Go Figure: What can 72 tell us about life?

The number 72

Is 72 the answer to life, the universe and everything? It's definitely the answer to a few economic questions, says Michael Blastland in his regular column.

You know the joke from The Hitchhikers Guide to the Galaxy in which the answer to the ultimate question about life, the universe and everything is 42?

It was a typo. Should have been 72. The author, Douglas Adams, was secretly an economist and statistician who pretended to be a sci-fi writer of comic brilliance to hide his shame. Possibly.

So, 72. Why 72? The rule of 72 is derived, approximately, from 100 times the natural logarithm of 2. But you don't have to worry about where it comes from, only that it works reasonably well.

The rule of 72 helps clarify half the serious economic issues of the day. Compared with a famous joke, this is a dull practicality. But boy it's one really useful dull practicality.

The rule of 72 helps reveal the full effects of change. What it particularly shows is how repeated small changes can blow up.

For example, we're worried at the moment about inflation. How long before inflation, of say 6% a year, halves the real value of your savings? Easy - take 72 and divide it by six. The answer is 12, twelve years before £1,000 under the mattress dribbles into purchasing power worth £500.

Another example. We're also worried about economic growth or growth we're missing while we struggle to rouse ourselves after recession. How long before economic growth of say 2.5% a year would make us collectively twice as rich? Take 72 and divide it by 2.5. The answer is 29, about 29 years at this rate to double the size of the economy.

graphic

The chart shows the difference that just 0.5% a year would make over a lifetime to growth in income per head in the UK. Beginning by taking a random round income of £25,000 today, it projects continuous real growth of 2% and 2.5%.

The 2% line is striking, ending at about £120,000 a year, but the effect of that extra 0.5% - worth about another £60,000 by the end - is even more so. This is not inflation, this is real money after inflation if - and I mean if - we achieve 2% or 2.5% real growth.

Since World War II, the national income per head has indeed roughly doubled twice. We are collectively about four times richer.

Another example. We're worried about depleting resources. If you want to know how much oil we'd be using if global consumption rose by, oh let's say a mere 2% a year, divide 72 by two. That's about 36 years before consumption would double. So if you think demand creates pressures now...

It's easy to underestimate the speed at which small changes add up. The rule of 72 spells it out. It shows that what often really matters are not one-off big numbers but small numbers that go on.

The rule of 72 also helps show how we could fix the national debt - pronto - if inclined.

Let's say there's 5.5% inflation - not far off the retail price index today - and 2.5% GDP growth, which is about what we hope for. Together that's an 8% change in the amount of money in the economy each year. So divide 72 by eight. The answer is nine. Nine years at those rates of growth and inflation would halve the value of the national debt as a share of national income. Bingo?

Maybe. Though playing with inflation isn't a great idea. And it could be said that this means fleecing people of the value of what they've lent us. It also depends on not adding to the stock of debt in the meantime, which is - how shall we put it - somewhat unlikely.

Money Small amounts of cash can grow into big problems

These are all examples of exponential or continuous and steady change. It was once said - a tad hyperbolically - that the greatest shortcoming of the human race was the inability to understand the exponential function.

A corollary is that if oil consumption did grow steadily every year, the amount consumed in the doubling period would be greater than all the oil consumed so far in human history.

If GDP did double every 29 years, then the national product would be greater in that period than the entire GDP of the UK so far - all years added together.

All this helps to show why some argue that long-term growth is just about everything, for good or ill - at least in economics, if not the universe.

But there's a problem with the rule of 72 that Douglas Adams would have loved. It's the wrong number. That is, it's not accurate.

If you want accuracy, better to use 70 or even 69. Those who favour 72 say it's only meant as a rough guide anyway and the great advantage is that 72 divides neatly by 2, 4, 6, 8 and 12, so most of the arithmetic is easier than with 69.

Either way, the insight stands. Watch out for that small stuff. It grows.

By the way, there's another useful animated graphic and map from the ONS You Tube this week. It shows how jobs in the West Midlands were most clobbered by recession, tallying with the damage to manufacturing.

Other ONS data has suggested the pain in the West Midlands even shows up in suicide figures. These ONS podcasts simplify the stats, some tell a good story of cause and effect, and they are well worth a look.

Send your answers using the form below.

The rule of 72 is just proof that economists are lazy, and also don't understand Douglas Adams. The formula quoted works out as 69.3 if the percentage is small, but it's not a difficult bit of maths to just work it out properly. (It's ln 2 over ln(1+x)). It's presented as some magical thing, but you could just as easily have a rule of 42 for making things "half as big again".

John Bates, Leeds

"The greatest shortcoming of the human race is our inability to understand the exponential function." Albert Bartlett. If this article has grabbed your attention then please check out the transcript of one of his excellent talks. It's an incredibly important topic in the modern world! Far from boring in its application, if only more people had thought about it we probably wouldn't be struggling with all this debt.

Bob Jones, London

Interesting article, but I find this comment confuses the issue: "These are all examples of exponential or continuous and steady change". I don't view "exponential" change as steady change. Steady change is an quantity changing by the same absolute amount in a given time interval. E.g. my tree grows by 5cm each year. Exponential change is change where the quantity changes by a proportion in the time period, e.g. my tree grows by 5% each year. This is what confuses people because as time goes on 5% of the tree becomes larger and larger.

Robery King, Geneva, Switzerland

72 of course only works for cumulative percentages you wish to double or halve. But if you use the same base that Douglas Adams used for 42 then your 72 is written 57. Have we just discovered the real reason for the success of Heinz?

Richard Gilby, Tequisquiapan, Mexico

What a waste of words just to tell us that exp(x) is approximated by 1+x for small values of x. Leonhard Euler in the 18th century knew this - and used it.

Amos Wittenberg, London

Actually the answer isn't a number, it's a sequence, the Fibonacci sequence (0,1,1,2,3,5 etc always adding the two numbers before it) to be precise.This "golden ratio" governs things as diverse as economic trends, the pattern of seeds on a sunflower head, even the proportions of the human body.

Sam, Brighton, UK

"The rule of 72 helps clarify half the serious economic issues of the day. Compared with a famous joke, this is a dull practicality. But boy it's one really useful dull practicality." Rather over-egged, don't you think? All those examples are different applications of the same equation. Basically telling us that rate of growth covers half of the serious economic issues of the day? Perhaps economics isn't as complicated as I thought then.

Walders, Nottingham

I noticed this phenomenon some time ago (using 70) but haven't been able to figure out why it works. Can anyone explain? It doesn't work so well with higher inlation rates (20% and above).

Bill Willoughby, St Ives, Cambridgeshire

As long as we use the same rule of thumb, we can make comparisons. But as the oil example shows, some things can't keep growing. Can real GDP keep increasing if the resources it depends on are limited? It's hard to avoid the feeling that the supply of money isn't limited, and not only will we eventually see Million-Pound notes, but tiny copper coins of the same value.

Dave Bell, Barnetby, N. Lincs

Today's oil driven society is driven by the price of a barrel of oil. But what is a barrel of oil? Answer: 42 US gallons (approx 160 litres) - so 42 really is the answer to life, the universe and everything.

Clive, Nottingham

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