Uncategorised – Page 59

Water found in Martian soil

During its first 100 Martian days (sols), NASA’s Curiosity rover had studied the atmosphere and soil of the red planet in some detail. The initial results from these studies trickled in on September 26 and 27, 2013, in a special issue of Science. The most significant find appeared to be that finer Martian soil had up to two pints of water per cubic foot, which the author of one of the studies called an “excellent resource for future explorers”. The water molecules appeared to be ‘locked up’ in amorphous minerals of basaltic origins. Another sign of water was the presence of carbonates, picked out when the Sample Analysis at Mars instrument heated a sample and found carbon dioxide among the vapours. Carbonates are usually formed in the presence of water. With the presence of methane having been declared trivial on the planet earlier this week, finding water rekindled hopes of the red planet having once harboured life. However, direct signs of this, such as organic molecules, remained elusive in the studies.

Read my report for The Hindu on this.

The Sample Analysis at Mars (SAM) instrument, shown here at NASA's Goddard Space Flight Center, analysed the samples of material collected by the rover's arm. — The Sample Analysis at Mars (SAM) instrument, shown here at NASA’s Goddard Space Flight Center, analysed the samples of material collected by the rover’s arm. Image: NASA-GSFC

Unusual third Van Allen belt explained

Remember that third Van Allen radiation belt that appeared in February and lasted for about a month? Scientists from the University of California, Los Angeles, have started to understand what it really was – a belt composed solely of electrons moving at almost light-speed – and why it occurred – because of a massive solar flare in September, 2012. Although these faster electrons aren’t unique, as they appear in the two original Van Allen belts as well, what scientists have to figure out now is what accelerates them to such high energies. My story on this development for The Hindu.

The numbers game

Cricket is a complex game – about as difficult to get a full hang of as a 21-year old trying to learn English from scratch. It takes a while, and a lot of practice. Even then, many people (I know) still have difficulty getting all the rules right. As a result, there are a lot of numbers that emerge after each game – so many runs scored in different directions, so many balls bowled at so-so speeds, at so-so lengths to so many batsmen, so many partnerships each lasting so many balls, so many successful and not-so-successful fielding positions, etc. In short, cricket is a statistics-heavy game, perhaps heavier than baseball itself. So if baseball had sabermetrics, what does cricket have?

Nothing official in place, for starters. Cricketing sabermetrics isn’t new, but it isn’t prevalent either – the reasons are too many to be dealt with here, but not the least of them is that cricket is also more complex than baseball. Building a statistical framework to encompass all of its nuances is difficult. So, a simplified version of cricketing sabermetrics – one making a lot of assumptions – assessing only the batsmen’s performance during Ashes 2013 caught my interest. Satyam Mukherjee, a post-doctoral fellow at the Kellogg School of Management, had used complex network analysis to figure out why Clarke, Trott and Bell were the better players during the tournament, and he establishes it with mathematical proof.

His work also raises a lot of questions on the relevance of such mechanisms in modern sport. Read my piece on this work for The Hindu.

Photo: Ashes2013.net

After-math of the Ashes

In the recently concluded Ashes test series, England retained the urn by beating Australia 3-0 in five games. England always looked the more confident team, reinforced as well as evinced by the confidence each player had on every other. They batted well, they bowled well, they fielded well.

Australian players, on the other hand, looked out of place. Often, great performances by a batsman or a bowler didn’t translate into the rest of the team moving with that spirit, betraying high – if not unreasonable – dependence on some players, who were expected to bear the burden.

Now, a post-doctoral fellow from the Kellogg School of Management, Northwestern University, has put these conclusions to the test. Satyam Mukherjee has used complex network analysis to determine how England and Australia differed in their strategies during the Ashes matches, to gauge the “quality” of wins and how much of a role each player played in it.

Satyam thinks that, to the best of his knowledge, “this work is the first of its kind in cricket”, and is hoped to motivate analysts to look at behind-the-scenes statistics of players whose best skills may not always be brought to the fore.

Specifically, Satyam uses concepts like the PageRank algorithm (which Google uses to determine the ‘influentiality’ of websites), betweenness and network centrality, and treats each team as a network of players who have to perform specific roles.

Math & matters of the heart

“Two football players are linked if one player passes the ball to another, a pitcher and batter is connected if they face each other, or Nadal and Federer get connected if they play against each other,” says Satyam, explaining how networks are built. “But in cricket, no such studies exist although there is no dearth of statistics.”

However, a network-analysis of a game of cricket is much less straightforward as the success of the game doesn’t depend solely on the ball being pass around or batsmen like Tendulkar and Lara facing each other off. Instead, they face off different bowlers, which means their performances can’t be compared directly, either.

What a self-organised social network looks like (nodes of the same colour are of the same group). Image: Wikimedia Commons

So he used publically available data from Cricinfo to compute the network performance of players and how well they’d performed different roles. “The network based approach gives us the hidden properties of the performance of players,” Satyam explains, adding that the advantage is that “it doesn’t suffer from any biases which exist in traditional schemes.”

In his network analysis, each player is thought of as a node (as shown above) in a network, with the lines connecting them being the runs scored by them together. This way, as the game progresses through different partnerships, nodes are added and connected, with the distance between nodes denoting the number of runs.

Then, Satyam brings his tools to reveal, when studied as a network of people trying to accomplish a common goal with different skills between them, how the team strategised and how it fell short.

According to his calculations, for example, Gautam Gambhir was the most successful player in terms of centrality scores during the 2011 ICC World Cup final for India. This means that he was involved in the most number of batting partnerships during the game (betweenness centrality). However, the man-of-the-match award went to skipper M.S. Dhoni.

“So there is a human bias coming into play,” exclaims Satyam. However, this doesn’t come across as a call to replace the more “spiritual” aspects of the game with a mathematical framework. Instead, Satyam is vouching for using such analytical methods to decrease the chances of missing out on important statistics that come into play during drafting, team-selection, etc.

Teams as competing networks

These and other network analysis concepts have been around for quite a while. They have been applied to sports for the last decade or so, quite famously to football using the Girvan-Newman algorithm and others. The parameters they use to “evaluate” teams are simple.

PageRank, a relatively newer measure developed by and named for Google co-founder Larry Page, measures the “quality” of outcomes (i.e. wins or losses).

In the context of a match, PageRank scores give a measure of the quality of wins. If a weak team wins against a relatively stronger team, it gains points. However, if the weak team loses to a strong team, it isn’t penalized that much. Each outcome’s PageRank is dependent on the performance of every player.

In the context of players’ performance, “it gives the importance of the player in the batting line up,” explains Satyam. In other words, it provides us with an idea of the importance of runs scored — such as Graeme Swann’s 34 in England’s first innings of the final test.

It is calculated as:

… where,

p_i = PageRank score

w_ij = weight of a link

s_j-out = out-strength of a link

i = whichever team it is

q = control parameter = 0.15 (default)

N = total number of players in the network

δ = a correcting term

In-strength is the sum of the fractions of runs a player has scored in partnership with others players.

Closeness measures the connectedness of a player in the team. The ‘closer’ he is, the more open he will be to his place in the playing order being changed. For example, the ‘closest’ batsmen will be comfortable opening the batting, playing in the middle order, or holding up the lower order. This can be decided based on the match situation, pitch conditions, availability of other players, etc. Thus, having ‘close’ players increases the adaptability of the team.

The results

Satyam put together a network of players in each of the five matches, and computed these scores for all of them in terms of their batting performances.

He found that, in the first and second games both of which England won, Ian Bell and Joe Root emerged as the best batsmen, respectively. Bell, especially, had the highest PageRank, in-strength, betweenness and closeness among all batsmen. In the second match, Root had the highest in-strength, betweenness and closeness, but Usman Khawaja and Michael Clarke beat him to the top on PageRank.

In the third test, Australia dominated the game. However, the domination arose through Clarke, the man of the match, while the rest of the players put up a less-than-dominating performance. In fact, this pattern was visible in Australia throughout the tournament. As opposed to it, England’s batsmen’s betweennesses were more evenly distributed. Everyone seems to have contributed, not just the top order.

For example, one batsman who regularly features in the top five players in terms of PageRank is Tim Bresnan, an all-rounder. Thus, his ability to build partnerships even when most specialist batsmen had departed was crucial for England to have stayed on top –such as in the fourth test at Riverside Ground. Looking at the overall scores: Bell – most betweenness centrality; Matt Prior – most closeness; Jonathan Trott – highest in-strength; Graeme Swann – highest PageRank.

A batsmen’s performance network as it transpired during the Ashes 2013. Notice how almost every player on the English side was capable of holding up partnerships while, for Australia, noticeable ‘hubs’ exist in the guise of Haddin, Hughes and Rogers. Image: Satyam Mukherjee

For Australia, on the other hand, Haddin, Hughes and Rogers have high betweenness centrality, which quickly drops off when other pairs are considered.

Accordingly, batsmen who received man-of-the-match awards during the series were Joe Root, Michael Clarke, and Shane Watson. This is an instance of simple mathematical concepts having encapsulated our practical considerations well enough to have reached almost the same conclusions (even though a lot of assumptions were made in the process). However, cricket is only new to this arena.

An informer

In 2003, Michael Lewis published a book titled Moneyball: The Art of Winning an Unfair Game. It brought to a wider audience the field of study called sabermetrics, which uses in-game statistics in baseball to separate objective judgments – “Who contributed the most…” – from subjective ones – “Was that a great…” – so that teams are aware of what their strongest and weakest resources are.

In 2011, this book was adapted into a successful movie, starring Brad Pitt. Although I’d heard of the book at the time, I hadn’t read it, and the movie helped me confront for the first time how managers unfamiliar with sabermetrics’ pros might react to the idea. In the movie, many of them quit (However, most of them were old, too, and just couldn’t cope with the power to pick or drop players leaving their hands and falling into those of some “new fangled, cold-and-calculated” sabermetrician).

For this, what network analysis in sports can bring to the fore has to be understood well before it is dismissed. In its simplest form, it makes correcting for regional biases in selections easy and helps spot ‘hidden’ talent in the domestic circuit. At its very nuanced, it could factor in bowlers and fielders, not just batsmen, and also include an “athletic index” for each batsman to denote how agile he is between the wickets, to see who has been the best performer (a suggestion included in Satyam Mukherjee’s paper).

Of course, for the game to stay competitive and entertaining, both subjective and objective methods are important. Even with cricket, I can’t imagine the BCCI resorting completely to sabermetrics’ version of cricket to choose the national cricket team – how would they be able to account for the reassuring presence of Captain Cool? Instead, they could use such tools to better inform their decision-making.

(For those interested, a more detailed presentation of Satyam’s methods is available in this paper.)

(This blog post first appeared at The Copernican on September 8, 2013.)

Clio’s passion

Dear Q,

This mail is not intended to be an apology as much as my own acknowledgment of my existence. Of late, I have become cognizant of what a significant role writing, and having my writing read, plays in the construction of my self-awareness – whether profound or mundane. Even as I live moments, I do not experience them with the same clarity and richness as I do when I write about those moments. Why, I don’t pause to think about something – anything – as much as when I do when I place commas and periods. I don’t recognize possession unless it comes with an apostrophe.

To some extent, this has slowed down the speed with which I can take on life in all its forms and guises; the exhilaration is more prodigious, and the conclusions and judgments more deliberated. To someone standing next to me, in a moment I would later discover to have been the host of an epiphany, I come across as detached and indifferent, as someone lacking empathy. But I have empathy, sometimes too much, at others even suffocating. However, I haven’t bothered explaining this to anyone… until now. And why do I choose to tell you? Because you will read me. You are reading me.

So much has kindled an awareness also of what each word brings with itself: a logbook of how memories have been created, recorded and recollected over centuries of the language’s existence. You read sentences from left to right, or right to left or top to bottom depending on the language, and you are attributing the purpose of the words you’re parsing to your interpretation of the text. Now, break the flow: go orthogonal and move your eyes in a direction perpendicular to the one that unlocks meaning. Suddenly, you are confronted with words – individual, nuclear words – silently staring at you. Isn’t it a scary sight to look at symbols that suddenly seem devoid of meaning or purpose?

Inky scratches on paper. Like what a prisoner in a high-security prison does with his nails on the walls after years of crippling solitude.

Count how many times each such word appears on the page, in the book, in all the books you own, in all the books that have ever existed. Each such word, whatever it is, has been invoked to evoke multiplets of emotions. Each such word has participated in all from the proclamation that burnt down Nero’s Rome to the one that ended slavery in Western civilization, from Anthony’s selfless lament to Nietzsche’s self-liberating one. Words have not been used but repeated to simply put together a finite number of intentions in seemingly infinite ways. Each such word gallantly harbors a legacy of the need for that word.

As Roland Barthes writes in Camera Lucida, look at a portrait photograph of Napoleon Bonaparte’s youngest brother, Jerome, taken in 1852. Imagine looking into the brother’s eyes – and tell yourself that you are now looking into the eyes that once looked into Napoleon’s. Don’t you feel a weight from the sensation that what you’re looking at may contain a scar from where a powerful man’s stare etched into? I feel a similar weight when I use words; I feel a constant reminder ringing in my head about using them in such a way that preserves their dignity, their heritage. I feel that there is wisdom in their shapes and strokes. It calms me deeply, just like a ritual and its processes might.

And when such legacies are brought to bear on every experience of mine – howsoever trivial – I can’t help but become addicted to their reassuring wisdom, their reassuring granular clarity. When writing with such words, I am more pushed to re-evaluate whatever it is that I am saying, more encouraged to plumb the murkier depths of my conscience that are closed to simpler wordless introspection. When I write, I feel like I finally have the tools I have long yearned for to build strong character, and find inner peace when I seek for it the most.

(Special thanks to The Hesitant Scribe for telling me it’s OK to live just to love words.)

Let’s unMonsanto the debate.

On August 28, I had the opportunity to attend a discussion on the BRAI Bill, currently in Lok Sabha. It was held at The Hindu, and attended by some of my colleagues and some representatives from the Association of Biotechnology Led Enterprises (ABLE). The point of the discussion according to ABLE, which had arranged it, was to create awareness of the bill and dispel some popular misconceptions.

The bill, if passed, will set up a Biotechnology Regulatory Authority of India (BRAI), whose purpose will be to oversee and administer all biotechnology-related activities in India. These powers are wide-ranging, going from fixing prices for genetically engineered seeds to having a hold on export and import of transgenic foodstuff to dictating safety standards for the research, cultivation, production and consumption of genetically modified (GM) crops.

As things stand, the bill is being opposed on many fronts. A Technical Experts Committee constituted by the Supreme Court last year recommended a 10-year moratorium on all field trials of Bt transgenic foodstuff. This was accompanied by the Union Ministry of Environment and Forests suspending all field trials on GM crops, licenses for which were granted by the Genetic Engineering Appraisal Committee (GEAC). Both were centered around India supposedly lacking the infrastructure, skill and manpower to handle transgenic consumables.

Our discussion with ABLE snaked this way and that. It touched upon the GEAC, pesticides use, the possibility of ‘superbugs’, data availability, the Right to Information, and India’s agricultural needs and water-politics. At times, the participants seemed adversarial; at others, convivial. Unfortunately, there was one issue that constantly underpinned the conversation, this one very little to do with what India was or wasn’t capable of: Monsanto, Inc.

Guilt by association

One among the ABLE delegation, Dr. J.S. Rehman, an entemologist and a former member of the Review Committee on Genetic Manipulation (constituted by the Department of Biotechnology), seemed very concerned about this. Monsanto’s unenviable environmental legacy worldwide had riled up activists to protest its coming with such vehemence that, he lamented, Indian biotech. was also being suppressed in the process.

Here are two questions that were addressed to Dr. Rehman during the discussion:

Do you think the entire atmosphere over the biotechnology bill and its understanding or misunderstanding – however you look at it – is largely because of one big MNC called Monsanto?

JSR: “Our using Monsanto as a synonym with GM technology is one of the worst things we’re doing – not only for farmers but also for our people who are trying to develop genes, and who are trying to compete with Monsanto. Every time, everywhere we go, we see people asking very general questions, and we’re wasting out time in educating those people rather than putting our efforts into the development of technology and other things.”

How much have Monsanto’s businesses hijacked the debate over biotech.?

JSR: “We’re in a very bad situation, I think: Monsanto is only the gene developer. It’s not a seed developer. It has the gene which it has given to Mahyco. In Andhra Pradesh, earlier, once Bt cotton was given, for example, and Rs. 1,700 was fixed as cost-per-packet. This was because artificial competition was created in the market by introducing the Bt gene, after which all competitors had to adopt it or face losses. Then, Monsanto demanded a royalty of Rs. 1,200 per packet. So, if I have been selling a packet at Rs. 400, then my new minimum cost is Rs. 1,600. So, the competition was exploited by Monsanto.

These prices are very high for farmers, and allows people to comment that the Bt technology has spiked the cost of packeted seeds. Then, the State intervened, and after a case was filed, Monsanto was forced temporarily to reduce royalty from Rs. 1,200 to Rs. 100. This brought down the price of Bt packets to around Rs. 750-950 per packet. So, both seed companies and the farmers are benefited by the Bt technology. Farmer will also get the benefit of reducing it from Rs. 1,600 to Rs. 750. The only person losing here is Monsanto.

Then, some time after this, the seed-rate was increased. New norms recommended that instead of one packet per acre, farmers use two packets per acre. However, another way to look at this is to see that in a net area, one can go for more productivity.”

So, Indians are succumbing to the fallacy of guilt-by-association – just like with our nuclear program: “Just because the Department of Atomic Energy is doing a bad job of administering India’s nuclear program, the idea of nuclear power is bad.” As Dr. Rehman said, Monsanto may have superior technology. However, it is exploiting the latency of its Indian competitors, and the preferential access it received in the 90s from the Indian government to promote free trade, to come out on top. And when activists assume that all of GM is bad because Monsanto – its leading researcher – is bad, they are suffocating the Indian competition and empowering Monsanto.

Daylight robbery

One other example specific to Monsanto that emerged during the discussion was brought up by Dr. T.M. Manjunath, of ABLE. Dr. Manjunath was a former director at the Monsanto Research Centre, Bangalore.

He felt the need to correct Dr. Rehman on one count: that of the habit of comparing the prices of traditional cotton seeds with Bt cotton seeds. He said, “We shouldn’t compare the two without taking into account the associated benefits from each. For example, if farmers bought traditional seeds at Rs. 400 a packet, then they would also have to spend an additional Rs. 3,000 to Rs. 5,000 to insecticides. So, these [numbers] should be added to that cost. On the other hand, if you buy a packet of Bt cotton seeds at, say, Rs. 1,700, that is all farmers will have to expend there. You wouldn’t have to spray insecticides. Thereby, the farmers are immensely benefited.”

The problem here is that Monsanto is attempting to justify its exorbitant profit margins by citing a higher cost-benefit ratio, forgetting that it does not have a license to rip farmers off. Instead, if the technology has improved enough to keep the cost-benefit ratio high, then the farmer must be the full and final beneficiary. As one of the participants put it: “Monsanto can’t say ‘I’m still giving him a 4,000-rupee window!'”

At the same time, it’d be beneficial for Indian decision-makers to remember that Bt cotton did see some kind of success in India, seeing adoption by over 70 lakh farmers, and lasting well beyond its initially perceived lifetime – 6 to 7 years – before worms developed resistance to it. “One of our recommendations to minimise resistance-development was asking for 20 per cent refugee area. However, we also knew that asking farmers to sacrifice 20 per cent of their land in the name of the yield wasn’t always going to work. But to our surprise, the resistance developed [by pests and worms] has been minimal,” said Dr. Rehman.

There were Bt cotton crop failures, too, but the moral is that Monsanto sucks, yes, but the technology is promising and could be useful for India. For instance, even though Monsanto’s Bt has defied resistance for more than a decade, scientists think the threat is always imminent and that we need to be prepared. If the pall of Monsanto could be cleared (and its monstrous royalties on seeds sales avoided), perhaps an indigenous developer of transgenic seeds (about 20 varieties of which are thought to be in the pipeline) has the answer.

Failure of the stakeholders

The appropriate place from which to address this “hijacking” would be to look at how much of and how well the public sector has been activated – not to compete with Monsanto, which is already spending $1.3 billion a year on GM tech., but to make India become a self-sustaining developer of indigenous biotech. capabilities that can address its immediate needs (such as water sufficiency, which has been worsened by Bt cotton varieties).

In this regard, there has been a failure among stakeholders to explain to the people that it’s not about MNCs v. India, that the BRAI Bill is not only for Monsanto but also for Indian players. The details of how it will take from and give back to them are out of focus.

For example:

Proposed: A single-window clearance system.
Actually: Seen from the pro-GM (“ergo pro-Monsanto”) side, it could be argued that the government wants to facilitate Indian applications. Seen from the anti-Monsanto (“ergo anti-GM”) side, it looks as if the government wants to fast-track dubious applications. Which one is it?
Proposed: BRAI “will not disclose confidential information made available in an application to the Authority.”
Actually: The representatives from ABLE clarified that while some information would be hidden from the public domain, research on and results from field trials would be on display on a website for all to see, and the rest could be obtained using the RTI.
Proposed: BRAI will be a centrally implemented body; State governments will have no say in its functioning and decision-making.
Actually: A proposal for a State Biotechnology Regulatory Advisory Committee has been included in the BRAI Bill. The committee is to act as an intermediary agency between the State government and BRAI. It is not as if States have no say; however, to what extent will such a body empower the State?
Proposed: Committees constituted by the BRAI Bill will approve and ratify applications from companies for the production and transportation of transgenic foodstuff.
Actually: While committees will approve applications, a third-party (non-governmental) agency will be required to validate the results first. At the same time, the bill also okays all DSIR-approved labs for validation, which means a company with its own DSIR-approved lab can validate its own results (DSIR is the Department of Scientific and Industrial Research).

As it is, the bill is currently being examined by a Parliamentary Standing Committee on Agriculture, which would do well to ask for increased clarity on these issues. Dr. Rehman noted that even though the last deadline for public feedback, August 25, had passed, the Committee was considering extending the period for a second time (having earlier pushed it by 45 days from June 10). If and when a new date is announced, let’s unMonsanto.

—

I originally wrote this post for The Copernican, the science blog over The Hindu, on September 2, 2013.

Hope.

Every time I read Orhan Pamuk’s Nobel Prize citation lecture, ‘My Father’s Suitcase’, I am transported to a day I can’t now fully recall. Every growing child has that day, when, shielded from the vicissitudes of reality, it wants to become a painter, a musician, a writer, something it knows bridges the gap between what it wants to do and what it thinks will sate its parents’ hopes for itself. Even though I can’t remember all about that day, I’m sure I thought I wanted to be a writer. I would have wanted to write all that I read, but in a way that it preserved me. I would have wanted to write to partake of the only tradition I knew – literature – so I would not be forgotten. At every turn, I would despair that I was going farther from my dream growing older, but I would still attempt to reach out to that tradition. What has kept me going till now is that every time I would reach out, it would reach into me, and remind me that I would only have to divert my gaze inward, to bring forth an imagined reality that would help me survive this one. All this Orhan speaks of. His insight is inescapable, I must admit; yet, I do not regret that I borrow from him without striving – with that stubbornness Orhan finds is central to being a writer – to find my own words. I am not yet a writer, but I still hope to be one. And ashamedly I admit: When that day comes, I hope I find the tradition is still alive in me.

The Indecipherable Familiarity

I like writing in italics.

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.

A leap forward in ‘flow’ batteries

Newly constructed windmills D4 (nearest) to D1 on the Thornton Bank, 28 km off shore, on the Belgian part of the North Sea. The windmills are 157 m (+TAW) high, 184 m above the sea bottom. — 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.

Where the Indian infiniteness?

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.

This piece was first published in The Copernican science blog on August 6, 2013.