Measuring

“Les chiffres sont les signes de Dieu”—Statistics are signs from God—is attributed to Prior Roger Schultz of Taize. It’s interesting that this is in the plural: a single number, existing on its own, does not tell us the whole story. Considering multiple ways of measuring a fact can give us more insight into what the signpost is telling us—if we take the time to do so.

The number itself is obviously the first and foremost piece of information. Three questions immediately arise: is the number truthful—is it accurate—is it precise?

  • In most cases that I run into, numbers do not represent intentional deceptions. Nevertheless, “trust, but verify” is a good axiom to consider at the foundations of data gathering.
  • Accuracy speaks to the question of error more than the question of deception. In my experience, small samples and bad math bring about far more faulty conclusions than deceptions ever do. As CS Lewis once noted, there are many answers to, “1+1=?”, but some are close to the right answer than others.
  • Finally, a question of precision—a number can be truthful and accurate while being imprecise. It is equally correct to say that the world has 7.8 billion people, or 7,875 million people, or, “we estimate that as of mid-2021, the world has 7,875,465,000 people.” Numbers given to the last digit can present an inaccurate impression of their precision; this is especially true of numbers (like population totals) which frequently change.


The context of the number is the first way of getting at the complexities of a situation. It’s a mistake to look at numerators without denominators. Many an article is written about China’s having more of _x_ than any other country: this is to be expected, when China has vastly more people than nearly any other country (though, of course, India is almost overtaking China in this regard).

Consider the size of the church in China. There are various estimates about the size of the church, but most cluster around ’140 million.’ There are more Christians in China than there are people in 200+ of the world’s countries: in fact, only 9 countries have more than 140 million people (China, India, the United States, Indonesia, Pakistan, Nigeria, Brazil, Bangladesh, and Russia). However, those 140 million believers represent about 10% of China’s total population. That is the context. While the number is large, it is not necessarily as influential as it would be elsewhere.

While a fraction can tell us something about the role of a number in its wider context, speed of growth tells us whether that role is increasing or shrinking. An annual growth rate (AGR) is fairly easy to compute. My formula is for calculating AGR as a percentage is: 

( (Pop. Present / Pop. Past) ^ (1/period of time—eg number of years) ) – 1

The point of an AGR is to consider the future influence of a number. For example, if you are driving at 20 miles per hour, you know something about your speed at the moment. If the speed limit is 60 miles per hour, you know something about your context. If your speed is increasing at a rate of an additional 5 miles per hour per second, you know that in eight seconds you will either have to slack off that rate of growth, or be increasingly in trouble should a police officer happen along.

In a population setting, one helpful measure is to compare the annual growth rate of a given population to that of the general population of the country it’s in. For example, globally, the total population of the world is increasing at 1.19% per annum. The ‘global north’ is increasing at an AGR of 0.1%, while the ‘global south’ is increasing at 1.82%. Thus we know that the global population is shifting in ‘favor’ of the global south. 

Perhaps more of interest, ‘religionists’ of all varieties are growing at a rate of 1.29% per year; this means the world is growing more religious, not less. Christians are growing at 1.18% per year, Muslims at 1.92%, and Hindus at 1.28%.

But this brings up another point. We could tell a fairly ominous (for us) story: “The world is getting more Islamic!” But this ignores two complexities that we must pay attention to.

First, no single factor – the number, the context, or the rate of growth – should be used in isolation. For example, while Islam has a higher AGR, the actual number of people being added to its population total as a result is smaller than the number added to Christianity, because Islam is a slightly smaller religion.

Christianity has 2.5 billion people today, will probably have 2.6 billion in 2025, and 3.4b in 2050.
Islam has 1.9 billion today, 2.0 billion in 2025, and 2.8 billion in 2050.
Islam is growing faster, but by this estimate will not overtake Christianity by 2050.
As a percentage the world is growing more Islamic.
In absolute numbers, the world will not be majority Islamic.

Second, the numbers cited just above bring us to a fourth complexity: change of speed of the speed of growth.

To use our speed example, let’s say you’re driving along at 20 miles per hour, and you’re pushing down or letting up on the accelerator to stay right around that speed. Then you merge on to a highway. The highway’s speed limit is 75 (here in Texas). So, of course, you push the accelerator down, and you change the speed of your speed of growth—accelerating toward 75. You have a zippy little car, and so you reach 75 within a matter of seconds—and then what do you do? You let up on the accelerator in order to stay at that constant speed.

Just because a population is growing—even rapidly—today, does not mean it will continue to do so forever. You can see some of the variations of speed between Christianity and Islam above. The larger a population gets, in most cases, the slower it grows. Tracking and estimating changes in the speed of growth is therefore an important context when considering where a trend is going or could go in the long-term future.

One final thought on growth rates leads us to the question of exponential increase: there is a difference between additive and multiplicative growth. When a company adds a new hire, a new customer, or a new member of a club, the growth is additive: 1-2-3-4. When one fan brings a carload of friends or two parents have four children, who each have four children, growth is multiplicative. Multiplication commonly leads to doublings: 1-2-4-8. As I’ve shown elsewhere, 27 doubles is enough to saturate nearly any province and even most countries.

Multiplication isn’t always smooth. Some families have one child, some have none, some have many. Some people keep a book to themselves, while others share it with hundreds of friends. Growth, especially over large numbers, is uneven. The easiest thing is to look for the doubling of populations in relatively short periods of time. 

Computing doubling time can be done simply if roughly with the Rule of 72: divide 72 by the growth rate. If your annual growth rate is 3%, your doubling time is 72/3=24 years. This is a fairly long time for a church, for example, to go from 100 to 200 members. If in the other hand your growth rate is in months, then 24 years would see 12 doubles, yielding about half a million members.(But remember, it’s unlikely anyone would maintain that consistent a doubling rate over that period of time.)

We usually track numbers to know where we are, and where we are going: we want a check on our current position but we often want to know something about our progress. We should be cautious, however. Even knowing some of the complexities of a number and its story, we often fail miserably at estimating the future.

In “Upstream: the quest to solve problems before they happen,” Dan Heath enumerates four kinds of situations that we try to forecast. We do increasingly worse at projecting with each level:

  1. The immediate future—for example, “I’m going to go by the office today.” Usually, the very close-range futures are things we can know with near 100% accuracy, although the effects of ‘wildcards’ or the unexpected are also felt here.
  2. The short range future—a limited range of exclusive scenarios, of which we know which one is most likely: “It will rain today, or it will not, and it is more likely not.” Or, “I could go to the store for groceries, or I could go get a coffee with my wife, or I could work on this spreadsheet.”
  3. The medium term future, when the actual thing that happens is hidden in a range of possibilities. To use a morbid example, the number of church leaders who die from Covid is somewhere in several range categories for a given country: “none,” “a few,” “a sizable minority percentage,” “a majority”, “most”, “all.” We could probably predict which category is most likely, but not the exact percentage or number ahead of time.
  4. The long-term future, which is nearly always messed up by unexpected wildcard changes, especially in the form of technologies that introduce unexpected societal shifts. Some of these can be generally expected but their impacts often aren’t; for example, there were many predictions and even plans for pandemic response, but how Covid-19 played out wasn’t on anyone’s radar that I’m aware of.

So, handle measurements with care. Verify data and methodologies. Don’t use numbers in isolation. And beware the numbers that you don’t know yet, which will change everything.