Homo sapiens – Close Read

A future obscured by exponential growth

A couple months into the COVID-19 pandemic, I think most of us realised how hard it is to comprehend the phenomenon of exponential growth. Mathematically, it’s trivial – a geometric progression – but more physically, the difference between linear and exponential growth is very non-trivial, as a cause-effect chain where each effect leads to multiple new cases according to a fixed growth ratio. The effect is an inability to fully anticipate future outcomes – to prepare mentally for the ‘speed’ with which an exponential series can scale up – rendered remarkable by us not having planned for it.

For example, the rice and chessboard problem is a wonderful story to tell because it’s hard for most people to see the punchline coming. To quote from Wikipedia: “If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?” The answer is 18,446,744,073,709,551,615 – a 100-million-times greater than the number of stars in the Milky Way. Many people I know have become benumbed by the scale of India’s COVID-19 epidemic, which zipped from 86k active cases on May 30 to 545k on July 31, and from 1M total cases on July 17 to 7.3M on October 15. On August 1, 1965, Vikram Sarabhai delivered the convocation address at IIT Madras, which included the following quip:

Everyone here is undoubtedly familiar with the expression ‘three raised to the power of eighteen’. It is a large number: 38,74,20,489, thirty-eight crore, seventy-four lakh, twenty thousand, four hundred and eighty-nine. What it means in dynamic terms is quite dramatic. If a person spreads gossip to just three others and the same is passed on by each of them to three others, and so on in succession, in just eighteen steps almost the entire population of India would share the spicy story.

Because of its mathematical triviality and physical non-triviality, I think we have a tendency to abstract away our impression of exponential growth – to banish it out of our imagination and lock it away into mathematical equations, such that we plug in some numbers and extract the answers without being able to immediately, intuitively, visualise or comprehend the magnitude of change, the delta as it were, in any other sense-based or emotional way. And by doing so, we are constantly surprised by the delta every time we’re confronted with it. Say the COVID-19 epidemic in India had a basic reproductive number of 1.4, and that everyone was familiar with this figure. But simply knowing this value, and the fundamental structure of a geometric progression, doesn’t prepare people for the answer. They know it’s not supposed to be N after N steps, but they’re typically not prepared for the magnitude of 1.4^N either.

I recently came across a physical manifestation of this phenomenon in a different arena – technology – through a Twitter account. The oldest Homo sapiens technologies include fire, tool-making, wheels and cropping. But while the recursive application of these technologies alone may have given rise, in a millennium (i.e. 1,000 steps), to, say, a subsistence agriculture economy with some trade, that’s not what happened. Instead, two other things did (extremely broadly speaking): the technologies cut down the time required for different processes, and which subsequently came to be occupied by the application of these technologies to solve other problems. The geometric-like progression that followed exponentiated not the technologies themselves but these two principles, of sorts, rapidly opening up new methods and opportunities to extract value from our surroundings, and eventually from ourselves, to add to the globalising value chain.

To get a quick sense of the rapidity of this progress, check out @MachinePix on Twitter. Their latest tweet (as of 11 am on October 17) describes a machine that provides a “motion-compensated” gangway for workers moving between a ship and an offshore wind turbine; many others depict ingenious contraptions ranging from joyously simple to elegantly complicated – from tape-dispensers and trains windows that auto-tint to automated food-packaging and super-scoopers. There’s even a face-mask gun that seems to deliver an amount of pain suitable for anti-maskers.

But closer to the point of this discussion: taken together, @MachinePix’s tweets demonstrate the extent to which we have simplified and/or automated different processes, and the amount of time humans have collectively saved as a result. This, again, can’t be a straightforward calculation: we don’t just apply the same technologies over and over to perform the same tasks. We also apply technologies to each other to compound or even modify their effects, effectively leading to new technologies and, thus, new applications – from the level of toothbrush plus toothpaste to liquefaction plus rocket engines. The tools we develop also alter the structure of society, which in turn changes aspirations and leads to the birth of yet more technologies, but ordered along different priorities.

In the last few months, I learnt many of these features in an intimate way through Factorio, a video-game that released earlier this year. The premise is that your spaceship has crashed on an alien planet, with many of the same natural resources as Earth. You now need to work your way through a variety of technologies and industrial systems and ultimately build a rocket, and launch yourself off to Earth. The ‘engine’ at the game’s centre, the thing that drives your progress, is a recipe-based manufacturing system. You mine resources, process them into different products, combine them to make components, and combine the components to make machines. The machines automate some or all of these processes to make more sophisticated machines and robots, and so forth. To move objects, you use different kinds of inserters and conveyor belts; for fluids – from water to lubricant – there are pipes, tanks, even fluid wagons attached to trains.

A zoomed-out scene from Factorio. This is ‘Main Station’, one of five bases I operate in this scenario.

I’m still finding my way around the extent of the game; the technology tree is very high and has scores of branches. The scenario I’m currently playing goes beyond a rocket to using satellites, but doesn’t include the planet’s alien creatures, who attack your base if you antagonise them or pollute too much. I often think it would’ve been much better to allow final-year students of mechanical engineering (which I studied) to play this game instead of making them sit through hours of boring lectures on logistics, quality control, operations research, supply-chain management, etc. Factorio doesn’t set out to teach you these things but that’s what you learn – and on the way, you also discover how easy it is for things to get out of control, become too complicated, too chaotic – sometimes just too big to fail.

Sometimes, you’ve invested so much in developing one technology that you’re unable to back out, and you start to disprivilege other ambitions in favour of this one. This happened to me recently: being hell-bent on building nuclear reactors to keep up with the demand for power, I had to give up on building a satellite.

Instead of a linear or even a tree-like model of technology development, imagine a circular one: at the centre is the origin, and the circumference is where you are, the present (it’s not a single point in space-time; it’s multiple points in space at one time). Technologies emerge from the origin and branch out towards the perimeter in increasingly intricate branches. By the time they’ve reached the outer limits, to where you are, you have nuclear power, rocketry, robotic construction networks and high-grade weapons. But in this exponentially interconnected world, what do you change and where to effect a difference somewhere else? And how can you hope to be sure there won’t be any other effects?

My new favourite example of this, from the few-score @MachinePix tweets I’ve scrolled through thus far, is the rotary screen printer. It shows, among many other things, that there’s a second way in which exponential growth disrupts our ability to predict its outcomes. Could a fantasy writer working all those millennia ago have predicted this device’s existence? They may have, they may have not, just as we contemplate what the future might look like from today, but sometimes presume to anticipate – even though we really can’t – the full breadth of what lies in store for humankind. Can we even say if the rotary screen printer will still be around?

Featured image: An artist’s rendering of spaceships hovering above a city. More importantly, this image belongs to a genre quite popular in the 2000s, perhaps the late 1990s too, when image-editing software wasn’t as versatile as it is today and when the internet was only just beginning to democratise access to literature and videos, among other things, so the most common idea of first contact looked a lot like this. Credit: Javier Rodriguez/pixabay.

On India’s path to community transmission

There’s a virus out there among many, many viruses that’s caught the world’s attention. This virus came into existence somewhere else, it doesn’t matter where, and developed a mutation at some point that allowed it to do what it needs to do inside the body of one specific kind of animal: Homo sapiens. And once it enters one Homo sapiens, it takes advantage of its new surroundings to produce more copies of itself. Then, its offspring wait for the animal to cough or sneeze – acts originally designed to expel irritating substances – to exit their current home and hopefully enter a new one. There, these viruses go through the same cycle of reproduction and expulsion, and so forth.

This way, the virus has infected over 210,000 people in the last hundred days or so. Some people’s bodies have been so invaded by the virus that their immune systems weren’t able to fight it off, and they – nearly 9,000 of them – succumbed to it.

Thus far, the virus has reportedly invaded the bodies of at least 282 people in India. There’s no telling how the virus will dissipate through the rest of the population – if it needs to – except by catching people who have the virus early, separating them from the rest of the population for long enough to ensure they don’t have and/or transmit the virus or, if they do, providing additional treatment, and finally reintegrating them with the general population.

But as the virus spreads among more and more people, it’s going to become harder and harder to tell how every single new patient got their particular infection. Ultimately, a situation is going to arise wherein too many people have the virus for public-health officials to be able to say how exactly the virus got to them. The WHO calls this phase ‘community transmission’.

India is a country of over 1.3 billion people, and is currently on the cusp of what the Indian Council of Medical Research (ICMR) has called ‘stage 3’ – the advent of community transmission. It’s impossible to expect a developing country as big and as densely populated as India to begin testing all 1.3 billion Indians for the virus as soon as there is news of the virus having entered the national border because the resource cost required to undertake such an exercise is extremely high, well beyond what India can generally afford. However, this doesn’t mean Indians are screwed.

Instead of testing every Indian, ICMR took a different route. Consider the following example: there’s a population of red flecks randomly interspersed with yellow flecks. You need to choose a small subset of flecks from this grid (shown below) such that checking for the number of yellow flecks in the subset gives you a reliable idea of the number of yellow flecks overall.

The ideal subset would be the whole set, of course, so there is one more catch: you have a fixed amount of money to figure out the correct answer (as well as for a bunch of other activities), so it’s in your best interests to keep the subset as small as possible. In effect, you need to balance the tension between two important demands: getting to a more accurate answer while spending less.

Similarly, ICMR assumed that the virus is randomly distributed in the Indian population, and decided to divide the population into different groups, for example by their relative proximity to a testing centre. That is, each testing centre would correspond to the group of all people who live closer to that testing centre than any other. Then, ICMR would pick a certain number of people from each group, collect their nasal and throat samples and send it to the corresponding labs for tests.

Say group size equals 100. For a Bernoulli random variable with unknown probability p, if no events occur in n independent trials, the maximum value of p (at 95% confidence) is approximately 3/n. In our case, n = 100 and p at 95% confidence is 3/100, which is 3%. Since this is the upper bound, it means less than 3% of the population has the ‘event’ which didn’t occur in n trials – which in our case is the event of ‘testing positive’. Do note, this is what is safe to say; it’s not what may actually be happening on the ground. So by increasing the sample size n as much as possible, ICMR can ascertain with higher and higher confidence as to whether the corresponding group has community transmission or not.

Thus far, ICMR has said there is no community transmission in India based on these calculations. Independent experts have been reluctant to take its word, however, because while ICMR has publicised what the sample size and the number of positives are, there is very little information about two other things.

First: we don’t know how ICMR selected the samples that it did for testing. While the virus’s distribution in the population can be considered to be random, especially if community transmission is said to have commenced, the selection of samples needs to have an underlying logic. What is that logic?

Second: we don’t know the group sizes. It’s important for the sample size to be proportionate to the group size. So without knowing what the group size underlying each sample is, it becomes impossible to tell if ICMR is doing its job right.

On March 17, one ICMR scientist said that some testing centres had admitted fewer people with COVID-19-like symptoms and the source of whose infections was unknown (i.e. community transmission) than the size of the sample chosen from their corresponding group. She was suggesting that ICMR’s choice of samples from each group was large enough to not overlook community transmission. To translate in terms of the example above: she was saying ICMR’s subset size was big enough to catch at least one yellow fleck – and didn’t.

As it happens, on March 20, ICMR announced that it would begin testing for a potential type of community-transmission cases even though its sampling exercise had produced 1,020 negative results in 1,020 samples (distributed across 51 testing centres).

The reasons for this are yet unclear but suggests that ICMR suspects there is community transmission of the virus in the country even though its methods – which ICMR has always stood by – haven’t found evidence of such transmission. This in turn prompts the following question: why not test for all types of community transmission? The answer is the same as before: ICMR has limited resources but at the same time has been tasked with discovering how many yellow flecks are there in the total population.

The virus is not an intelligent creature. In fact, it’s extremely primitive. Each virus is in its essence a packet of chemical reactions, and when each reaction happens depends on a combination of internal and external conditions. Other than this, the virus does not harbour any intentions or aspirations. It simply responds to stimuli that it cannot manipulate or affect in any way.

The overarching implication is that beyond how good the virus is at spreading from person to person, a pandemic is what it is because of human interactions, and because of human adaptation and mitigation systems. And as more and more people get infected, and their groups verge towards the WHO’s definition of ‘community transmission’, the virus’s path through the population becomes less and less obvious, but at the same time a greater depth of transmission opens the path to better epidemiological modelling.

When such transmission happens in a country like India, the body responsible for keeping the people safe – whether the Union health ministry, ICMR or any other entity – faces the same challenge that ICMR did. This is also why direct comparisons of India’s and South Korea’s testing strategies are difficult to justify, especially of the number of people tested per million: India has nearly 26-times as many people but spends 11.5-times less on healthcare per capita.

At the same time, ICMR isn’t making it easy for anyone – least of all itself – when it doesn’t communicate properly, and leaves itself open to criticism, which in turn chips away at its authority and trustworthiness in a time as testing as this. Demonetisation taught us very well that a strategy is only as good as its implementation.

But on the flip side, it wouldn’t be amiss to make a distinction here: between testing enough to get a sense of the virus’s prevalence in the population – in order to guide further action and policy – and the fact that the low expenditure on public healthcare is always going to incentivise India to skew towards a sampling strategy instead of an alternative that requires mass-testing. ICMR and the Union health ministry haven’t inspired confidence on the first count but it’s important to ensure criticism of the former doesn’t spillover into criticism of the latter as well.

Anyway, the corresponding sampling strategy is going to have to be based on a logic. Why? Because while the resources for the virus to spread exist abundantly in nature (in the form of humans), the human response to containing the spread requires resources that humans find hard to get. Against the background of this disparity, sampling, testing and treatment logics – such as Italy’s brutal triaging policy – help us choose better sampling strategies; predict approximately how many people will need to be quarantined in the near future; prepare our medical supplies; recruit the requisite number of health workers; stockpile important drugs; prepare for economic losses; issue rules of social conduct for the people; and so forth.

A logic could even help anticipate (or perpetuate, depending on your appetite for cynicism) ‘leakages’ arising due to, say, caste or class issues. Think of it like trying to draw a circle with only straight lines of a fixed length: with 200 strokes, you could technically draw a polygon with 200 sides that looks approximately like a circle – but it will still have some discernible edges and vertices that won’t exactly map on a circle, leaving a small part of the latter out. Similarly, using a properly designed technique that can predict which person might get infected and who might not can still catch a large number of people – but the technique won’t catch all of them.

One obvious way to significantly improve the technique’s efficacy as it stands is to account for the fact that more than half of all Indians are treated at private hospitals whereas you can be tested for COVID-19 only at a government facility, and not all VRDLs receive samples from all private hospitals in their respective areas.

Ultimately, the officials who devise the logics must be expected to justify how the combination of all logics can – even if only on paper – uncover most, if not all, cases of the virus’s infection in India.