A long struggle
Our struggle in grasping exponential growth is not new. According to a classic Indian legend from the sixth century AD, the Brahmin Sissa ibn Dahir, who invented the game of chess, presented it to King Shihram. The king was so impressed by its ingenuity that he offered to grant any reward to the inventor that he desired. The inventor humbly asked for one grain of rice on the first square of the chessboard, two grains on the second, four on the third, and so on, doubling the amount on each of the 64 squares. He wanted all the rice on the board. The king, amused by what appeared to be such a small request, readily agreed, only to discover the true consequence of the arrangement. As the grains doubled with each square, it soon surpassed all reasonable quantities, exceeding the entire rice supply of the kingdom long before the last square was reached. The exact number after 64 squares is 2 64 – 1, which equals 18 446 744 073 709 551 615. I remember calculating this number for my own amusement in primary school in the 1970s before we had computers; those actuarial genes were already lurking! This tale is most probably not historically true, but if the morbid consequences are to be believed, the Brahmin was summarily executed!
The king suffered from what psychologists call“ exponential growth bias”. A bias that is in all of us, including graduate professionals.
Another amusing example: Suppose a particular daily walk that you undertake( to the car or to get some coffee) involves 30 steps. How far could you go if each stride is double the previous one? The first four steps would take you 15 meters, assuming the first step is a meter: 1 + 2 + 4 + 8. How far would you go after thirty such super-steps? To Cape Town if you start in Johannesburg? To the UK? Well, you would travel around the Earth 26 times!
on delayed risks – we are quite skilled at tackling problems that impact us in the moment, but we are exceptionally poor at tackling much bigger problems that are still beyond the moment in the distant future. Scientists tell us that many systems might already be near vital tipping points, which could lead to irreversible environmental damage, yet we still fail to act decisively.
Another topical example is technological threats( artificial intelligence( AI) and cyber risk). Capabilities improve exponentially( think Moore’ s Law) and risks scale faster than regulation or controls can keep up with. Early impacts seem harmless or limited, but the ultimate impact can be massive, unpredictable and lead to huge social, ethical and security crises. Because we think linearly, we consistently underestimate how quickly such processes can escalate. This failure to think beyond the moment, especially in the face of exponential change, is not merely a cognitive weakness; it is a fundamental risk that threatens both individual well-being and the long-term stability of human societies.
Scaling beyond the imagination
Although a stretch, we can still apply our minds to a particular exponential growth problem. But there are many examples in mathematics where the scaling from one state to the next quickly grows beyond anything that we can humanly fathom, and in fact even beyond what supercomputers can calculate. One such example is the so-called Travelling Salesman problem, a classic problem that asks a
Defying instincts
The nature of exponential growth defies our gut instincts. And this exponential growth bias can have dire consequences. Whether in personal well-being and finances, or global challenges, the early stages of compounding appear insignificant, encouraging complacency and short-term thinking. Debt feels manageable until interest accelerates beyond control; unhealthy habits( poor diet, lack of exercise) seem harmless until they result in chronic disease; and environmental damage appears gradual until systems reach irreversible tipping points. Carbon emissions accumulate over decades and the early effects seem small. Humans struggle to act
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