Human beings possess several distinct skills that have to do with numbers. First, we can attach labels to different numbers of things: we know that three oranges and three skyscrapers both share the label ‘three’. Another way of saying this is that we recognize that there is a property, ‘three-ness’, that very different sets of objects can take on. Second, we have what is called an ordinal concept of number. This means that we think of numbers as having an order: one comes before two, which comes before three, and so on. Finally, we can do arithmetic with our numbers (well, some of us can). There are more possible sub-divisions of numerical skills, but let’s stick with those three.

Quite early on in the study of animal cognition, people wondered whether animals could also use numbers. George Romanes, a student of Darwin, wrote in 1888 that he had

          “…succeeded in teaching [a] Chimpanzee… to count correctly as far as five. The method  
          adopted is to ask her for one straw, two straws… or five straws… Thus, there can be no
          doubt that the animal is able to distinguish receptually [meaning conceptually] between
          the numbers 1, 2, 3, 4, 5, and understands the name for each… But the ape is capricious,
          and, unless she happens to be in a favourable mood at the time, visitors must not be
          disappointed if they fail to be entertained by an exhibition of her learning” [1].

As you can see, Romanes demonstrated only that his chimp had the first of the three different numerical skills listed above: putting labels to numbers of objects. Later work has, however, shown that chimps and a few other animals will also arrange numbers ordinally and can even do simple arithmetic [2].

What about fish? We’ve actually known for a while that fish also possess some numerical skills. About 20 different species of fish have now demonstrated the ability to tell apart two sets that differ only on number [3]. The usual method of doing this is to present the test fish with two groups of other fish, on opposite sides of its tank. Fish prefer to be part of a larger group, because it is safer, and so will swim towards the more numerous of the two groups, if they can tell the difference. You can also train fish to choose, between two cards with dots on them, the more (or less) numerous one (see the image at the top of this post, of a goldfish doing just that; [4]), which suggests an ability to order numbers. Nobody, as far as I know, has yet shown that fish can (or can’t) do arithmetic.

One of the interesting things about how humans (and probably most other mammals) estimate numbers is that we actually use two separate systems. For small numbers, up to about 4, we do something called ‘subitizing’, which is a little magical and involves simply seeing the number of items, all at once. For numbers larger than that, assuming we don’t have time to count them off one by one, we use an approximate system. The accuracy of this second system decreases as the number of items gets bigger, following something called Weber’s Law. Basically, your ability to tell apart two groups of objects (each of more than 4) depends on the ratio of their numbers, not the numbers themselves. So, telling 10 from 20 is as easy as telling 20 from 40, and both are far easier than telling 10 from 15.

As I mentioned, there is quite a bit of evidence that other mammals also have two similar systems for estimating number. However, there is currently a lively debate about what fish have. Some experiments seem to show that fish accurately represent small numbers and use ratio for large numbers [5] – just like humans – but other experiments show no dependence on ratio for any number [4]. There’s even a suggestion that this depends on the age and experience of the fish: one day old guppies (one day!) can tell 2 from 3 but only develop the ability to tell apart larger numbers as they age, and do so more quickly if they are raised in a group (where they can practice counting how many friends they have; [6]).

So, we’ve arrived at one of those places where science gets really fun: we know that fish can use a concept of number, that they have at least the first of the three skills I listed above, but we really don’t know how they do it. Are they using the same two systems as mammals, which would suggest that these systems both evolved a very long time ago, or do they just have one system, which might mean that our other system (whichever one they don’t have) evolved after we parted ways about 400 million years ago? We don’t know yet, but we’ll keep looking. Count on it.
 

1. Romanes GJ (1888). Mental evolution in man: origin of human faculty. (London: Kegan Paul, Trench & Co.), p. 58.
   
2. Cantlon JF, Brannon EM (2010). Animal arithmetic. In Clayton N (ed.), Encyclopedia of Animal Behavior (Oxford: Elsevier Press), pp. 55-62.
3. Agrillo C, Miletto Petrazzini ME, Bisazza A (2017). Numerical abilities in fish: a methodological review. Behavioural Processes, doi: 10.1016/j.beproc.2017.02.001.
4. DeLong CM, Barbato S, O’Leary T, Wilcox KT (2017). Small and large number discrimination in goldfish (Carassius auratus) with extensive training. Behavioural Processes, doi: 10.1016/j.beproc.2016.11.011.
5. Agrillo C, Dadda M, Serena G, Bisazza A (2008). Do fish count? Spontaneous discrimination of quantity in female mosquitofish. Animal Cognition, 11:495-503.
6. Bisazza A, Piffer L, Serena G, Agrillo C (2010). Ontogeny of Numerical Abilities in Fish. PLoS One, doi: 10.1371/journal.pone.0015516.
   

One of the things we humans used to think made us unique was making and using tools. However, we now know that plenty of animals use tools and sometimes make them. Most of the evidence for tool-use in non-humans comes from apes and corvids. Fish, despite having nothing with which to grab a tool except their mouths, do use tools and, on occasion, make (or modify) them. There are some pretty cool examples of this, from cichlids that use leaves as platters to transport their eggs [1], to wrasse that crack shellfish by throwing them against rocks ([2] which, to be pedantic, doesn’t qualify as tool-use under most definitions; if they threw the rock at the mollusc, rather than the other way around, it would).

The star tool-user amongst fish, though, must surely be the archerfish. Archerfish suck water into their mouths, place their ‘lips’ right at the surface, and shoot a jet of water at unsuspecting insects sitting on branches over the water. The jets of water knock the insects into the water and the archerfish eat them. If you’ve never seen this, there are videos of it all over the internet (like this one). So archerfish use water as a tool; in fact, they use it as a weapon, in the same way that riot police use water-cannons (except that the cops fire on conspecifics who they then do not consume, usually).

Whenever comparative psychologists observe this sort of behavior they immediately ask the question: how flexible is it? In other words, is this a simple reflexive behavior (say, like your knee-jerk reflex), or does the fish ‘understand’ something about the physics of what it does, which might allow it to modify the behavior in response to changes in the situation (like your ability to throw a ball fast or slow or curved)?

By filming archerfish at very high frame rates, researchers have found that their shots are tuned in a lot of different ways. They can hit objects with breathtaking precision at ranges from a couple of centimeters to almost two meters away. They adjust the amount of water they shoot to the distance and size of their target (more water to knock down larger prey), correct the angle of their shot for the visual distortion caused by the transition from water to air, and can learn to hit rapidly moving targets simply by watching another fish do so [3]. Let’s pause for a second to marvel at that last one. When they first see a moving target, archerfish are very bad at hitting it. It takes a lot of practice until they get good. However, other fish that merely watch this practice happening (and probably heckle), without ever getting to shoot at the moving target themselves, are almost as good as the practiced fish.

Most impressively, in my opinion, archerfish modify the speed of the water leaving their mouths so that the back of the jet is moving more quickly than the front. This means that as the water jet flies through the air, the back catches up to the front so that all the water hits the prey at the same time, as a blob, delivering a much stronger punch [4]. They even adjust this according to the object’s distance, so that the maximal focusing of the blob happens just as it reaches the target. This has been taken by some people as evidence that they are ‘shaping’ their liquid weapon: not just using a tool but making one as well.

This is one sort of flexibility in the behavior, and it’s pretty impressive. Very recently, however, it has been found that archerfish will also use jets of water under the water. Researchers gave the fish a piece of food buried under some sand in a bowl and the fish used jets of water to blow away the sand and expose the food. Interestingly, they used the same sequence of mouth movements as they do when shooting down prey outside the water [5]. This is especially interesting from a cognitive perspective because it suggests that the fish can adaptively use their tools for different, possibly new, things. Kind of like MacGyver (the original, not the remake). This kind of flexibility requires that you know something about the properties of your tool and how it interacts with other objects in the world (sometimes referred to as the ‘affordance’ of the tool). It may be a bit early to claim that archerfish have this level of understanding, since blowing sand off food is likely something they also do often in the wild, so it isn’t a completely novel use of their tool (we’d be less impressed with MacGyver if we knew that he practices making tanks out of shoelaces and olive oil every evening).

Finally, there is one more thing that makes archerfish exciting to researchers. One of the difficulties in doing research on fish is getting them to make distinct choices. Usually, animals make choices in experiments by moving. Fish, however, move a lot (compared to, say, rats) and it is hard to make them choose one spot and stay there long enough for you to reward them for it. One of the reasons for this is that movement is cheap for fish: they don’t have to support their own weight and experience almost no friction, so there is very little cost to them in going to the wrong place first. This tends to mess up learning experiments. Archerfish, however, make distinct choices (what to shoot at) which are quite costly in terms of energy. Researchers are increasingly using this to show that they can learn all sorts of amazing things, such as telling apart human faces [6]. So they can spit in your eye, from two meters away, while you’re moving.

1. Keenleyside MHA, Prince CE (1976). Spawning-site selection in relation to parental care of eggs in Aequidens paraguayensis (Pisces: Cichlidae). Canadian Journal of Zoology, 54:2135-2139.
2. Bernardi G (2012). The use of tools by wrasses (Labridae). Coral Reefs, 31:39-39.
3. Schuster S, Wöhl S, Griebsch M, Klostermeier I (2006). Animal cognition: how archer fish learn to down rapidly moving targets. Current Biology, 16:378-383.
4. Gerullis P, Schuster S (2014). Archerfish actively control the hydrodynamics of their jets. Current Biology, 24:2156-2160.
5. Dewenter J, Gerullis P, Hecker A, Schuster S (2017). Archerfish  use their shooting technique to produce adaptive underwater jets. Journal of Experimental Biology. doi: 10.1242/jeb.146936.
6. Newport C, Wallis G, Reshitnyk Y, Siebeck UE (2016). Discrimination of human faces by archerfish (Toxotes chatareus). Scientific Reports, 6. doi: 10.1038/srep27523.