Instant Genius - The animal kingdom’s mathematicians, with Brian Butterworth

Episode Date: March 27, 2022

Brian Butterworth, author of Can Fish Count, explains how animals approach counting and mathematics, and how they are more like humans than you might expect. Once you’ve mastered the basics with Instant Genius, dive deeper with Instant Genius Extra, where you’ll find longer, richer discussions about the most exciting ideas in the world of science and technology. Only available on Apple Podcasts. Produced by the team behind BBC Science Focus Magazine. Visit our website: sciencefocus.com Hosted on Acast. See acast.com/privacy for more information. Learn more about your ad choices. Visit podcastchoices.com/adchoices

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delivering digital precision with analogue warmth. So you can experience exceptional sound at home. Music just as the artist intended. Visit name audio.com to learn more. From BBC Science Focus magazine, this is Instant Genius, a bite-sized masterclass in podcast form. I'm Alex Hughes, staff writer at BBC Science Focus magazine. This week, I'm joined by Brian Butterworth. He is the author of Can Fish Count, a new book looking into the numerical ability of animals. He explains whether animals are actually able to count and how their numerical ability differs to that of humans. It may seem quite an obvious question, but I think it's a good place to start with this,

is to ask what is counting and is it the same for everyone? everything? Well, when humans count, they usually use counting words like one, two, three, four. And they use that very often to establish the number of objects in a set. Now, of course, animals don't have counting words, so they can't use counting words to establish the number of objects in a set. So they have to use a different method. So when I talk about counting, I just mean a method by which an animal or a human establishes the number of objects in a set, which technically we call numerosity. And so in order to say that an animal can count, it has to be able to establish the numerosity of a set. And it has to be able to do something

with that information. For example, say this set, is bigger than that set or that this set plus that set equals some other set. So it has to be able to do something with the results of counting, which is sort of equivalent to, isomorphic with the arithmetical operations such as greater than less than equals to add, subtract, multiply, or divide. obviously there's a huge amount of animals out there but as the nearest animals for humans do monkeys and apes and that kind of area so they have a similar counting method to us or is that also quite different well neither monkeys nor apes use counting words but you can teach apes to use the digit symbols you know are familiar digit symbols from you know one two three

so-called Arabic numerals. And they can learn to match those digits with a set of objects. So if there are three objects, they'll click on the digit three. If there are seven objects, they'll click on the digit seven. And some of these chimpanzees have had quite a lot of training, do this at least as well as humans and sometimes better. What would you say is the best Arabic? Animal mathematician, would it be apes and grillers?

Or in your book you highlight the ability of birds as being surprisingly good? Yeah, but birds seem to be at least as good as monkeys on the same sorts of tests. But they've used the stimuli, the materials that you test monkeys with, with the crows, for example. And crows are just as good as monkeys on these tests. I wouldn't say they're as good as chimpanzees, but the methods in which are, which they've been trained, is a bit different. And of course, there is a famous parrot called Alex, alas, no longer with us, who could actually use counting words.

It took quite a bit of trading, but he could say, if asked, how many objects are on the tray, he might well say seven, if indeed it was seven. In fact, he could do quite well on this. So if you say how many blue objects on the tray, and there were seven blue objects, he would say seven. He wouldn't count all of them. He just count the ones he'd been asked to.

So that bird was probably as good as some chimpanzees who've been trained. But there are chimpanzees who are better than Alex, particularly on a task where what you have to do is you have to touch each of the digits in order, having remembered where they are. And there at least one chimpanzee, might you, had started very young in his training, he could do it better than Japanese graduate students. I think there's a lot of famous examples of animals where, when we've looked further into it, there's been a realization that maybe they were picking up on queues or that they were maybe getting hints from humans in ways that were unintended.

How do you know that an animal is really counting and how do you know when it's maybe picking up on a queue or finding a way around that methodology? That's a very good question. I mean, there is a famous case of the horse, Clever Hans, who was terrifically good, apparently, at calculation. He could find squares, they can find square roots, as well as doing all the usual calculations. And people couldn't figure out how he did it. It turns out that he was particularly good at picking up Q. So even when the, investigator who discovered how this was working, try to stop himself giving Hans these cues. He couldn't. And so you say, what are the factors of 28? And Hans would tap out seven and two and so on. Clever Hans was certainly clever, but he was clever at picking up cues even from somebody who was

trying to suppress those cues. So subsequent to Hans, the investigators trying to try and and stay out of the way so the animal can't see the investigator or hear the investigator or even smell the investigator. So those problems, I think, are not really a problem for modern investigations. For humans, there's arguably a more cultured method of counting. I mean, as you mentioned earlier, we have words for numbers, but are there ways in which animals are more advanced in their counting? then humans are? Well, there are ways in which they are very similar if you stop them using counting words. So, for example, you can get a mouse or a rat to press a leave for a certain number of times as many as 40 times. And if you ask a human to do that, but prevent him from using the

counting words out loud. So, for example, by going the, the, the, the, the, while he or she is pressing the lever, then they behave very similarly. So they'll get to around about 40, usually just over 40, showing that they can, they have at least a good estimate of what 40ness is, both mice and humans, and indeed rats and humans. For humans, a lot of the time when we're counting or doing any kind of addition or mathematics, that's done around finance, science, or another highly numerical field. What's the priority in animals when it comes to counting? Well, there are all the usual evolutionary issues, essentially food, sex and the avoidance of death. So for some animals, in some situations, it could be the avoidance of death.

One example of this are lions in the Serengeti, investigated by Karen McComb. Now, lions live in prides. Pides are territorial, but they sometimes get invaded by lions from neighbouring prides. Now, if lions fight, because they're big and strong, they can inflict serious damage on the lion that they, they're fighting with and suffer serious damage themselves.

However, if the pride outnumbers the intruders, then the intruders will back off and run away. And so the pride wins that particular battle without actually having incurred any serious loss. Now, that means that the pride has to count how many of the lions are intruding and how many of them there are defending. So, for example, if there are three lions that seem to be intruding and six lions defending,

the six lions defending will attack the three intruding. Now, what's particularly interesting to me about this is that when lions intrude, they usually do it at dusk or in darkness, and they roar as they come in. And the lions who are defending can't see the lions that are coming in. So they're counting the number of rares, if you will, and comparing them with the number of their own pride they can see. So it's an abstract comparison, sort of the numerosity of the sets of seen lions

compared to the numerosity of the set of only heard lions. Now, the way this was done was quite clever. Instead of using real intruding lions, Karen Pekum set up loudspeakers at the... periphery of the Pride's territory. And so she could control how many apparent intruders there were, and she could observe when and if the defenders would attack the intruders. That's avoidance of death.

Another example of avoidance of death is something which we've been working on, which is little fish get predated by big fish. And the chances of a particular little fish being predated by a big fish, is reduced if the little fish goes into a shoal of other like fish. And of course, the bigger the shoal, the more likely that that particular individual little fish is likely to survive. Therefore, the fish choosing a shoal has to decide which shoal has more fish in it than which other shoal. And we've done this experimentally in the lab, and we know that it works also in the wild. So these little fish can avoid predation by joining a larger shoal.

That means assessing the numerosity of the shoals that it might join. Also, being in a larger shoal means you've got a better chance of finding a mate. You've also got a better chance of finding food. So there are advantages in being able to count the number of what we call conspecifics, that is, other fish in the same species, in order to give yourself an advantage. Has humans lack of need for accounting to survive, dampened our ability to count in any way or our ability to recognise patterns? Well, the short answer to that is no. We've tested Indigenous children in Australia from two different groups,

the Walbury and the Anandulyagua who live in remote communities. And their languages don't have any counting words. But we've tested their numerical abilities. and compared them with the numerical liberties of children brought up in Melbourne, same age, who had learnt to count at home and in school. And we found that there was actually no difference in their abilities. So there's something that you inherit, some brain mechanism that you inherit, which enables you to do these sorts of numerical assessments and numerical calculations.

So we tested not only numerical comparisons, we also tested addition and subtraction and provided you do it in the right way the kids in these remote communities did as well as the kids in Melbourne. A lot of the research that's been done into animals and their mathematical ability, it tends to be done with animals that are in captivity

or that are in a lab setting. Is there any obvious differences between animals in captivity or domesticated animals and those in the wild and their abilities to count? Well, they're usually different species. So you don't test lions in the lab as a rule. They're rather big, rather expensive and rather dangerous.

And you don't test rats and mice and guinea pigs in the wild. Of course, it's much easy to test them in the lab. So we can't do a direct comparison of that sort. I mean, the one time that I thought about this very seriously was in the case of chimpanzees, who I said earlier were very good with numbers. But it's not at all clear why they use disability in the wild. There's very little evidence that they do use it in the wild, but maybe we're missing something.

To the extent that you can test the same animals in two situations, they seem to be about the same. So, for example, you can test monkeys. free-range monkeys who, let's say, come to your testing site if they want to, then you can show them, for example, pieces of food going one by one into bucket A, and then other pieces of food going one by one into bucket B, and you can see how well they can select the bucket with more pieces of food. And they're pretty good at this, and they can do it just about as well.

these free-range monkeys as they do in the lab. So there probably isn't any difference, but there's not been very much comparative research on this, I'm sorry to say. Something that you discussed in your book that I thought was really interesting is are all animals that have numerical ability social, or do you find it in animals that are apt alone as well? this is a terrifically good question and I was once asked this a few years ago by a student exactly the same question

and I didn't have an answer but I do have an answer now which is that there are solitary animals that have been tested and one of them is North American bears grizzlies that live by themselves and they only interact very occasionally in order to mate and they seem to have a reasonable numerical ability as well. So it probably isn't necessary for the animals to be social, but since most animals are social, clearly it helps them in their social life to be able to count the number of friends or the number of enemies and make decisions accordingly. But even if you don't have to make social numerical assessments, you also have to assess, for example, the amount of food up that tree versus the amount of food up the other tree. And so you do better if you

choose the tree with the most fruit on, because that gives you the best, if you like, bang for your buck. You get more food for the same amount of work. Something that I would imagine is a common belief is that the size of the brain will have a direct correlation to an animal's ability to count, is that something that's true or can that vary quite drastically? When you say size, do you mean physical size or number of neurons? I think number of neurons would be, well, both, but number of neurons maybe mean the more interesting way to measure that. Well, okay, well, let's just take size for a start. As we discussed earlier,

Birds are as good as monkeys at numerical tasks, and birds have tiny, physically tiny brains, because these brains have to fit into very small skulls, very small aerodynamically shaped skulls in order for the bird to fly. In gross terms, it doesn't really matter. Even if you look at it in terms of number of neurons, there doesn't seem to be a good correlation. So, for example, mice are very good at counting, at least as good at lever pressing as rats. Rats have brains twice as big as mouse brains. So there isn't a direct correlation.

The other way you could look at this is to think about animals with very, very tiny brains, such as bees and ants. And we know that bees can count. And one thing that we know about their counting ability, is that they can use it to count the number of landmarks between the hive and a food source. And this is very useful in order, first of all, to tell their hive mates where the food is, because they need to tell them using the famous waggle dance, how far the food is and in which direction. And they also need to know where they are when they've got to the food source,

so they can plot a route back. and they have brains of about a million neurons, whereas we've got brains of about 86 billion neurons. So they can do some quite good counting. They can probably do better counting than that, though it's harder to test. And in fact, Lars Chitka at Queen Mary University of London has modelled the bee brain

and reckons that the bee brain needs only about four brain cells properly wired up in order to do that kind of counting. I think a good way to round off is to ask, is there any animals whose numeracy ability might surprise people? Well, I would have thought bees might surprise people. And there's ants as well. Now, one of the things we know about ants is that they can measure distance by counting the number of steps they make,

at least one species of ant does this. And that's pretty well the only way it can make a good assessment of how far it's gone. And you can tell that they're counting because if you change the length of their legs in the appropriate experimental way, then they'll get it wrong. So if they go off to and they find a food source, then they have to find their way back. and then at the food source you change the length of their legs, for example, by making them longer, by adding a bit of hair to their legs, they won't go back to their nest, they'll go beyond the nest because they've been counting their steps going out and counting their steps coming back,

but they're getting the distance wrong because the same number of steps takes them further. Now, this is a very extraordinary finding, and they're counting hundreds of perhaps thousands, of steps in order to do this. And they have really, really tiny brains about quarter of the size of a bee brain. There's these little ants. So I would say these are examples of very small brains with very good counting abilities. Thank you for listening to this episode of Instant Genius. That was Brian Butterworth. To hear him tell me more about the counting ability of humans, head over to Instant Genius Extra, available only on Apple Podcasts.

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