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.
   

Since this is my first post, I want to discuss fish memory, which is where I got the title for the blog: >3s (greater than 3 seconds). This comes from the myth that fish only have a 3-second memory, recently reinforced by the character of Dory in Disney’s Finding Nemo (and its sequel, Finding Dory). I haven’t been able to find the origin of the 3-second memory myth, but people that keep fish have known it to be false for a very long time. In 1883, Hugo Mulertt wrote The Goldfish and its Culture, which first popularized home aquaria (he also founded and owned the magazine The Aquarium, marketed his own line of fish food, and translated a book of German fish recipes to increase Americans’ consumption of fish). Mulertt had this to say:

        “Goldfish have a good memory; they will soon learn to know their master, remember their
        feeding-place and time. They can be trained to good manners, as they are easily influenced
        by their surroundings, and good qualities of individuals can be perpetuated in their
        offspring.” [1]

Ok, so he wasn’t so strong on how genetics works.

The kind of memory Mulertt mentions, learning when, where, and by whom they are fed, is the most common type of learning demonstrated in fish, and there are plenty of examples of it. Rainbow trout can remember that pressing a bar leads to food even after not seeing the bar for 3 months [2]; goldfish may remember a color that was paired with food for almost a year [3]; and one researcher who trained common rudd to eat out of his hand found that they would still eat of his hand (but not anybody else’s) after not seeing him for 6 months [4].

Some of the more impressive feats of fish memory involve spatial learning. Salmon, returning from a few years of adventure on the high seas, can identify the exact stream where they were spawned by its unique odor [5]. It smells like home. However, you can only smell which stream is home when you are already in the right river system. How do you get from the middle of the Pacific to the right river-mouth? Salmon, it seems, can use variations in the magnetic field of the earth to achieve this, which means they have to also remember what the strength of the field was at the mouth of the river when they left home, several years ago [6].

So why do people think that fish only have a 3-second memory? I can only speculate, but it might have something to do with the small round aquaria that goldfish are often kept in (like Elmo’s pet goldfish Dorothy, from Sesame Street, watched by millions of impressionable two-year olds). Maybe a child asked whether the fish get bored in so small a space and some well-meaning adult came up with the meme, little realizing how it would spread. I guess the moral of this is: when lying to children, keep in mind that they have memories every bit as good as the average goldfish.

1. Mulertt, H. (1910). The goldfish and its culture. (Sixth ed.), p. 14.
   
2. Adron JW, Grant PT, Cowey CB (1973). A system for the quantitative study of the learning capacity of rainbow trout and its application to the study of food preferences and behaviour. Journal of Fish Biology, 5:625-636.
3. Pitcher T (2006). Foreword to Fish cognition and behavior, C Brown, K Laland, J Krause, eds. (Oxford: Blackwell), p. xvi.
4. Bshary R, Wickler W, Fricke H (2002). Fish cognition: a primate’s eye view. Animal Cognition, 5:1-13.
5. Hasler AD, Scholz AT (1983). Olfactory Imprinting and Homing in Salmon (Berlin: Springer).
6. Putman NF, Lohman KJ, Putman EM, Quinn TP, Klimley AP, Noakes DLG (2013). Evidence for geomagnetic imprinting as a homing mechanism in Pacific salmon. Current Biology, 23:312-316.