# Our economy keeps doubling in size. You won’t believe what happens next.

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Legend has it that a wise traveller once wondered into an Indian kingdom. Challenging the Sultan to a game of chess, he asked for an apparently pitiful reward were he to win: a single grain of rice, placed on the first square of the chessboard; two grains on the second square; four on the third; and so on, with the amount of rice placed on each square doubling all the way to the end of the board.

Baffled by his meagre request, the Sultan agreed. It was only when he lost and they began to calculate the wise man’s prize did he realise the gravity of his error. The extraordinary power of doubling meant that, by the time they had reached the 32nd square, the Sultan owed a debt of more than four billion grains of rice — and the second half of the board would see the damage spiral out of control.

The traveller’s little bet had cost the Sultan his empire. A thousand years of history felled by a moment of arrogance and the magnificent power of maths.

## Sultan, we have a problem

I’ve read this story, or variants of it, a dozen times. Each time, I wonder: at what exact moment did the Sultan feel the full weight of his mistake?

Let’s start by charting the amount of rice owed per square in ascending order:

It looks like not much happens until the last few squares. Then it goes berserk and our chessboard turns rice monster. Take a look at the scale on the chart. On the 64th square of the board, the amount of rice owed is nine billion billion.

That’s a lot of rice.

But, oddly, on the 56th square of the board, all looks pretty calm. So maybe the Sultan had to wait a long time to notice how bad things were for him.

Let’s scale back to the 56th square to see what’s going on.

Do not adjust your TV set. This really is what the rice ladder of doom looks like when you cut it off on square 56. Are you thinking what I’m thinking? It looks like the same chart!

But take a look again at the scale. Instead of measuring rice in billions of billions, we’re now in far safer territory — the debt on square 56 is just 36 million billion. Nearly a thousand times less bad. But let’s face it, pretty bad. It looks like the Sultan would have got his wake-up call long before he got anywhere near this part of the board.

But here’s the weird thing about exponential growth, that is growth which involves doubling at some regular interval. Wherever you start from, things get pretty wacky pretty fast.

Let’s go back to my original question: when did the Sultan first clock he was in schtook?

The chart below shows what the Sultan faced as they began counting out the wise traveller’s prize. It’s clear that, by the end of the second row, things were looking bad. Square 16 is the first time the rice would need to be measured by the bag.

But, in reality, I reckon the problem would have been obvious almost immediately. Although the Sultan could scarcely imagine that putting a single grain of rice on square 1 would cause such heartache, by square 4 he was looking at eight grains; by the end of the first row, 128 grains; and by the middle of the second row, it would have tipped over 1,000.

The power of doubling eats everything in its way with extraordinary speed.

One last thing before we leave the chessboard. How can it be that the right hand side of each chart dominates so dramatically over the rest? After all, the rice on every square of the board benefited equally from exponential growth.

This is where things get really amazing. Every time you move one square up, and double the amount of rice, the rice piled on the very last square is always greater than all the rice on every square that came before.

## Which square are we on?

And so to the economy. You might have guessed by now that the economy and that chessboard share one incredible feature: they both double with alarming regularity.

The economy, of course, doesn’t double every year. But growth of nearly 3% per year, the average for the world economy over the last 200 years, means the whole shebang gets twice as big every quarter century.

Doesn’t sound like a big deal… but then remember the chessboard. An economy that doubles every 25 years will double eight times in two centuries. Which is why the world’s output in the year 2000 was more than 200 times bigger than it was when Thomas Jefferson won the presidency and Napoleon crossed the Alps.

What does that kind of growth look like in the long run? Let’s take a look at the economic output of the whole world from 1 AD to the present day.

Holy macaroni! It’s the same chart as the rice and the chessboard.

OK, but let’s be sensible. Let’s start when the action really began — the start of the industrial revolution in 1750.

Wow, looks like those first 150 years were pretty boring. Though thinking back on the chessboard, I’m not sure it would have felt boring at the time.

## The changing change in the rate of change

One of the odd features of contemporary conversations is the constant refrain that “things are changing faster than ever”. Yet it seems like people said much the same thing 20 years ago, and 50 years ago, and 100 years ago.

And maybe that’s because they were right. With exponential growth, things are always changing at a faster pace (in absolute terms) than ever before.

In 1980, a 3% economic growth rate would have added about 19 trillion dollars to global economic output. The same growth in 2016 could have added nearly 70 trillion dollars, building on a much larger economic base. Yet back in 1900, that same growth rate would have meant just one more trillion for the world to consume.

So it’s as true today to say that the pace of change is accelerating as it was in 1980 and 1900. Wherever you stand, the numbers keep going up faster than they ever have before.

Where does that leave us now? What square of the chessboard do we find ourselves on as 2016 comes to an end?

We know that the rate of technological change has become thunderous. In one single year, 2016, Artificial Intelligence, drones, driverless cars, virtual and augmented reality, and reusable spaceship rocket boosters have all gone from lab to live product.

We also know that the power of doubling means the size of the economy is almost incomprehensibly bigger than it was in yesteryear. Remember that weird feature of the chessboard — that the amount of rice on any square was more than all the rice on every square before. Well, that’s true of our economy too.

In 2016, the output generated by factories and offices and service industries around the world exceeded, in this one year, all the output that mankind had ever produced in every year of our existence up to 1750. More than ten millennia of building pyramids and palaces, harvesting wheat and hunting deer, carving stone and laying bricks — all of it worth less than what we made in the last 365 days.

But can it carry on forever? Our ability to keep growing has been hotly debated. Some believe we will run into natural constraints, for example when we’ve used up too many resources. Others think technology will eventually surpass us, with existential consequences for our race.

If, somehow, we do manage to keep the wheels turning, this is what the 21st century might look like:

Everything we think is amazing. The change we perceive as exciting or terrifying. The sheer capacity of the human race to create. All of it will seem trivial in 2100.

Whether the robots take over or just hoody-sporting tech zillionaires, it’s going to be a wild ride.

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Harrow C'llr, lead on finance. Work in social investment on health & employment. Write in a personal capacity - all views (& errors) my own! Tweets @adamswersky