On the origin of numbers

Host: Nick Petrić Howe

Welcome back to the Nature Podcast. This week, the ancient history of counting…

Host: Benjamin Thompson

And the latest from the Nature Briefing. I’m Benjamin Thompson.

Host: Nick Petrić Howe

And I’m Nick Petrić Howe.

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Host: Nick Petrić Howe

First up on the show, reporter Adam Levy has been pondering some important questions.

Interviewer: Adam Levy

Hello there. How old are you? How tall are you? How many siblings do you have, and how much money do you have in your wallet right now? Whatever your answers, they reveal a fundamental way in which we see the world – through numbers. But how did our ancient ancestors start to think in numbers, and how can researchers even begin to unearth the history of such an intangible idea? Well, in this week’s Nature, reporter Colin Barras has written a feature all about the efforts to uncover the human history of numbers.

Interviewee: Colin Barras

It’s something that seems so familiar and yet when you begin to look into the origins of something like numbers it sort of quickly becomes a little unfamiliar when you realise how strange it is that we do this.

Interviewer: Adam Levy

So, what is it about numbers that is strange and unique to us humans? After all, other species can roughly assess quantities. But humans have formalised numbers into concrete ideas and symbols far beyond what any wild animal does. We can…

Interviewee: Colin Barras

Understand quantity using these abstract ideas such as twoness or symbols such as the number ‘2’ written on a piece of paper or words like the number ‘two’ spoken out loud.

Interviewer: Adam Levy

To answer this question of how we built up our understanding of numbers, researchers are using evidence from across the globe and spanning disciplines of science. Through such work, scientists hope they can begin to dig up the origins of humans’ relationship with numbers. Archaeologist Francesco d’Errico has found instances of bones marked by humans, hinting at the origins of counting, one of these dates back some 40,000 years, uncovered in a cave in South Africa as Francesco describes.

Interviewee: Francesco d’Errico

A fibular of a baboon with 29 notches deeply cut into it, which showed that they have not just decorated, so the best interpretation for that is that something was recording numerical quantities.

Interviewer: Adam Levy

One theory is that humans first created notches on bones for other purposes, maybe through butchering meat or through decoration. This allowed them to make the mental leap that these symbols could be used for counting. But interpreting such evidence, let alone creating a complete theory from it, is incredibly challenging. Here’s Colin again.

Interviewee: Colin Barras

It’s fascinating but very, very difficult to understand what an individual who was living 50,000-60,000 years ago was thinking, what they had in mind when they were doing particular activities. All we have is artefacts that they leave behind and then we have to try to interpret what those artefacts might mean.

Interviewer: Adam Levy

For cognitive archaeologist Karenleigh Overmann, the artefacts that researchers uncover can only tell a part of the story. She argues that the first steps humans took could have been much the same as the first steps we all take today as little kids – representing numbers with fingers on the hand.

Interviewee: Karenleigh Overmann

Sooner or later, you need to use your hand for something other than representing quantity, so you might go to some kind of device that does what the hand does but can do it for longer and a typical device that you might use would be a tally or maybe a group of stones.

Interviewer: Adam Levy

Of course, a group of stones, let alone finger counting, can’t be preserved easily in the archaeological record, so researchers are using evidence from fields as wide-ranging as psychology, anthropology, archaeology and evolutionary biology to shed light on the matter.

Interviewee: Karenleigh Overmann

You have to look at a wide variety of different sources of evidence and then infer from them how it might have worked in the past.

Interviewer: Adam Levy

For Karenleigh, contemporary cultures have a lot to teach us about the evolution of numbers in our ancestors. Researchers can, for example, look at certain hunter-gatherer societies today who only have words for the first few numbers – ‘one’, ‘two’, ‘three’, perhaps before jumping to ‘many’. The varying use of numbers across different groups suggests that their use is strongly connected to possessions and materials.

Interviewee: Karenleigh Overmann

So, we do tend to count the things that are important to us. If you’re worried about survival then you might be counting how much food you need to get you through the long, cold winter into the spring when the food comes back.

Interviewer: Adam Levy

Other researchers look at how our words for numbers vary across languages. Comparing the words for small numbers suggests that such words have changed very slowly over the time since those languages split.

Interviewee: Karenleigh Overmann

So, when they project that rate of change, or I should say that rate of stability, backwards, it suggests that words for the numbers ‘one’ through ‘five’ in some language families could be 100,000 years or older.

Interviewer: Adam Levy

The origin of numbers may date back many thousands of years, but the research that hopes to get at these origins is still relatively new. For Colin, speaking to different researchers and putting together his feature has revealed a blossoming field.

Interviewee: Colin Barras

Yeah, it’s an exciting time. It feels like there’s going to be quite a lot of interesting work coming out over the next five or ten years or so as more people begin to think about this topic.

Interviewer: Adam Levy

And different researchers come to different conclusions as they think more about this topic. Were fingers on our hands or notches on a bone the crucial ingredient to start representing numbers? Or perhaps our ancestors used something else entirely. It may be impossible to ever know for sure. But one thing we can count on is that researchers aren’t going to stop trying to dig up the answer. Here’s Francesco.

Interviewee: Francesco d’Errico

There is a strong disagreement, and I think that is the key for science. Disagreement is something we need to build on in order to test the theories.

Host: Nick Petrić Howe

That was Francesco d’Errico of the University of Bordeaux in France. You also heard from Karenleigh Overmann of the University of Colorado in the US and Colin Barras who’s now at New Scientist, all speaking to Adam Levy. To read more, there’ll be a link to Colin’s feature article in the show notes.

Host: Benjamin Thompson

Coming up in the show, we’ll be hearing the latest estimates for humans’ maximum lifespan and the likelihood that tardigrades survived a crash landing on the Moon. Both of those stories coming up in the Briefing Chat. Before that, though, it’s time for the Research Highlights, read this week by Noah Baker.

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Noah Baker

Clownfish are some of the most recognisable creatures in the oceans. In part, that’s down to some successful cinematic outings, but it’s also because of their distinctive patterns and colours. Now, a team of researchers have observed that the pattern of white stripes on clownfish is dependent on the species of sea anemone in which the fish developed. The researchers analysed the concentration of a key growth hormone – thyroid hormone – in clownfish that lived in different species of anemone, and found that the levels of the hormone varied depending on the anemone they grew up in. Then they exposed clownfish larvae to varying concentrations of thyroid hormone and found that the clownfishes’ characteristic white stripes appeared sooner in fish that received the highest dose. The authors say this could explain why white stripes develop faster in fish that live in certain species of anemone. Find that research in full in the Proceedings of the National Academy of Sciences USA.

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Noah Baker

Nestling skin-to-skin immediately after birth has been found to sharply cut the risk of death for high-risk newborns. So-called ‘kangaroo mother care’ is known to cut the risk of death for babies born early or very small, but such care, which also entails feeding babies exclusively on breast milk, is usually started after babies show signs of a stable condition, even though most mortality occurs before these babies’ conditions stabilise. In the new trial, researchers started kangaroo mother care immediately after birth and found that it improved babies’ chance of survival by around 25% – a benefit so clear that the trial monitors stopped the trial early. Read that research in full in the New England Journal of Medicine.

Host: Benjamin Thompson

Finally on the show this week, it’s time for the Briefing chat, where we highlight a couple of stories from the Nature Briefing. Nick, what have you got for us this time round?

Host: Nick Petrić Howe

Well, Ben, I’ve been looking into the latest estimate for how long humans can live for and this was an article in Scientific American.

Host: Benjamin Thompson

Right, I mean, I guess humans are living maybe longer and longer as generations go on, but I suppose I still consider maybe 100 as being a really, really good innings. Is that there or thereabouts right?

Host: Nick Petrić Howe

Well, people have lived longer than that, and this is trying to work out what would be the maximum ever. So, you may remember – I’m going to mangle this name, sorry French listeners – Jeanne Calment, who lives until she was 122, and she was the oldest ever person. And this article discusses a study that has been trying to work out like if nothing really went wrong, there was no sort of disease and things like that that normally cause people to die, how long could you possibly live for? And their estimate is somewhere between 120 and 150 years old.

Host: Benjamin Thompson

Goodness, so maybe in an idealised scenario – which of course very rarely exist – we might be able to push 150. I mean, that’s a lot longer than we’ve got now.

Host: Nick Petrić Howe

Yeah, almost certainly. I mean, you have to solve some big problems. For instance, cancer becomes a lot more common as you get older. But the important thing about this study, according to the article, is that it gives us an estimate of the pace of ageing, so how quickly things start to deteriorate as we get older. And so, they looked at things like blood cell counts and step counts, and as we get older, those things change, and in the case of step counts, they start to decline. And also, when things happen – so you have an illness or something like that – it takes longer to get these things back to normal as well. And the authors of the paper, they discuss how if we know the sort of pace of change, we can perhaps then work out what we can do as sort of interventions into that and potentially get people closer to this limit.

Host: Benjamin Thompson

Well, my goodness, Nick. I mean, I suppose there aren’t many people then, as you say, that reach 120+. Where is the data coming from that these researchers have been using and have they just sort of extrapolated it out from there?

Host: Nick Petrić Howe

So, this data comes from three different cohorts in the US, UK and Russia. And there aren’t any people who are over 120 years old alive today and so they’re basically working out how these things start to degenerate over time as you age and then from that they extrapolate out to work out, well, this is where things would be at a point where you wouldn’t be able to continue to live. And so, that doesn’t necessarily mean that that’s the upper, upper limit but it’s just with what we currently have and how ageing progresses according to this study, between 120 and 150 years is about as long as we could live if we can solve everything else, which is not an easy task.

Host: Benjamin Thompson

Yeah, I mean, that’s probably the kicker isn’t it, Nick. I mean, it’s very much an ‘if’. We could live to 150 if we can solve a multitude of problems. So, it may be that we’re not going to get there any time soon.

Host: Nick Petrić Howe

Well, I’m going to hope so for my lifespan but we’ll see. I’ve got another 100 years yet. But what’s your story for this week, Ben?

Host: Benjamin Thompson

Well, Nick, I am fast becoming the Nature Podcast’s unofficial tardigrade correspondent, and I’ve been reading a story from a couple of weeks back that was reported in Science and based upon a paper in Astrobiology and I really wanted to share it with you.

Host: Nick Petrić Howe

Okay, well you’ve piqued by interest. So, what is happening in the world of tardigrades?

Host: Benjamin Thompson

Well, of course, tardigrades are these little animals and they are pretty amazing, right? Extreme temperature, freezing, radiation – they just shrug it off. It doesn’t really bother them that much. But there’s a question that’s been going around a little bit and that is could tardigrades have survived a crash landing on the Moon.

Host: Nick Petrić Howe

Wow, okay. The Moon is quite an inhospitable place from what I know about it but if anything could survive, I guess tardigrades could because they are very hardy. But I guess the question is could they?

Host: Benjamin Thompson

Well, let’s find out, Nick. Let’s give a little bit of context here. So, back in 2019, you may remember the Israeli space mission Beresheet it was called and it crashed on the Moon, and in turned out that on board were some tardigrades. And this question, could they have survived, has inspired some research and some researchers wanted to find out, but it’s also thrown up some interesting insights which maybe we can talk about in a little bit. And this is kind of how they did it. So, they fed 20 tardigrades some moss and some mineral water and then they froze them for a couple of days so they entered this state of hibernation, and then they fired them out of a gun.

Host: Nick Petrić Howe

Laughs. Okay, I’m guessing, is that to simulate crashing on the Moon?

Host: Benjamin Thompson

Bingo. And it’s not any sort of gun, Nick. This is a two-stage light gas gun, which has a higher velocity than a conventional gun. And so these deeply hibernating tardigrades were placed in a nylon bullet a few at a time and fired at increasing speeds into some sand, and it seems that the upper limit that they could survive was 900 metres per second, and this gives a momentary shock pressure of up to 1.14 gigapascals, which trust me is really, really high. And anything kind of above this was sadly curtains for the tardigrades, but below this some of them actually made it.

Host: Nick Petrić Howe

Well, that sounds like a heck of an impact, but is that similar to the impact that actually happened when Beresheet crashed onto the Moon?

Host: Benjamin Thompson

So the top line is that the tardigrades that hit the Moon were unlikely to survive. The lander crashed at a slower speed than the bullet, but apparently the shock pressure caused by the frame of the spacecraft meant that this kind of shock would have been much higher and that really would have done for the tardigrades. But this research is interesting because it’s not necessarily just about that. It actually may give some information into this theory called panspermia, and I don’t know if you know what this is, Nick, but this is the theory that life could hitchhike from maybe a meteorite onto another planet.

Host: Nick Petrić Howe

Oh, okay, yeah, so I guess if they could survive landing on the Moon or something, potentially they could seed more life. But it doesn’t seem like they were able to this time, but would a meteor be a different thing and maybe they could survive that?

Host: Benjamin Thompson

So, I think that this theory of panspermia is considered pretty unlikely and this isn’t going to change that view, but it’s not necessarily impossible. So, the speeds that meteorites hit the Earth or Mars are higher than the bullets but some of the sections within a meteorite might experience lower shock pressure. So, it’s a possibility, but maybe putting that to one side, this research and the calculations in it could offer some useful insights into other things as well. So, in this article I read, it could be used maybe to check for life on one of Saturn’s moon called Enceladus, which ejects plumes of water out into space. And I think what this research has shown is that if a probe could move slow enough maybe it could pass through these plumes and see if there’s any life there, for example. And that’s an interesting one to check, right, because if you detect something that’s dead, you don’t know whether it died because you hit it at hundreds of miles a second with a spacecraft or whether it’s been dead for a very, very long time. So, maybe finding that sweet spot where you can sort of gently cruise through without causing any serious damage could be a useful one to answering that question is there life out there in the Solar System, and it seems that tardigrades have played a little role in maybe helping calculate how it could be discovered.

Host: Nick Petrić Howe

Well, thanks for that insight, Ben. It’s always fascinating to hear more about these strange creatures, and it’s good that we’ve got our own tardigrade correspondent so we’ll hear more about them in the near future. And listeners, if you want more stories like these but delivered directly to your inbox, make sure you sign up to the Nature Briefing. Look out for a link of where to do so in the show notes, and you’ll also find links to today’s stories as well.

Host: Benjamin Thompson

That’s all for this week, but of course you can drop us a line any time on email – podcast@nature.com – or on Twitter – we’re @NaturePodcast. I’m Benjamin Thompson.

Host: Nick Petrić Howe

And I’m Nick Petrić Howe. Thanks for listening.