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Big numbers and strategies that count – with Andrew Elliott

The human brain is not wired to cope with big numbers so, argues author Andrew Elliott, we should look to identify strategies to help cut all the millions, billions and trillions down to size

16/08/2021

Juan Torres Rodriguez

Juan Torres Rodriguez

Fund Manager, Equity Value

Roberta Barr

Roberta Barr

Head of Value ESG Analyst

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How many zeros are there in a billion? In a trillion? In a googol? If you answered the last one immediately – a googol is a one followed by 100 zeros – you are probably an academic or a trivia buff. If you replied nine and 12 to the first two questions without thinking, however, you are still in pretty rarefied company – as our latest guest on The Value Perspective podcast makes clear, the human brain is not wired to cope with big numbers.

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“There is no shame in not intuitively understanding big numbers,” says Andrew Elliott, the author of What are the Chances of That? and, appropriately enough given where our conversation has led, Is That a Big Number?. “Our brains are made up of organic matter, not microchips, and our ability to directly perceive numbers is extremely limited – more limited than you probably would imagine.”

According to Elliott, humans can intuitively assimilate and understand numbers up to three or four but then it gets tricky. “Throw three beans on the table and I can tell it is three beans and not two or four without counting them,” he explains. “If they are arranged in a pattern, I can do a bit better – for example, if I throw a dice, I can spot a six is a six without counting the dots, because I know and recognise the pattern.

“At some point, however, I need to start counting the beans on the table. Still, that is easy enough – we learned how to count as children and we go up step by step – but, again, there comes a point where counting one by one ‘runs out’. I would say that happens somewhere in the high hundreds going into the 1000s, where it stops being something practical to do and you start needing to take other approaches.”

A bank teller will bundle set numbers of notes together and start counting those, for example, and television cameras show something similar happening with piles of ballot papers on election day. “It is my belief that, for most of us, our ability directly or intuitively to understand numbers runs out at around 1000, which in the scheme of things is quite a small number,” Elliott continues. “So then we start developing strategies.”

Effective strategies

Elliott considers a number of these strategies in Is That a Big Number?, including scientific notification. Here 900 billion – a number he picks as an official 2021 estimate of UK government spending in pounds – would be set out as nine times 10 to the power of 11, or 9 × 1011. “That is a very common and effective strategy and one that scientists would be very comfortable and fluent working with,” he adds.

“On the other hand, you are not going to have a radio newscaster announcing, ‘UK government spending this year will be nine times 10 to the 11 pounds – that is a quick way to lose 90% of your audience. And so instead they will say ‘900 billion pounds’ – and we are straight back to the problem of having to stop and think hard about millions and billions and so on.”

An alternative strategy, Elliott suggests, is to break a big number down by comparing it with something else – so, for example, dividing £900bn by the UK’s 67 million population works out at roughly £13,500 of spending per person, or about £37 per person per day. “Breaking big numbers down like this can help us reach the point where we can make meaningful comparisons,” he explains.

“When they see the title of my book, Is That a Big Number?, some people immediately ask, ‘Compared to what?’ – but that is the crux of the matter. You have to find things to compare numbers to because then you can start making informed judgements – you can compare this year’s UK government spending with previous years or spending per head in the UK with that in the US or France or wherever.

“You cannot look at big numbers in isolation. Mount Everest is 8,849m high – almost nine kilometres – which is huge if you a mountaineer but a 10-minute drive in the country if it is laid on its side. You have to have a strategy to bring a big number down to something comprehensible and, once you have a basis for making a comparison, you can start understanding – is this really a big number or not?”

Author

Juan Torres Rodriguez

Juan Torres Rodriguez

Fund Manager, Equity Value

I joined Schroders in January 2017 as a member of the Global Value Investment team and manage Emerging Market Value. Prior to joining Schroders I worked for the Global Emerging Markets value and income funds at Pictet Asset Management with responsibility over different sectors, among those Consumer, Telecoms and Utilities. Before joining Pictet, I was a member of the Customs Solution Group at HOLT Credit Suisse.  

Roberta Barr

Roberta Barr

Head of Value ESG Analyst

I am an investment analyst for the Global Value Team, having joined Schroders in 2016 as part of the graduate programme. After spending a year as an investment analyst for the Quantitative Equity Products team, I realised my affinity for the deep value investment mindset and joined the Global Value Team in 2017 and manage Global Sustainable Value. Prior to working for Schroders, I studied mathematics at Oxford University.

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