Once every two or three months, she makes me feel weak in the knees. Catches me off guard, when I’m not ready, when I’m not looking, when I can’t see her walking toward me. Then she hugs me, long enough for me to know she’ll always be there, but never long enough to feel the diseased coldness I feel inside every time she has to walk away. Because soon enough, there’s someone at the door, someone on the phone, someone… and she lets go. Like the elusive current of air whipping astride a tornado, quickly shifting and blowing upwards and away, and my wings are caught on nothing but still air falling downward. Sometimes I want to tell her how I feel, that I wished she didn’t walk away, but I don’t. What if she chooses not to return? A premonition of a breathless, airless world, where my pale wings are useless.
And that is where my strength lies. In loss, parting, departure, whatever it is called. All things new that I cared for – care for – come from the breaking of a bond, from tottering on the brink of that cliff and laughing to myself while the sea roars beneath my feet. All that I am, or have ever become, over and over, starting anew each time is founded on studying my roots, on what purchase each moment holds for me, and holding on to the splinters of what each bereaving has left behind. Constancy is both incentive and threat, fortune and misfortune, and to realize I might be in a moment of one makes me feel like I’m standing on a floor of glass. It is a stupendously disruptive moment of clarity and a warning that I have reached my end, that I have solved what I set out to solve. I must do something!, I think to myself, and what do I do?
I break away. I need the unknown because the familiar and its caprice scare me – there is too much to fear in the light and its deceptions even as shadows and darkness hold promise, an eternal promise. They frame the maw through which I desire to walk, to explore. I walk away from what I have earned for myself and burn a hole through the pages of my history, destroy the continuity that has trailed me all these years and replace it with cold, calming contiguity, like a tall wall erected in the middle of a bristling city, an inexplicable period for a well-deserved comma, like extinguishing the sun while I prepare to light a candle. And in the darkness, I am reborn. Here, I am reminded of the sea, and it calls me home. Here, cradled in the assurance of uncertainty and free from the binding wills of freedom and its threats to unleash my disease upon myself, I find control in knowing my opponent is just as crippled as I am, just as marooned. That humanity… That humanity.
She lacks that humanity – rather, I haven’t found it yet. I look, I always keep looking, and I can’t find it. I have no idea what it looks or feels like! And wielding that paucity, she lays me to waste, like a goddess mending me and mocking me at the same time. She defeats every deliberated parry with whispered breaths, carefully chosen gusts of air on which wings won’t beat but simply fray. She is a world unto herself, a continuum of surging currents that flays through my hauberks with every innocuous breath… and then walks away. She is the indecipherable familiarity that stalks me, the perpetual clarity that blinds me. Did I say she makes me go weak in the knees? I think I meant she makes me go weak all over.
Newly constructed windmills D4 (nearest) to D1 on the Thornton Bank, 28 km off shore, on the Belgian part of the North Sea.
Polymer-based separators in conventional batteries bring their share of structural and operational defects to the table, and reduce the efficiency and lifetime of the battery. To circumvent this issue, researchers at the Massachusetts Institute of Technology (MIT) have developed a membrane-less battery, a.k.a. a ‘flow’ battery. It stores and releases energy using electrochemical reactions between hydrogen and bromine. Within the battery, bromine and hydrogen bromide are pumped in through a channel between the electrodes. They keep the flow rate really low, prompting the fluids to achieve laminar flow: in this state, they flow parallely instead of mixing with each other, creating a ‘natural’ membrane that still keeps the ion-transfer channel open. The researchers, led by doctoral student William Braff, estimate that the battery, if scaled up to megawatts, could incur a one-time cost of as little as $100/kWh. This is value that’s quite attractive to the emerging renewable energy economy. From a purely research perspective, this H-Br variant is significant also for being the first rechargeable ‘flow’ battery. I covered this development for The Hindu.
I didn’t know Kenneth Wilson had died on June 15 until an obituary appeared in Nature on August 1. He was a Nobel Prize winning physicist and mathematician whose contribution to science was and is great. He gave scientists the tools to imagine the laws of physics at different scales — large and small — and to translate causes and effects from one scale into another. Without him, we’d struggle not only to solve physics problems at cosmological and nuclear distances at the same time but also to comprehend the universe from the dimensionless to the infinite.
Wilson won his Nobel Prize in physics in 1982 for his work with phase transitions — when substances go from solid to liquid or liquid to gas, etc. Specifically, he extended its study to include particle physics as well, and was able to derive precise results that agreed with experiment. At the heart of this approach lay inclusivity: to think that events not just at this scale but at extremely large and extremely small scales, too, were affecting the system. It was the same approach that has enabled many physicists and mathematicians take stock of infinity.
The idea of infinity
As physicist Leo Kadanoff’s obituary in Nature begins, “Before Kenneth Wilson’s work, calculations in particle physics were plagued by infinities.” Many great scientists had struggled to confine the ‘innumerable number’ into a form that would sit quietly within their theories and equations. They eventually resorting to an alternative called renormalisation. With this technique, scientists would form relationships between equations that worked at large scales and those that worked at small ones, and then solve the problem.
Even Dirac, renormalisation’s originator, called the technique “dirty”. And Wilson’s biggest contribution came when he reformulated renormalisation in the 1970s, and proved its newfound effectiveness using experiments in condensed matter physics. Like Wilson’s work, the idea was interdisciplinary. But how original was it?
The incalculable number
Kenneth Wilson did not come up with inclusivity. Yes, he found a way to use it in the problems that were prevalent in mid-20th century physics. But in the Mahavaipulya Buddhavatamsaka Sutra, an influential text of Mahayana Buddhism written in the third or fourth century AD, lies a treatment of very large numbers centered on the struggle to comprehend divinity. The largest titled meaningful number in this work appears to be the bodhisattva(10^37218383881977644441306597687849648128) and the largest titled number as such, thejyotiba (10^80000 infinities).
The jyotiba may not make much sense today, but it represents the early days of a centuries-old tradition that felt such numbers had to exist, a tradition that acknowledged and included the upper-limits of human comprehension while on its quest to deciphering the true nature of ‘god’.
Avatamsaka Sutra, vol. 12: frontispiece in gold and silver text on indigo blue paper, from the Ho-Am Art Museum. Photo: Wikimedia Commons
The Mahavaipulya Buddhavatamsaka Sutra itself, also known as the Avatamsaka Sutra, also contains a description of an “incalculable” number divined to describe the innumerable names and forms of the principal deities Vishnu and Siva. By definition, it had to lie outside the bounds of human calculability. This number, known as the asamkhyeya, owes its value to one of three arrived at because of an ambiguity in the sutra. Asamkhyeya is defined as a particular power of a laksha, but there is no indication of how much a laksha is!
One translation, from Sanskrit to the Chinese by Shikshananda, says one asamkhyeya is equal to 10 to the power of 7.1-times 10-to-the-power-of-31. Another translation, to English by Thomas Cleary, says it is 10 to the power of 2.03-times 10-to-the-power-of-32. The third, by Buddhabhadra to the Chinese again, says it is 10 to the power of 5.07-times 10-to-the-power-of-31. If they have recognisable values, you ask, why the title “incalculable”?
Lesser infinities
For this, turn to the Jain text Surya Prajnapati, dated c. 400 BC, which records how people knew even at that time that some kinds of infinities are, somehow, larger than others (e.g., countable and uncountable infinities). In fact, this is an idea that Galileo more famously wrote of in 1638 in his On two New Sciences:
“So far as I see we can only infer that the totality of all numbers is infinite, that the number of squares is infinite, and that the number of their roots is infinite; neither is the number of squares less than the totality of all numbers, nor the latter greater than the former; and finally the attributes ‘equal,’ ‘greater,’ and ‘less,’ are not applicable to infinite, but only to finite, quantities.”
Archimedes, whose Syracusani Arenarius & Dimensio Circuli predated the Avatamsaka Sutra by about 300-400 years, adopted a more rationalist approach that employed the myriad, or ten thousand, to derive higher multiples of itself, such as the myriad-myriad. However, he didn’t venture far: he stopped at 10^64 for lack of a name! The father of algebra (disputed), Diophantus of Alexandria, and the noted astronomer Apollonius of Perga, who lived around Archimedes’ time, also stopped themselves with powers of a myriad, venturing no further.
Unlike the efforts recorded in the Avatamsaka Sutra, however, Archimedes’ work was mathematical. He wasn’t looking for a greater meaning of anything. His questions were of numbers and their values, simply.
In comparison — and only in an effort to establish the origin of the idea of infinity — 10^64 is a number only two orders of magnitude higher than one that appears in Vedic literature, 10^62, dated 1000-1500 BC. In fact, in the Isa Upanishad of the Yajurveda (1000-600 BC: Mauryan times), a famous incancation first appears: “purnam-adah purnnam-idam purnat purnam-udacyate purnashya purnamadaaya puram-eva-avashisyate“. It translates: “From fullness comes fullness, and removing fullness from fullness, what remains is also fullness”.
If this isn’t infinity, what is?
In search of meaning
Importantly, the Indian “proclamation” of infinity was not mathematical in nature but — even if by being invoked as a representation of godliness — rooted in pagan realism. It existed together with a number system, one conceived to keep track of the sun and the moon, of the changing seasons, of the rise and fall of tides and the coming and going of droughts and floods. There is a calming universality to the idea — a calming inclusivity, rather — akin to what a particle physicists might call naturalness. Inifinity was a human attempt make a divine being all-inclusive. The infinity of modern mathematics, on the other hand, is contrarily so removed from the human condition, its nature seemingly alien.
Even though the number as such is not understood today as much as ignored for its recalcitrance, infinity has lost its nebulous character — as a cloud of ideas always on the verge of coalescing into comprehension — that for once was necessary to understand it. Infinity, rather infiniteness, is an entity that transcends the character typical of the inbetweens, the positive numbers and the rational numbers. If zero is nothingness, an absence, a void, then infinity, at the other end is… what? “Everythingness”? How does one get there?
(There is a related problem here in physics, similar to the paradox of Zeno’s arrow: if a point is defined as being dimensionless and a one-dimensional line as being a collection of points, how and when did dimension come into being? Incidentally, the earliest recorded incidence of infinities in Early Greek mathematics is attributed to Zeno.)
The lemniscate
As it so happened, the same people who first recorded the notion of infiniteness were also those who recorded the notion of a positional numbering system, i.e. the number line, which quickly consigned infinity to an extremum, out of sight, out of mind. In 1655, it suffered another blow to its inconfinable nature: John Wallis accorded it the symbol of a lemniscate, reducing its communication to an horizontal figure-of-eight rather than sustaining a tradition of recounting its character through words and sense-based descriptions. We were quick to understand that it saved time, but slow to care for what it chopped off in the process.
Of course, none of this has much to do with Wilson, who by his heyday must have been looking at a universe through a lens intricately carved out of quantum mechanics, particle physics and the like. What I wonder is why did an Indian scientific tradition that was conceived with the idea of infinity firmly lodged in its canons struggle to make the leap from theoretical to practical problem-solving? There are answers aplenty, of course: wars, empires, scientific and cultural revolutions, industrialisation, etc.
Remembering too much
Wilson’s demise was an opportunity for me to dig up the origins of infinity — and I wasn’t surprised that it was firmly rooted in the early days of Indian philosophy. The Isa Upanishad incancation was firmly implanted in my head while I was growing up: the Brahminical household remembers. I was also taught while growing up that by the seventh century AD, Indians knew that infinity and division-by-zero were equatable.
It’d be immensely difficult, if not altogether stupid, to attempt to replace modern mathematical tools with Vedic ones today. At this stage, modern tools save time — they do have the advantage of being necessitated by a system that it helped create. Instead, the Vedic philosophies must be preserved — not just the incantations but how they were conceived, what is their empirical basis, etc. Yes, the household remembers, but it remembers too specifically. What it preserves has only historical value.
The Indian introspective and dialectic tradition has not given us just liturgy but an insight into the modes of introspection. If we’d preserved such knowledge better, the epiphany of perspectives that Wilson inspired in the late 1970s wouldn’t be so few nor so far between.
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This piece was first published in The Copernican science blog on August 6, 2013.
efskehfsfrhlrfkdrslfhrgrgwfwfsfrehfIDROPPEDMYHARDDRIVE! From a height of six feet. Now it makes a high-pitched noise every time I plug it in, and refuses to be read. I know this isn’t a big issue, one that’s easily fixed, but temporary lack of data access is unsettling for me. More so that such a situation has been precipitated by (accidental) physical violence, not a software-related one, and the lack of access suddenly casts my digital data as a fragile entity. There is something eerily comedic about how data ‘created’ with one of the stronger of the four natural fundamental forces can be ‘destroyed’ by the weakest.
Book review: A Ball of Fire, John Montague (Bloomsbury, Rs. 299)
When Gwendolyn Brooks remarked that poetry was “life distilled”, she may have overlooked John Montague and his collection of short stories, A Ball of Fire, which, true to its name, comes alive in “a smothered explosion of color”. Using tight poetic prose that is still conversational and a rhetorical diction evocative of Yeats, Montague does not need the sustained tension of a full novel to make you mourn an actor when he dies; five pages will suffice.
Born in Depression-era Brooklyn to a father he can’t recall, separated from his siblings four years later and sent to an Irish farmhouse to live with his aunts, losing his mother young but knowing a string of lovely ladies through his college and teaching days in the 1960s and 1970s, ultimately marrying thrice, all the time grappling with the meaning of rebellion, sex and identity, Montague’s experiences show in his writing.
In many stories, there is a boy, a young man, a traveler or an unhappy old man constantly placed in a situation he hasn’t been in before, still doused in desires he left the cradle with. There is always a quest, too — to know what love can be devoid of sex, what history can be bereft of adventure, what death can be in the absence of life … most exemplified in the collection’s three longer pieces, The Lost Notebook, Death of a Chieftain and Three Last Things respectively, all constructed in fine detail with a masterful understanding of human nature.
In fact, The Lost Notebook overshadows all the stories that follow, except perhaps Three Last Things, with its portrayal of two characters’ groping exploration of freedom and immortality while still trapped in their adolescent visions of grandeur. Using the first person, Montague draws attention to a young Irish poet touring Paris during a summer when he meets a troubled young American woman, and there begins a petulant affair. As he fumbles in bed so does she fumble with her aspirations to be a painter. The metaphors in it are everything from sumptuous to galling – in sharp contrast to the more languorous yet still ambitious Death of a Chieftain — as the couple explores Paris, its museums, their paintings and sculptures, its tradition-laden streets brimming with opportunities for each to discover more about the other.
Despite the suggestion that sexual maturity has much to do with its artistic counterpart, the author keeps reminding you that they aren’t simply spanned by yearning. In fact, he often seems to reflect that the only true freedom that can be experienced in between birth and death is to be found in the bedroom. Montague alludes to this opinion in the ultimate Three Last Things, a profound meditation on what death could mean simply by virtue of being the end of a lifetime.
The other, shorter pieces are remarkable too, but just not as spectacular. A personal favorite is A Love Present, a story of a young boy who finds love residing in the proverbial last place that he’s looking, but still written with a warm conviction that makes you want to relive the episode. Another such tale is Sugarbush, I Love You So.
A Ball of Fire holds you with stories that start and end similarly but leave you with hard-earned insights that soothe. The reader is bound to chance upon moments frothing with just the same emotions you remember experiencing in similar instances from your life. To this end, and in the company of Montague’s poetic penmanship, the book is unforgettable.
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I wrote this for The Hindu Literary Review under the title ‘Life distilled’. It was published online on August 3, 2013.
A paper published last week in the Journal of Communication indicates that couples in long-distance relationships could be more intimate than those in geographically close ones. The researchers, Crystal Jiang and Jeffrey Hancock, think this is because partners could be adapting more optimistically to each other behaviours to compensate for the mediating communication technology’s shortcomings. While the study is definitely not representative because of statistical limitations, it suggests that an erstwhile atypical social interaction could actually have a larger role to play in social networks than thought. Here’s more by me for The Hindu.
A study of studies by economists from Princeton and UCal, Berkeley, has found that as the climate worsens due to global warming, human violence is likely to get more frequent and intensified. The economists don’t know the precise terms of this intriguing relationship, but think a broad range of factors including neurophysiology and economic duress could be driving it. One significant finding is that one standard-deviation’s increase in some key climate variable’s value, like temperature, is likely to cause a whopping 14% rise in violence.
The study is also important, claimed Edward Miguel, one of the authors from UCal, because it provides a lot of quantitative evidence to their claims that was missing earlier. It tracked the climate and human conflicts since 8,000 BC, and studied them in a regression framework that threw up the positive correlation conclusion. I corresponded with Prof. Miguel on this for my story in The Hindu. Also, here’s the abstract of their paper.
