Month: November 2024

  • Correlation isn’t causation — the EVM edition

    The space to disagree with the Election Commission’s position vis-à-vis the integrity of electronic voting machines without finding oneself backtracking into the Congress or the BJP camps is shrinking, and both national parties as well as the Supreme Court have been wilfully engendering this state of affairs at the expense of — ironically — logic.

    The Congress on November 24, 2024:

    Dr. Parameshwara, who was also the AICC observer for Maharashtra elections, told presspersons that his party leaders, including former Rajasthan Chief Minister Ashok Gehlot and former Chhattisgarh Chief Minister Bhupesh Baghel, discussed the EVM issues and were planning to appeal to the Election Commission of India (ECI) in this regard. “We are now sure that till the EVMs are used, there is no hope for the Congress or any other party other than the BJP. There is an urgent need to return to ballot papers,” he said.

    The Supreme Court on November 26, 2024:

    The Supreme Court on Tuesday (November 26, 2024) indicated a level of hypocrisy attached to criticism about Electronic Voting Machines (EVM), saying “EVMs are tampered when you lose and fine if you win”. The oral remark was made by Justice Vikram Nath before dismissing a petition filed by evangelist K.A. Paul, who sought a judicial order to return to paper ballots.

    Also the Supreme Court in April 2024:

    The Supreme Court on Wednesday underscored that it cannot ask the Election Commission of India (ECI) to disclose the source codes of the Electronic Voting Machines (EVMs) as it can result in its misuse. The source code often called “the brain” refers to a set of instructions that tells the machine how to function. A Bench comprising Justices Sanjiv Khanna and Dipankar Datta made the observation while hearing a batch of petitions seeking 100% cross-verification of the vote count in EVMs with Voter Verifiable Paper Audit Trail (VVPAT) paper slips.

    The BJP on November 27, 2024:

    Taking a swipe at the Congress president over his latest remarks on the EVMs, BJP Lok Sabha MP and national spokesperson Sambit Patra also said Mr. Kharge can go to “planet Mars” taking Gandhi with him and “live there happily” if he doesn’t want electronic voting machines, Election Commission, Enforcement Directorate, Central Bureau of Investigation, judiciary and the Modi government.

    And the Congress on November 30, 2024:

    In his opening remarks to the CWC, party president Mallikarjun Kharge mentioned the electronic voting machines (EVMs) making the poll process “suspect”. And that set the tone for the speakers who followed him, as the discussions mostly focussed on EVMs and the Election Commission (EC).Veteran leader Digvijaya Singh was the first among CWC members to question EVMs. While Rajya Sabha member Abhishek Singhvi argued for a nuanced approach and pitched for 100 per cent voter verifiable paper audit trail (VVPAT), Ms. Vadra said the party should press for a return to ballot paper. Mr. Gandhi urged his colleagues to “adopt a firm stand and take the issues to the hilt and convert it into a movement”.

    We don’t need a “movement” because we don’t know that EVMs are the issue! This is a farce. It’s helping only the Congress — and then again only by fanning the flames of a misguided suspicion. The BJP’s overreach vis-à-vis many of the institutions of Indian democracy, including the Reserve Bank (RBI), the Enforcement Directorate (ED), and the Central Bureau of Investigation (CBI), has rendered all of them suspect, especially when some outcome goes the BJP’s way when it wasn’t expected to.

    But a mismatch between expectations and outcomes alone can never be conclusive proof of malfeasance. Today many people harbour similar doubts about the Election Commission — and it’s easy to understand this isn’t implicitly unwarranted or even unfair. However, the Election Commission’s integrity vis-à-vis the tallies of votes cast in an election offers a handle on the situation that the RBI, ED, the CBI or any other such institution can’t offer: mathematics.

    Contrary to the Supreme Court’s views about electronic voting machines (EVMs) harbouring some kind of “source code” that must be protected at all costs, EVMs are simple signal counters whose security arises from more sophisticated means. Their electronics are isolated from external sources of input and their ability to count votes is tested in a specific way at each polling booth before the machines are set up for public use. Indeed, as a counter of votes, ‘leaking’ the “source code” of EVMs is pointless because anyone can write it up on their own: it’s after all an algorithm to count how many different buttons are pushed, each of which produces a distinct signal.

    But thanks to the Election Commission’s reluctance to submit its machines to independent testing and abetted by the Supreme Court’s refusal, inability or disinterest in the technical architecture of EVMs, any questions about the integrity of EVMs — specifically their abilities to count votes a specific way and of an external actor to interfere in this process — falls under the wheels of contempt of the Supreme Court or, thanks to the BJP’s habitual overreach, allegations of anti-nationalist activity. This is unfortunate.

    EVMs make use of mathematics to operate just the way modern computers do. They both have the same fundamental components, just put together differently for different purposes. And just as it’s possible to test whether a computer is working as intended without taking it apart, it’s possible to test EVMs without taking them apart. Independent researchers can test an EVM without touching it, without in any way being able to access its constituent components (except to supply input signals and receive output signals), and without even knowing its internal logic — and with an Election Commission official monitoring the whole process.

    Even Congress leader and Rajya Sabha member Abhishek Singhvi’s demand for 100% VVPAT has met with a corresponding fate at the apex court (brought there by a different petitioner) — and yet which is similarly unnecessary. From The Hindu, April 15, 2024:

    The VVPAT-based audit of EVMs … very similar to the “lot acceptance sampling technique” that is widely used in industry and trade. If the number of defectives found in a randomly drawn statistical sample is less than or equal to a specified acceptance number, the lot (or ‘population’) is accepted; otherwise, the lot is rejected. … The hypergeometric distribution model should form the basis of the sampling plan for the VVPAT-based audit of EVMs because it is an exact fit. In the discussion that follows, we assume the percentage of defective EVMs in the population (P) to be 1%, and calculate sample sizes, for various population sizes, for 99% probability of detecting at least one defective EVM. We also compute the probability that the ECI-prescribed sample size of “five EVMs per Assembly constituency” will fail to detect a defective EVM for different population sizes. The great merit of the hypergeometric distribution model is that the sample size is the greatest when P is very close to zero (which is what the ECI claims it is), and it becomes lesser as P increases. …

    We can use the ‘plateau effect’ of sample sizes to divide the bigger States into ‘regions’ (an integral number of districts) with EVM population sizes of about 5,000 each. We treat “EVMs deployed in the region” as the ‘population’. On average, there would be about 20 Assembly constituencies in a region. The sample size required is 438 and the average number of EVMs per Assembly constituency whose VVPAT slips are to be hand counted is 22. For example, U.P with 1,50,000 EVMs can be divided into 30 regions with roughly 5,000 EVMs each. In the event of a defective EVM turning up, the hand counting of VVPAT slips of the remaining EVMs will confined to the region. This option is statistically robust and administratively viable.

    But like the Supreme Court, the Congress isn’t interested in mathematical tests of EVMs’ integrity. This sounds bizarre because the Congress wants something the Supreme Court won’t give — but instead of disagreeing with the court’s refusal to have EVMs independently tested, which is where the problem really lies, the party has elected to disagree with the Indian government’s decision in the 1990s to switch paper ballots with EVMs.

    A return to paper ballots is a terrible, terrible idea that forgets how much EVMs simplify the vote-casting activity (while removing ‘bad votes’) and speed up the whole process, all the way up to recounting, while requiring fewer safeguards to prevent mistakes or interference. But worse: neither the Congress nor any activists supporting the demand to revert to paper ballots can claim to understand how EVMs work or what really could be going wrong, if it is.

    The party may lack a member with the skills to test the machines and the Election Commission may be disinclined to comply to requests — but this doesn’t mean “it’s working as intended” and “it’s not working as intended” are the only two possible outcomes here. There’s a third: “we don’t know”. And the ignorant views of both political and judicial leaders are eroding the space for this possibility in public dialogue.

    Because the outcomes in the Maharashtra state assembly election defied the expectations of Congress et al., the party and its allies have stretched their latent distrust of the Election Commission to the extreme of assuming they also know the EVMs malfunctioned and/or the commission misbehaved. No one in this milieu is stopping to consider they don’t know something because they lack proof of malfeasance and/or misbehaviour.

    Thus no one will pursue even a public debate on an independent democratic mechanism that acquires and places in the public domain data from the integrity tests of EVMs slated for use in specific elections. But they will pursue a (presumably) national “movement” by attributing with no evidence their loss in a recent election on EVMs with or without the Election Commission’s imaginary complicity while demanding a return to a primitive voting system, and about which the commission and the national government will do nothing other than to make snarky comments while the Supreme Court issues uncritical remarks.

    Featured image credit: Dmitrii Vaccinium/Unsplash.

  • Review: ‘Vettaiyan’ (2024)

    Watch it, but fast-forward through some parts.

    Vettaiyan steers clear of unconditionally qualifying “encounter killings” as the only way out — a line many Tamil films have been only too happy to tout of late. There’s in fact an instructive passage at the film’s start that’s probably deliberate. Rajinikanth’s character says there is no personal gain to be had or personal grouse to be avenged in an “encounter killing”, that a police officer who kills in this way has to suffer the “risk” of enquiries by departmental, magisterial, and human-rights commissions, and that the officer may be dismissed or “even” jailed. The choice of words here sets up a narrative whose denouement, pronounced by Rajinikanth’s character in the same scene, is the idea that police personnel are prepared to protect the people at large at risk to their own lives.

    The film intercalates elements of this scene with another in which Amitabh Bachchan’s character is being persuasive in his own right about the pitfalls of “encounter killings”. The virtue of this arrangement is that it reveals a fundamental truth about the world: when a narrative triumphs, it isn’t because it has vanquished other narratives. It’s the idea that many narratives, even those at odds with each other, can be simultaneously true, and that we always have the option to choose the one we’d like to adopt — and suddenly the world could look very different. The tenets of populism can fully explain the (alleged) public support for “encounter killings” but the deeper issue is that we need people to want to adopt a different narrative of the phenomenon.

    Vettaiyan uses Rajinikanth’s character to embody this arc, and attempts to bend it slowly over its 160-minute runtime to intersect with Amitabh Bachchan’s character’s demand: that we need education as a public service and that it needs to be universally accessible, so that from the more learned foundations that result, people will demand timely justice instead of a rushed one. That there are two scenes later in the narrative explicitly acknowledging the risk of “encounter killings” becoming misappropriated by vested interests — à la Vikram Vedha — is only to the writers’ credit.

    In fact, since a single film has come this far, I only wish Vettaiyan also examined the belief, which Rajinikanth’s character articulates in the film without challenge, that “encounter killings” can deter similar crimes in future by scaring potential perpetrators away. Such beliefs are mistaken because they presume there is no relationship between the particulars of violent crimes and how the law punishes them, or overlook it altogether. In reality, there is ample evidence that harsher punishment for a sexual violence conviction can incentivise perpetrators to kill the victims (i.e. prevent their survival) in order to minimise the perpetrators’ chances of being caught.

    Nonetheless the film’s decision to draw its driving force from sexual violence, especially gratuitous sexual violence reinforced with graphic imagery, is deeply disconcerting. Repeatedly setting up the ‘dishonouring’ of a woman as the raison d’être of the pursuit of justice is dangerous because it also sets up any crime less heinous — as deemed by the socio-cultural mores of the time — as undeserving of such pursuits. The practice of refrigeration certainly needs to end. The film also maintains the film industry’s tradition of not thinking about the tropes that concern women. The protagonist’s second in command is a woman in both phases of the film — Ritika Singh first and Rohini Molleti second — and the distribution of labour (especially of the tedious variety) and credit is correspondingly lopsided. The antagonist’s lieutenant is a woman, too.

    Yet even after all these missteps — and the many others a contemporary superstar vehicle demands — on the scale of badness Vettaiyan steers clear of Annaatthe (undoubtedly Rajinikanth’s worst outing since Baba) and, importantly, of Maharaja, whose diet was even heavier on sexual violence. And to achieve all this, Vettaiyan expects us to overlook all sorts of small but mighty details, including (i) a company’s monarch storing details of the bribes he’s given on the company servers; (ii) a wasp-sized drone that could transmit high-definition images in near-real-time with what could only have been a profoundly energy-dense battery; (iii) an otherwise devious antagonist being unable to think of any ways around a protagonist who’s being a nuisance other than to offer bribes or organise hitmen; and (iv) the spectacle of one-on-one physical violence to pad the otherwise feeble arguments to suspend disbelief.

    There’s a fifth detail that’s also my favourite: in many, many Tamil films (and quite possibly in films made around the country; I’m leaving them out only because I haven’t watched most of them), the protagonist has need for great public support to surmount a great challenge — and immediately finds it. I found both parts of Dhanush’s Velailla Pattadhaari completely uninspiring for this reason: both narratives would’ve gone to pot if certain social media posts hadn’t gone viral. Garnering enthusiastic public support for a common cause is an extremely valuable thing and thus quite rare in reality. But in Tamil films it happens with an astounding success rate of 100%.

    “These are small prices to pay,” you say, and I’m not so sure. If it weren’t for these details, Vettaiyan would have no feet to stand on. Given a film’s claims to grandness — depicted by the scope of its characters’ actions and the virtues its makers allege the characters are showcasing — we’re often expected to overlook such details. And we do because if we apply this lens to one film at a time, it seems okay. But zoom out and a rash of films comes into view that has progressively rendered the terms of the buy-in more and more exorbitant until, at one point, we’re being asked to overlook patently absurd claims in the service of some unattainable, even deceptive, virtue. Vettaiyan, for example, would’ve had trouble just getting off the ground if that drone hadn’t or achieving any of the major leads in its central procedural without its “fight scenes”.

    The film is ultimately a good hand with the misfortune of being erected as a house of cards. And the reason it doesn’t collapse at the first breeze is its principled refusal to lose sight of the corruption at the heart of “encounter killings”.

    Featured image: A scene from Vettaiyan (2024). Source: Amazon Prime Video.

  • Externalised costs and the human on the bicycle

    Remember the most common question the protagonists of the eponymous British sitcom The IT Crowd asked a caller checking why a computer wasn’t working? “Have you tried turning it off and on again?” Nine times out of 10, this fixed the problem, whatever it was, and the IT team could get on with its life.

    Around COP26 or so, I acquired a similar habit: every time someone presented something as a model of energy and/or cost efficiency, my first thought was whether they’d included the externalised costs. This is clearly a global problem today yet many people continue to overlook it in contexts big and small. So when I came across a neat graph on Bluesky (shown below), drawn from an old article in Scientific American, I began to wonder if the awesome transportation efficiency of the human on the bicycle (HotB) included the energy costs of making the bicycle as well.

    According to the article, written by an SS Wilson and published in 1973, the HotB required 1-2 calories per gram per km to move around. The next most efficient mover was the salmon, which needed 4 cal/g/km. If the energy costs of making the bicycle are included, the energy cost per g/km would shoot up and, depending on the distance the MotB travels, the total cost may never become fully amortised. (It also matters that the math works out only this way at the scale of the human: anything smaller or bigger and the energy cost increases per unit weight per unit distance.)

    But there’s a problem with this line of thinking. On a more basic level, neither Wilson nor Scientific American intended the graph to be completely accurate or claimed it was backed by any research more than that required to estimate the energy costs of moving different kinds of moving things through some distance. It was a graph to make one limited point. More importantly, it illustrates how externalised costs can become counterproductive if attempts to factor them in are not guided by subjective, qualitative assessments of what we’re arguing for or against.

    Of course the question of external costs is an important one to ask — more so today, when climate commitments and actions are being reinterpreted in dollar figures and quantitative assessments are gaining in prominence as the carbon budget may well have to be strictly rationed among the world’s countries. But whether or not some activity is rendered more or less efficient by factoring in its externalised costs, any human industrial activities — including those to manufacture bicycles — are polluting. There’s no escaping that. And the struggle to mitigate climate change is a struggle to mitigate climate change while ensuring we don’t undermine or compromise the developmental imperative. Otherwise the struggle isn’t one at all.

    Even more importantly, this balancing act isn’t a strategy and isn’t the product of consensus: it’s an implicit and morally and ethically correct assumption, an implicit and inviolable component of global climate mitigation efforts. Put another way, this is how it needs to be. In this milieu, and at a time it’s becoming clear the world’s richer countries have a limit to how much they’re prepared to spend to help poorer countries deal with climate change, the impulse to consider externalised costs can mislead decision-making by making some choices seem more undesirable than they really are.

    Externalised costs are, or ought to be, important when the emissions from some activity don’t stack up commensurately with any social, cultural, and/or political advantages they confer as well. These costs are not always unavoidable nor undesirable, and we need to keep an eye on where we’re drawing the line between acceptable and unacceptable costs. The danger is that as richer countries both expect and force poorer ones to make more emissions cuts, the latter may have to adopt more robust quantitative rationales to determine what emissions to cut from which sources and when. Should they include externalised costs, many enterprises that should actually live on may face the axe instead.

    For one, the HotB should be able to continue to ride on.


    Addendum: Here’s an (extended) excerpt from the Scientific American article on where the HotB scores their efficiency gains.

    Before considering these developments in detail it is worth asking why such an apparently simple device as the bicycle should have had such a major effect on the acceleration of technology.The answer surely lies in the sheer humanity of the machine. Its purpose is to make it easier for an individual to move about, and this the bicycle achieves in a way that quite outdoes natural evolution. When one compares the energy consumed in moving a certain distance as a function of body weight for a variety of animals and machines, one finds that an unaided walking man does fairly well (consuming about .75 calorie per gram per kilometer), but he is not as efficient as a horse, a salmon or a jet transport. With the aid of a bicycle, however, the man’s energy consumption for a given distance is reduced to about a fifth (roughly .15 calorie per gram per kilometer). Therefore, apart from increasing his unaided speed by a factor of three or four, the cyclist improves his efficiency rating to No. 1 among moving creatures and machines.

    … The reason for the high energy efficiency of cycling compared with walking appears to lie mainly in the mode of action of the muscles. … the cyclist … saves energy by sitting, thus relieving his leg muscles of their supporting function and accompanying energy consumption. The only reciprocating parts of his body are his knees and thighs; his feet rotate smoothly at a constant speed and the rest of his body is still. Even the acceleration and deceleration of his legs are achieved efficiently, since the strongest muscles are used almost exclusively; the rising leg does not have to be lifted but is raised by the downward thrust of the other leg. The back muscles must be used to support the trunk, but the arms can also help to do this, resulting (in the normal cycling attitude) in a little residual strain on the hands and arms.

    Featured image credit: Luca Zanon/Unsplash.

  • A not-so-random walk through random walks

    Though I’ve been interested of late with the idea of random walks, I was introduced to the concept when, more than two decades ago, I stumbled across Conway’s Game of Life, the cellular automaton built by John Conway in 1970. A cellular automaton is a grid of cells in which each cell has a value depending on the values of its neighbours. The automaton simulates the evolution of the grid as the cells’ values change dynamically.

    Langton’s ant was a popular instance of the simulator and one of my favourites, too. One 2001 conference paper described it as “a simple … system with a surprisingly complex behaviour.” Here, a (virtual) ant starts off at a random cell on the grid and moves randomly into one of the four neighbouring squares (diagonal squares aren’t accessible). There are three rules:

    (i) A cell can be either black or white in colour;

    (ii) If the square is white when the ant moves into it, the colour is flipped, and the ant turns 90º clockwise and moves forward;

    (iii) If the square is black, the colour is flipped, and the ant turns 90º counter-clockwise and moves forward.

    As the ant moves across the grid in this way, the first hundred or so steps produce a symmetric pattern before chaos ensues. For the next 9,900 or so steps, an image devoid of any patterns comes into view. But after around 10,000 steps, there’s magic: the ant suddenly enters into a repetitive 104-step pattern that it continues until the end of time. You can run your own simulation and check.

    The path of a Langton’s ant. The repetitive pattern after ~10,000 steps is the ‘highway’ growing at the bottom. The location of the ant is shown in red. Credit: Krwarobrody and Ferkel/Wikimedia Commons

    The march of the Langton’s ant before the repetitive portion has been described as a pseudorandom walk — a walk whose pattern appears random but whose next step is not quite random (because of the rules). In a truly random walk, the length of each step is fixed and the direction of each step is chosen at random from a fixed number of options.

    If it sounds simple, it is, but you might be forgiven for thinking it’s only a mathematical flight of fancy. Random walks have applications in numerous areas, including econometrics, finance, biology, chemistry, and quantum physics.

    The trajectory of a random walk after 25,000 steps. Credit: László Németh/Wikimedia Commons

    Specific variants of the random walk behave in ways that closely match the properties of some complex system evolving in time. For example, in a Gaussian random walk, the direction of each step is random and the length of each step is sampled randomly from a Gaussian distribution (the classic example of a bell curve). Experts use the evolution of this walk to evaluate the risk exposure of investment portfolios.

    The Lévy flight is a random walk with a small change: instead of the step length being determined by a random pick from the Gaussian distribution, it comes from any distribution with a heavy tail. One common example is the gamma distribution. Each such distribution can be tweaked with two parameters called κ (kappa) and θ (theta) to produce different plots on a graph, all with the same general properties. In the examples shown below, focus on the orange line (κ = 2, θ = 2): it shows a gamma distribution with a heavy tail.

    Various gamma distributions for different values of κ and θ. Credit: MarkSweep and Cburnett/Wikimedia Commons, CC BY-SA 3.0

    Put another way, the distribution has some large values but mostly small values. A Lévy flight is a random walk where the step length is sampled randomly from this distribution, and as a result has a few large steps and many small steps. Research has shown that the foraging path of animals looking for food that is scarce can be modelled as a Lévy flight: the large steps correspond to the long distances towards food sources that are located far apart and the short steps to finding food spread in a small area at each source.

    A Lévy flight simulated for 1,000 steps.
    A Lévy flight simulated for 1,000 steps. Credit: PAR/Wikimedia Commons

    Perhaps the most famous ‘example’ of a random walk is Brownian motion; it isn’t a perfect example however. Brownian motion can describe, say, the path of a single atom over time in a gas of billions of atoms by using a Lévy process. Whereas a random walk proceeds in discrete steps, a Lévy process is continuous; they are in other respects the same. The motion itself refers to the atom’s journey in some time period, frequently bumping into other atoms (depending on the gas’s density) and shifting its path in random ways.

    The yellow circle depicts the motion of a larger particle in a container filled with smaller particles moving in random directions at different speeds. Credit: Francisco Esquembre, Fu-Kwun and lookang/Wikimedia Commons, CC BY-SA 3.0

    Brownian motion in particular uses a type of Lévy process called the Wiener process, where the path evolves according to the following rules:

    (i) Each increment of the process is independent of other (non-overlapping) increments;

    (ii) How much the process changes over a period of time depends only on the duration of the period;

    (iii) Increments in the process are randomly sampled from a Gaussian distribution;

    (iv) The process has a statistical mean equal to zero;

    (v) The process’s covariance between any two time points is equal to the lower variance at those two points (variance denotes how quickly the value of a variable is spreading out over time).

    The path of the atom in the gas follows a Wiener process and is thus Brownian motion. The Wiener process has a wealth of applications across both the pure and the applied sciences. Just to name one: say there is a small particle — e.g. an ion — trapped in a cell. It can’t escape the cell except through a small opening. The Wiener process, which models the Brownian motion of the ion through the cell, can be used to estimate the average amount of time the ion will need to reach the opening and escape.

    Like random walks, Wiener processes can also be tweaked to produce models for different conditions. One example is the Brownian bridge, which arises when a Wiener process is limited to appear at the start of an interval and disappear at the end, with the start and end points fixed. A different, more visual way to put this is in terms of a graph with two y-axes and one x-axis. Say the point 0 is the start of the interval on the left y-axis and 1 is the end of the interval on the right y-axis. A Wiener process in the interval [0, 1] will be a ‘bridge’ that connects 0 and 1 in a path that follows Brownian motion.

    A Brownian bridge pinned at the two endpoints of an interval. Credit: Zemyla/Wikimedia Commons, CC BY-SA 3.0

    By analogy, a random bridge in the interval [0, 1] will be a random walk based on the Gaussian distribution between 0 and 1; a gamma random bridge in the interval [0, 1] will be a random walk based on the gamma distribution between 0 and 1; and so on. (This said, a Wiener process and a random walk are distinct: a Wiener process will play out the same way if the underlying grid is rotated by an arbitrary angle but a random walk won’t.)

    It’s a wonder of mathematics that it can discern recurring behaviours in such highly noisy systems and with its finite tools distil from them glimpses into their future. According to a 2020 preprint paper on arXiv, “Various random-walk-related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding.”

    If some basic conditions are met, there are random walks out in the universe as well. In 2004, researchers estimated the Brownian velocity of the black hole at the Milky Way’s centre to be less than 1 km/s.

    For a more mathematical example, in a ‘conventional’ random walk, after N steps the walker’s distance from the origin will be comparable to the square root of N. Further, it takes on average S2 steps to travel a distance of S from the origin. For a long time, researchers believed this so-called S → S2 scaling law could model almost any process in which a physical entity was moving from one location to another. The law captured the notion of how much a given distribution would spread out over time.

    One of the earliest deviations from this law was fractals, where there is an S → Sβ law but such that β is always greater than 2, implying a greater amount of spread relative to the step length vis-à-vis random walks. (Factoid: a random walk on a fractal also gives rise to a fractal.)

    A Sierpinski triangle fractal. Credit: Beojan Stanislaus/Wikimedia Commons, CC BY-SA 3.0

    For yet another example, random walks have a famously deep connection to resistor networks: electric circuits where a bunch of resistors are connected in some configuration, plus a power source and a grounding. Researchers have found that the effective voltage between any two points in the circuit is proportional to the time a random-walker would take to travel between those two points for the first time.

    A schematic diagram of an electrical circuit where the challenge is to determine the resistance to the flow of an electric current at each of the in-between nodes. Source: math.ucla.edu

    The resistor model speaks to a beautiful thing random walks bring to light: the influence an underlying structure exerts on a stochastic process — one governed entirely by chance — playing out on that structure, its inherent geometry imposing unexpected limits on the randomness and keeping it from wheeling away into chaos. At each step the random walk makes an unpredictable choice but the big picture in which these steps are individual strokes is a picture of predictability, to some degree at least.

    Flip this conclusion on its head and an even more captivating notion emerges: that though two random walks may resemble each other in their statistical properties, they can still be very different journeys.

  • Keeper of the foul air

    This city is essentially uninhabitable from November to January inclusive and barely liveable the rest of the year. Should it even remain the nation’s capital?

    I realise Shashi Tharoor is frustrated here — revealing the increasingly evident gap between what the Delhi and the Indian governments can do about air pollution and the scale of improvements on the ground — but Delhi should certainly remain the national capital. Changing this designation because the existing one has become nearly uninhabitable for four months out of 12 is to say the capitalhood of the city is the problem, not the pollution itself. Low hanging fruit but still.

    The country’s mainstream press has also been cynical enough to remember there’s an air pollution crisis only when Delhi’s air becomes patently foul, not the air in any other city. Ambient pollution in places like Guwahati and Katihar is also not concentrated in the winter months, although this isn’t to say Delhi’s air is better during the summer. If the national capital moves away from Delhi, the press spotlight will move with it, and rather than deal with Delhi’s pollution now, we’ll all deal with the new capital’s pollution a few years later.

    Then again Prime Minister Narendra Modi isn’t bound to go anywhere considering he just had a fancy new parliament built for himself.

  • Tamil Nadu’s lukewarm heatwave policy

    From ‘Tamil Nadu heatwave policy is only a start’, The Hindu, November 21, 2024:

    Estimates of a heatwave’s deadliness are typically based on the extent to which the ambient temperature deviates from the historical average at a specific location and the number of lives lost during and because of the heatwave. This is a tricky, even devious, combination as illustrated by the accompanying rider: “to the reasonable exclusion of other causes of hyperthermia”.

    A heatwave injures and/or kills by first pushing more vulnerable people over the edge; the less vulnerable are further down the line. The new policy is presumably designed to help the State catch those whose risk exposure the State has not been able to mitigate in time. However, the goal should be to altogether reduce the number of people requiring such catching. The policy lacks the instruments to guide the State toward this outcome.

  • Rule o flaw — part III

    Make sure you’ve read part I and part II.

    The project of demolishing the building opposite my house has taken a new turn. As part of the deal between me and my neighbours and the contractor, Monday, November 18, was his deadline to finish the part of the job that required the use of the offensively loud pneumatic jackhammers. The contractor was also to pause work on Sunday (November 17), which he didn’t: the workers didn’t use the jackhammers but continued working with sledgehammers and the much simpler electric drills.

    My neighbours and I also noticed the two tractors that powered the jackhammers were driven away on Sunday morning. We simply assumed the contractor had leased the equipment and was returning them for the day to avoid paying rent. However, the workers continued to demolish the building on Monday with sledgehammers and electric drills. (One of us went over but the contractor wasn’t on site.) The tractors didn’t return either.

    The situation continued into Tuesday. At this point we began to wonder if the article in The Hindu might have had anything to do with it. Late last week, after we’d lodged out complaint with the Tamil Nadu Pollution Control Board (TNPCB), I reached out to one of my colleagues at The Hindu asking if they could help expedite the board’s response. Apparently they did, and they also arranged for the noise complaints to be covered as a small item in the paper the next day (November 16).

    It wasn’t implausible that the people who made the work noisy in the first place decided to take a step back at this point and revert to more peaceable methods. A user named “Joseph” also posted an encouraging comment on the article: “If the TNPCB cannot take action on a complaint already received, then what is the drafted jurisprudence and responsibility of the TNPCB? Hope the lawmakers amend the defective law and permit the TNPCB to take suitable action against willful noise pollutors.”

    But my neighbours and I also began to feel guilty: if that bigwig at the other end of the road didn’t allow the contractor to use an excavator and we didn’t want him to use pneumatic jackhammers, were we condemning the workers the contractor had hired to slowly, painstakingly demolish the building with sledgehammers and electric drills over several weeks?

    Fortunately, Wednesday (November 20) dawned with good news for us as well as the workers: the contractor brought the excavator back. Unlikely though it may be, I’m tempted to think the article in The Hindu also spooked the bigwig. The excavator is currently parked on the front side of the building and we’re all excited for it to bring what remains of the structure down in a day or two.

  • The farm fires paradox

    From The Times of India on November 18, 2024:

    A curious claim by all means. The scientist, a Hiren Jethva at NASA Goddard, compared data from the Aqua, Suomi-NPP, and GEO-KOMPSAT 2A satellites and reported that the number of farm fires over North India and Pakistan had dropped whereas the aerosol optical depth — a proxy measure of the aerosol load in the atmosphere — has remained what it’s been over the last half decade or so. He interpreted this to suggest farmers could be burning paddy stubble after the Aqua and Suomi-NPP satellites had completed their overpass. GEO-KOMPSAT 2A is in a geostationary orbit so there’s no evading its gaze.

    The idea that farmers across the many paddy-growing states in North India collectively decided to postpone their fires to keep them out of the satellites’ sight seems preposterous. The The Times of India article has some experts towards the end saying this…

    … and I sort of agree because it’s in farmers’ interests for the satellites to see more of their fires so the national and state governments can give them better alternatives with better incentives.

    The farmers aren’t particularly keen on burning the stubble — they’re doing it because it’s what’s cheapest and quickest. It also matters that there is no surer path to national headlines than being one of the causes of air pollution in New Delhi, much more than dirtying the air in any other city in the country, and that both national and states’ governments have thus far failed to institute sustainable alternatives to burning the stubble. Taken together, if any farmers are looking for better alternatives, more farm fires seem to be the best way to put pressure on governments to do better.

    All this said, there may be a fallacy lurking in Jethva’s decision to interpret the timing change solely with respect to the overpass times of the two US satellites and not with any other factor. It’s amusing with a tinge of disappointment that the possibility of someone somewhere “educating” farmers to change their behaviour — and then them following suit en masse — was more within reach than the possibility of satellite data being flawed. If a fire burns in a farm and no satellite is around to see it, does it still produce smoke?

    As The Hindu reported:

    The data on fire counts are from a heat-sensing instrument on two American satellites — Suomi-NPP and NOAA-20 polar-orbiting satellites. Instruments on polar-orbiting satellites typically observe a wildfire at a given location a few times a day as they orbit the Earth, pole to pole. They pass over India from 1 p.m. to 2 p.m. …

    Other researchers also suggest that merely relying on fire counts from the polar satellites may be inadequate and newer satellite data parameters, such as estimating the actual extent of fields burned, may be a more accurate indicator of the true measure of stubble burning.

  • An infuriating editorial in Science

    I’m not just disappointed with an editorial published by the journal Science on November 14, I’m angry.

    Irrespective of whether the Republican Party in the US has shifted more or less rightward on specific issues, it has certainly shifted towards falsehoods on many of them. Party leaders, including Donald Trump, have been using everything from lazily inaccurate information to deliberately misleading messages to preserve conservative attitudes wherever that’s been the status quo and to stoke fear, confusion, uncertainty, and animosity where peace and good sense have thus far prevailed.

    Against this backdrop, which the COVID-19 pandemic revealed in all its glory, Science‘s editorial is headlined “Science is neither red nor blue”. (Whether this is a reference to the journal itself is immaterial.) Its author, Marcia McNutt, president of the US National Academy of Sciences (NAS), writes (emphasis added):

    … scientists need to better explain the norms and values of science to reinforce the notion—with the public and their elected representatives—that science, at its most basic, is apolitical. Careers of scientists advance when they improve upon, or show the errors in, the work of others, not by simply agreeing with prior work. Whether conservative or liberal, citizens ignore the nature of reality at their peril. A recent example is the increased death rate from COVID-19 (as much as 26% higher) in US regions where political leaders dismissed the science on the effectiveness of vaccines. Scientists should better explain the scientific process and what makes it so trustworthy, while more candidly acknowledging that science can only provide the best available evidence and cannot dictate what people should value. Science cannot say whether society should prioritize allocating river water for sustaining fish or for irrigating farms, but it can predict immediate and long-term outcomes of any allocation scheme. Science can also find solutions that avoid the zero-sum dilemma by finding conservation approaches to water management that benefit both fish and farms.

    Can anyone explain to me what the first portion in bold even means? Because I don’t want to assume a science administrator as accomplished as McNutt is able to ignore the narratives and scholarship roiling around the sociology of science at large or the cruel and relentless vitiation of scientific knowledge the first Trump administration practiced in particular. Even if the editorial’s purpose is to extend an olive branch to Trump et al., it’s bound to fail. If, say, a Republican leader makes a patently false claim in public, are we to believe an institution as influential as the NAS will not call it out for fear of being cast as “blue” in the public eye?

    The second portion in bold is slightly less ridiculous: “science can only provide the best available evidence and cannot dictate what people should value.” McNutt is creating a false impression here by failing to present the full picture. During a crisis, science has to be able to tell people what to value more or less rather than what to value at all. Crises create uncertainty whereas science creates knowledge that is free from bias (at least it can be). It offers a pillar to lean on while we figure out everything else. People should value these pillars.

    When a national government — in this case the government of one of the world’s most powerful countries — gives conspiracies and lies free reign, crises will be everywhere. If McNutt means to suggest these crises are so only insofar as the liberal order is faced with changes inimical to its sustenance, she will be confusing what is today the evidence-conspiracy divide for what was once, but is no longer, the conservative-liberal divide.

    As if to illustrate this point, she follows up with the third portion in bold: “Science cannot say whether society should prioritize allocating river water for sustaining fish or for irrigating farms, but it can predict immediate and long-term outcomes of any allocation scheme.” Her choice of example is clever because it’s also fallacious: it presents a difficult decision with two reasonable outcomes, ‘reasonable’ being the clincher. The political character of science-in-practice is rarely revealed in debates where reasonability is allowed through the front door and given the power to cast the decisive vote. This was almost never the case under the first Trump administration nor the parts of the Republican Party devoted to him (which I assume is the whole party now), where crazy* has had the final say.

    The choice McNutt should really have deliberated is “promoting the use of scientifically tested vaccines during a pandemic versus urging people to be cautious about these vaccines” or “increasing the stockpile of evidence-backed drugs and building social resilience versus hawking speculative ideas and demoralising science administrators”. When the choice is between irrigation for farms and water for fisheries, science can present the evidence and then watch. When the choice is between reason and bullshit, still advocating present-and-watch would be bullshit, too — i.e. science would be “red”.

    This is just my clumsy, anger-flecked take on what John Stuart Mill and many others recognised long past: “Bad men need nothing more to compass their ends than that good men should look on and do nothing.” But if McNutt would still rather push the line that what seem like “bad men” to me might be good men to others, she and the policies she influences will have committed themselves to the sort of moral relativism that could never be relevant to politics in practice, which in turn would be a blow for us all.


    (* My colloquialism for the policy of being in power for the sake of being in power, rather than to govern.)

  • Rule o flaw — part II

    Make sure you’ve read part I.

    On November 15, I lodged a complaint of excessive noise with the Tamil Nadu Pollution Control Board (TNPCB), whereupon I received an update saying the complaint was pending with the district environment engineer. Later the same evening, someone from the TNPCB called to say he was at the demolition spot and making inquiries. He called back 10 minutes later to say he’d spoken to the contractor and that the contractor had promised to wrap up work with the jackhammers next week.

    Funny thing is what the TNPCB caller had also said: that the contractor was caught between the guy (who’d chased the excavator away) and me, that I should empathise with the contractor and, “as a member of the public”, come to a mutually convenient agreement with him — and not, as I’d expected, ensure that the contractor switched to using sound-proofed equipment or make sure that the guy’s complaint drew further probing considering no other house in the neighbourhood was so rattled.

    Before he cut the call, the TNPCB caller said two more interesting things. First, the TNPCB was currently dealing with a similar but also “strange” complaint centred on Raman Street where people had complained not about the obnoxiously loud machines in use at a demolition site but that the workers there were working past 10 pm when they shouldn’t be. I wonder why this sounded “strange” to him. Second, he said if we wanted “more” action to be taken against the contractor, we’d have to approach the local body and the police, who may then contact the TNPCB for noise data and then decide whether and/or how to act on it.

    I’m sharing all this here in case this is useful to readers faced with loud demolitions in their neighbourhoods.