, عصر الانحطاط), it is becoming increasingly clear that this is a case of people selectively rewriting history by privileging certain parts and certain elements over others. 

I’m not taking a definite stance here because I don’t know enough about both sides, but after having read Ibn al-Naḥḥās’s beautiful qaṣīdah “He saw blame pouring in from all sides, and it scared him” (ِرأی اللومَ من كلِّ الجهات فَراعَهُ), I think we do ourselves a great injustice by writing off a giant period of time as entirely lacking in poetic merit. This one line, where Ibn al-Naḥḥās talks about how he is forced to leave Aleppo after a scandal involving him and his (male) beloved, is just gorgeous:

فَرُحْتُ وَسَيْري خَطْوَةٌ وَالْتِفاتَةُ ❊ إلى فائتٍ مِنْهُ أُرَجِّي ارْتِجاعَهُ

So I left; and every for’ard step was a glance backward
Looking for a lost past, whose return was the thing I craved.

I’ve committed the cardinal sin of trying to emulate the rhythm of the ṭawīl meter in English, which I fear has straitjacketed my translation. But perhaps this may give you some sense of how cleverly, and poignantly, Ibn al-Naḥḥās is able to play with the ideas of looking backward in space—towards a city he loves, in which dwells the young man he loves, who has chosen not to come bid him farewell; and in time—towards a past when they were together, when all was well. And, perhaps most interestingly, with the idea that looking vainly backward in space for his missing beloved is also looking vainly forward in time for a lovers’ reunion that will never be. 

Why pearls, and why strung at random?

In his translation of the famous "Turk of Shirazghazal of Hafez into florid English, Sir William Jones, the philologist and Sanskrit scholar and polyglot extraordinaire, transformed the following couplet:

غزل گفتی و در سفتی بیا و خوش بخوان حافظ

که بر نظم تو افشاند فلک عقد ثریا را


Go boldly forth, my simple lay,
Whose accents flow with artless ease,
Like orient pearls at random strung.

The "translation" is terribly inaccurate, but worse, the phrase is a gross misrepresentation of the highly structured organization of Persian poetry. Regardless, I picked it as the name of my blog for a number of reasons: 
1) I don't expect the ordering of my posts to follow any rhyme or reason
2) Since "at random strung" is a rather meaningless phrase, I decided to go with the longer but more pompous "pearls at random strung". I rest assured that my readers are unlikely to deduce from this an effort on my part to arrogate some of Hafez's peerless brilliance!

About Me

My Photo
Cambridge, Massachusetts, United States
What is this life if, full of care,
We have no time to stand and stare.
—W.H. Davies, “Leisure”