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.
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.