How Tall is an Alpaca: Or, How Basic Maths Can Change History

This post is an (only very slightly) edited version of the article I submitted to the Wellcome Trust Science Writing Prize 2013*.

There is a common understanding that people in the past died young. How often have you heard that early hunter-gatherers were six feet under in their twenties, Romans were kicking the bucket by the time they were thirty, or people in the Medieval period were lucky to make it to forty?

What a fleeting existence it would have been! Oh woe is … Okay, STOP. Stop right there. I hate to be the one to break it to you, but it is just not true. I mean, of course some people died young, but some people died, well … old. So why do we think that people in the past were pushing up daisies by an age when we’re only just becoming self-sufficient?

It is very likely that this (mis)understanding stems from the fact that the average age at death was lower in past populations. Confused? You’re not alone.

Re-read the sentence above again. Go ahead, I’ll wait. When archaeologists talk about past populations they often refer to the average age at death. We use averages – the “typical” value of a data set – all the time. As in, on average British people drink two and a half cups of tea each per day. One of the most frequently-used types of averages is the “mean.” To calculate the mean you add all the numbers from your data set together and then divide the total by the amount of numbers. Ring any bells? Yet despite our familiarity with it, people skim over the word “average” in the context above.

Perhaps the reason for this oversight is that many people don’t consider archaeology a science; which it is (yes, we’re having that discussion). Although perhaps, more accurately, archaeology is a subject that straddles both the sciences and humanities. It is accessible. It is tangible. People have a natural curiosity of the past and, let’s be fair, many people spent their childhoods watching Time Team or being chased by imaginary boulders. While this has earned archaeology a place in our imaginations (Richard III, anyone?) it can also lead to confusion. It is easy to forget that the past presented by archaeologists is based on results obtained from scientific research; and, like any other science, is open to misinterpretation and misunderstanding.

Let me give you an example. If you were to read that the average height of an alpaca is 1.35m (hoof to head) you wouldn’t think that all alpacas are 1.35m tall – of course there would be some shorter and some taller alpacas! Yet, if you read that the average age at death for an Inca population was in the mid-20s†, you start to picture people all keeling over – or perhaps being sacrificed – in the prime of life or merely at the cusp of it! In order to get the average age at death for a past population (or rather, a sample of one) all the individual ages of people are added together and then divided by the total number of people‡. Just as alpacas are different heights, people in the past died both young and old, tall and short.

It seems obvious when it is pointed out, but by forgetting the significance of the word “average,” our perception of the past becomes incredibly skewed. We never imagine ageing Anglo-Saxons, wrinkly-faced Romans, melancholy Mesopotamians, tired Tudors, grey-haired Gauls, feeble Phoenicians, cantankerous Celts, I could go on (no, seriously I could), exhausted Egyptians … OKAY, I’ll stop. By ignoring old age in the past (even unintentionally) we fail to consider an entire aspect of humanity. This impacts our understanding of ageing both biologically and socially through time, which is relevant to our relationship with ageing today.

We recognise that our knowledge of basic concepts in maths and science influences our understanding of results in these subjects (like why the absence of lanolin makes alpaca fibre hypoallergenic and therefore a perfect choice for the Incas to have used for wool)—but few people consider how they affect our perception of the past.

Of course, the average age at death was actually lower in past populations. If you lived in the past you would be less likely to live as long as you would today (the current average UK life expectancy is 77 for men and 82 for women). The reasons for this make up an entire field of study on their own. However, unlike life expectancy, the life span of humans hasn’t really changed—the maximum-documented life span for humans is just over 122 years.

So, the next time you’re reading about the Incas and their alpacas—whatever their height—or any other past population, spare a thought for the seniors among them, because people were most certainly living into their 50s, 60s, and 70s on a regular basis.

Oh, and in case you’re wondering, the average life expectancy for an alpaca is between 15 and 20 years, but their maximum life span is just over 30 years – and on average they drink zero cups of tea each per day (but if they did, it would be yerba mate).Machu PicchuRight. And with that, I’m outta here!

*It did not make the short-list, probably for one of the following reasons: 1) it was not ‘science-y’ enough; 2) the Guardian/Observer hates alpacas; 3) there were better articles submitted.

†Based on data from ‘The bioarchaeology of Inca imperialism in the heartland : an analysis of prehistoric burials from the Cuzco region of Peru’ purposefully simplified by this author (that’s me) in order to illustrate the main concept of this post (for a more accurate and detailed presentation of the data see Chapter 5. Demography in the above thesis).

‡In a few words; although it is increasingly common for individuals and populations to be divided into age categories such as sub-adult, young adult, middle adult, and old adult. But that’s another post entirely, as it would require broaching the massive subject of how exactly adults are aged (short answer: not very well).

3 responses to “How Tall is an Alpaca: Or, How Basic Maths Can Change History

  1. Pingback: Carnival of Mathematics #101: Prime Numbered Special Edition | The Aperiodical·

  2. Pingback: Weekly links for August 19 | God plays dice·

  3. Pingback: From Dinosaurs to Astronauts, Long-Live the Bone Cells (Part I) | Deathsplanation·

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