Counting fish

Here’s my most recent piece for BBC Future (although a new one appears today).

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Newborn fish not only can count, but can be taught to count better. This discovery by a team of psychologists at the University of Padova in Italy [1], might seem bizarre, even frivolous at first glance, but in fact it bears on a deep and interesting question: how do we make quantitative estimates based on what we see?

There’s a long tradition of psychological and anthropological research on the question of innate counting systems in humans, which underpins familiar popular notions such as the existence of cultures whose number system goes “one, two three, many.” These simplistic ideas can obscure the fact that even some non-human animals recognize that there are different degrees of “many”: that ten objects are not equivalent to a hundred.

Such distinctions matter in the wild. Animals need, for example, to be able to tell which of two food sources is the largest, or to selectively join the largest group of peers so as to maximize their chance of evading predators.

However, there is a difference between seeing that one group is bigger than another, and actually counting the numbers in each group. One suggestion is that animals use a numerical system for very small numbers – up to about 4, say – but a cruder “this is more than that” ratio-based system for larger numbers. The two methods aren’t easy to tell apart – there’s only so much that a fish will tell you about its reasoning – but it can be done. For example, if an animal makes an assessment based on just the ratio of two quantities, discrimination should get less accurate as the ratio approaches 1: better for 1 vs 4 (ratio 0.25) than for 3 vs 4 (ratio 0.75). But if they’re ‘counting’, the performance should be much the same for all of these pairs.

On this basis, Laura Piffer and her colleagues at Padova have previously shown that some fish can use purely numerical information, and not just ratios, to distinguish numbers of objects more than 4 [2]. Nevertheless, fish seem to prefer a number system only up to about 4, and the ratio method thereafter. An ability to make quantitative distinctions based on ratios is something that develops gradually in humans. Six-month-olds can tell apart a 1:2 ratio (not just one and two objects, but, say, 8 and 16), but not until about 10 months do they distinguish 2:3. Pre-schoolers can handle 3:4 ratios, and 6-year-olds 5:6 [3]. On this basis, fish are approaching a preschooler’s numerical literacy, and it’s not unreasonable to suspect that studying fish might shed some light on the mathematical competencies of humans too.

For one thing, fish, like children, learn numeracy as they grow. Newborn guppies can discriminate 1 from 2, and even 3 from 4, but the ability to distinguish 4 from 8 or 12 emerges only between 20 and 40 days later. That’s a bit surprising, given that the adult guppies use ratios to judge the larger numbers: you’d think that telling 3 from 4 would be harder than telling 4 from 12. So the newborns seem innately blessed with the capacity to count to 4, but have to learn the ratio method as they grow.

The latest set of experiments by Piffer and colleagues then asks: do newborn guppies already have the mental capacity to learn ratios, or does that neural hardware develop later? Can they be taught?

But how do you teach maths to a fish? Just offer them food as a reward. The researchers put the fish in a rectangular tank and displayed images of dots at each end, delivering food near the largest quantity. The fishes’ ability to distinguish the two numbers can then be inferred from the length of time they spend near each end: they learn to wait for food by what they think is the larger number of dots.

While newborn guppies couldn’t distinguish 7 dots from 14, after about 20 trials they had learnt to do so. They were then about two weeks old, but still well below the age at which the ratio discrimination system seemed to kick in for untrained guppies. So they seem indeed to be born with this potential ability, and just need to exercise it. Might human babies have such hidden talents too?

Does this mean fish are smarter than we give them credit for? You could choose to see it that way, but in fact it supports a growing recognition that cognitive processes like counting, which we might imagine to be quite complex, can in fact be achieved with a surprisingly small number of neurons [4]. Counting and comparing numbers might not be as hard as we think.

References
1. L. Piffer, M. E. Miletto Petrazzini & C. Agrillo, PLoS ONE 8, e62466 (2013).
2. C. Agrillo, L. Piffer & A. Bisazza, PLoS ONE 5, e15232 (2010).
3. J. Halberda & L. Feigenson, Developmental Psychology 44, 1457 (2008).
4. T. Hope, I. Stoianov & M. Zorzi, Cognitive Science 34, 406 (2010).