Listen to the Maths: How teaching doubles encourages us to care for the world.

‘We Should Look After Our Own’ is a familiar echo heard from a range of people who get annoyed at efforts to support the poor in other countries. What about our own? Of course, but personally, I have never been able to differentiate need. From an early age, I was taught to care for the poor and look after my neighbour: lessons from a Catholic education, but by no means exclusive to it. Many consider this thinking as ‘soft’ at best and traitorous at worst. Still, the divine, also teaches us through science and maths, why it is prudent to look after everyone on the planet.


Image by Gerd Altmann from Pixabay

One of the ‘four pillars’ of number is the concept of doubling and halving. It is something we teach and lay the foundations for from the very start of primary school. It is a powerful thing. Carl Sagan (astrophysicist), in Billions and Billions, explains how repeated doubling, known as exponential increase or geometric progression, is an astounding and often misunderstood truth with lessons for our flourishing.

Life on Earth multiplies. From microscopic organisms to human beings, our reproduction rate has the potential to explode. Here are a couple of examples of how fast it can happen:

Sagan uses the story of the invention of Chess to illustrate. The game originated in Persia, the brainchild of one of the king’s aids. It quickly spread throughout the Eastern world and the king, delighted with it, granted his aid whatever he desired in reward. What he asks for shows how unsuited the natural thinking of the human brain is to bare mathematical truths. The aid, using the 8 x 8 (64 square) chessboard, asked for a grain of wheat, doubled by each square. That is one on the first, two on the second, four on the third, eight on the fourth and so on. The king, believing his aid to be too humble, pressed him to ask for more.

Here is, in truth, what the wily servant asked for. By the 64th square, there would be 18.5 quintillion grains.

18.5 quintillion grains! What the?! What even is a quintillion?

Our brains find it hard to visualise this, and it is why mathematical exponents were created. A quintillion is 10 to the power 18 – or ten multiplied by itself 18 times – 1 000 000 000 000 000 000. To help put this into perspective, if each grain of wheat was 1mm in size, the last pile of wheat would weigh 75 billion metric tonnes. Staggering. It is equivalent to 150 years of the world’s modern-day wheat production. (Sagan 1997). Not such a humble servant, after all!

The numbers are astounding. Personally, I find it scary that we go about our daily business with little clue of the potential impact exponential growth has for our planet. We think of ourselves as kings of our own reality, but in truth, we occupy a tiny space in the universe. Our recent experience of coronavirus has brought the idea of geometric progression (i e exponential increases) closer to home. Sagan illustrates further: if one bacteria weighed a trillionth of a gram, after a day of doubling, the collective weight would be as much as a mountain; after day and a half, the weight of the Earth; after two days, the weight of the sun. Incredible – no wonder certain viruses can dominate the globe so quickly.

Image by Gerd Altmann from Pixabay

In reality, however, an explosion in exponential growth does not always happen, even though the potential is there. A reduction in resources, poisons and maybe even the lack of privacy of living in too close quarters with your neighbour prevents this happening. But the growth will rise up again. There is something else, though, that slows exponential population growth for good.

The world is not black and white. Sometimes, we struggle to make sense of things, and have to admit; things do not always make sense. Paradoxes are hard to get the head around. Many have argued that natural disasters, wars, natural selection, famine, disease are ways the Earth manages the exploding population. (In 1997, 247K more people were born a day than died – today it is higher). What science has found is that exponential reproductive growth stops, not when people are killed off, but when a steady-state is reached – when resources are balanced.

Some countries, such as America and Russia, have almost reached zero population growth (ZPG). About the same number of people are born to the number of people who die. The link? The number of births reduces as the number of people in extreme poverty lowers. Equality is key. ‘The Spirit Level: Why More Equal Societies Almost Always Do Better’ by Kate Pickett and Richard Wilkinson makes the same argument. Surprisingly, (or perhaps not, given these strange times), this book isn’t all that well known. 

So, we can look after our own?

No. We share our planet. We can’t live upstairs with the kitchen on fire.

In 1997, Carl Sagan predicted that the world population was set to double every 40 years. Back then, we were at 6 billion. Today, we are infringing on 8 billion. Although separate countries can almost reach ZPG, the overall exponential growth of the human race is easily tipped by other countries. Our neighbours. Our common home.

Reducing global poverty reduces exponential growth in our world population. The best of ancient wisdom, religion, faith, social contract – whatever you want to call it – has always taught collaboration and compassion over competition and ‘each for themselves’. Survival of the fittest is largely misunderstood.

There is also a link between quality education of the masses and poverty—something to ponder. And something, as an educator, I have always felt. I’ll save that for another blog.

We can’t just ‘take care of our own’. It is more than our moral duty; it is our only chance of long term survival.

If you can’t listen to your heart, listen to the maths.

Who would have thought teaching doubles to four-year-olds had the potential to save the world?

Image by Gordon Johnson from Pixabay

Leave a Reply