The mathematical insight which explains why lockdown might drag on

There's a reason Australia's Prime Minister Scott Morrison says his country's households may have to self-isolate for another six months.

It's the maths.

There's a mathematical law driving the growth in the number of coronavirus cases globally, which makes health experts so fearful.

Frustratingly, some of Australia's highest-paid commentators can't wrap their heads around it, which is why they're telling their listeners and readers the Government is overreacting by shuttering parts of the economy and enforcing strict social distancing measures for the winter.

The human brain wasn't built to think naturally about complicated mathematical phenomena. It's fine with basic maths, like simple percentages.

After a certain level of education, the brain intuitively understands that if you put $100 in a savings account with a 1 percent interest rate, you'll have $101 after a specific period.

But the brain can turn to mush when faced with more complicated problems, if it hasn't been taught how to think them through.

A famous example is the rice and chessboard problem.

If someone gave you a chessboard (which has 64 squares on it) and asked you to put one grain of rice on the first square, two grains of rice on the second square, four grains of rice on the third, eight grains on the fourth, and so on, how many grains of rice would end up on the 64th square?

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It sounds like an easy question - it's simply asking you to double the number of rice grains from one square to the next, from 1 grain to 2 to 4 to 8 to 16 to 32 to 64, and so on, until the 64th square.

What's the answer? You'd need 9,223,372,036,854,775,808 grains of rice for the 64th square.

That's nine quintillion, two hundred and twenty-three quadrillion, three hundred and seventy-two trillion, thirty-six billion, etc, grains.

And the amount of rice you'd need to cover the entire board - from squares 1 to 64 - would be 18.4 quintillion grains.

That's 923 times the entire estimated global production of rice this financial year.

The educational joy of that problem comes from the lesson that when something tiny begins expanding at a constant rate it can become mindbogglingly large within a surprisingly short amount of time.

It also reveals how the human brain struggles with the concept of exponential growth - it can't fathom how something growing slowly can suddenly explode in size.

That's the phenomenon driving the growth in the number of coronavirus cases globally, which is why the virus is so dangerous.

Fears for the US well founded

It's also why people can look foolish when they complain that authorities in Australia are overreacting.

The total number of new cases of the virus is currently doubling every six to seven days in Australia. It was previously doubling every three or four days, so means extreme efforts to slow the rate of contagion may be working.

But in the United States the situation is horrifying.

The total number of new cases there is doubling at a scary pace. According to the New York Times on Friday, the US death toll had grown six-fold in the previous eight days.

The healthcare system in some of its major cities is already at breaking point. New York is currently the country's ground zero, and the city's governor, Andrew Cuomo, says the city will run out of ventilators by the middle of this week.

They've built a field hospital in Central Park to cope with the overflow of critical patients.

A few weeks ago, President Donald Trump was still saying Democrats were overhyping the situation, claiming "this is their new hoax".

But now, a few weeks later, his administration admits 100,000 to 240,000 Americans will probably die from the virus - and that's its best-case scenario.

It demonstrates why an intuitive understanding of the maths of contagion is so important.

If you don't want a deadly virus to spread through a population to the point where it overwhelms your healthcare system and other institutions, it pays to try to slow the rate of growth in new cases as early as possible.

If you don't want your chessboard to start billowing grains of rice, you need to reduce the rate at which the rice is doubling.

Beware the 'second half of the chessboard'

In the late 1990s, the US inventor Ray Kurzweil wrote about the importance of the "second half of the chessboard", saying exponential growth is still crucial in the first half, but it's in the second half when growth appears to move into hyper-speed and the human mind gets overwhelmed.

Australia and New Zealand do not want to get anywhere near the second half of that board.

Australia's healthcare system, for example, has finite resources - a small number of hospitals, nurses, doctors, surgeons, and equipment - which is a deliberate policy choice.

If it had 50,000 more hospitals, millions more medical staff, and all the equipment we needed, we wouldn't have to worry. But it can only work with the system it's built.

For Morrison, if things go well in Australia and the country "flattens the curve" of transmission to the point where its healthcare system isn't overwhelmed and can crawl through the pandemic until a vaccine is discovered, he'll have to live with the fact that millions of Australians will believe he's wasted all that money - $AU213 billion ($NZ218b) in stimulus - and pushed the country into recession for nothing.

He's already acknowledged that.

It's similar to the problem former prime minister Kevin Rudd faced after he spent $AU67 billion ($NZ68.5b) to prevent Australia falling into recession during the global financial crisis.

But when it comes to financial markets, investors shrugged last week when a record 6.6 million Americans applied for unemployment benefits, with large parts of the US economy finally shutting down to impede the transmission of Covid-19.

It was the largest number of initial jobless claims in a single week in America's history, by a gigantic margin, but markets were more interested in Trump's claim that Saudi Arabia and Russia would soon be cutting oil production by 10 million barrels a day in a bid to stabilise oil prices.

Oil prices an unlikely beneficiary

Some of the investors who understand the maths of the pandemic, like the experts advising Morrison, have clearly accepted that we're in this for the long haul.

But others are grasping for any hint of good news.

The head of the International Energy Agency, Faith Birol, said on Friday if Saudi Arabia and Russia could agree to radical cuts in oil production it still wouldn't be enough to stop a huge build-up of oil inventories in the June quarter, because global efforts to prevent the coronavirus spreading have destroyed oil demand in an unprecedented way.

Now the world's major oil producers will be holding a 'virtual' emergency meeting on Monday to discuss possible production cuts, but will they be able to agree to a plan that puts a floor under oil prices for good?

Plenty of investors hope so, but they're likely clutching at straws.

Meanwhile, Australia's Reserve Bank is meeting this Tuesday to discuss interest rates. But what will they discuss? They've already cut the official cash rate to 0.25 per cent and RBA governor Philip Lowe's confirmed it will stay there for years.

It all depends on the maths of the coronavirus pandemic. From little things, big things grow.

- ABC

Read more about the Covid-19 coronavirus:

• See all RNZ Covid-19 news
• A timeline: How the coronavirus started, spread and stalled life in New Zealand
• Covid-19 symptoms: What they are and how they make you feel
• Touching your Face: Why do we do it and how to stop
• Scientific hand-washing advice to avoid infection
• Coronavirus: A glossary of terms
• The Coronavirus Podcast