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Some Fish Can Count, But No One Knows Why

  • While fish don’t have much mathematical ability, a new study shows that some species can add and subtract by one in a group of up to five.
  • Other animals have demonstrated this ability, such as bees, some primates, and some birds.
  • Scientists don’t know why these fish can calculate, since they don’t seem to need this ability in the wild.

    Can fish do math? Well, no, not like people, but cichlids and stingrays have demonstrated that they can add and subtract by one when shown a group of up to five objects.

    Don’t believe it? Even the researchers, from the University of Bonn in Germany, were surprised by their findings. After all, fish don’t have a cerebral cortex, which helps other animals perform complex tasks.

    🐠 Animals constantly surprise us. Read more stories like this one with Pop Mech Pro.

    For the experiment, the team trained eight cichlids and eight stingrays to associate blue with “add one,” and yellow with “subtract one.” The fish looked at a collection of three geometric shapes (square, circle, or triangle) projected on their tank wall. If these shapes were blue, the color meant the fish should choose the group of five in the next projection. If they were yellow, it meant the fish should choose the group of three in the next projection.

    Next, the animals saw two new pictures: one with three squares and one with five squares. Those who swam to the correct picture won a food pellet. If they gave the wrong answer, the fish received nothing. Gradually, they learned to associate the blue color with adding one more shape, and yellow with subtracting one shape.

    The fish were successful in completing similar plus-one and minus-one calculations with up to five different shapes. But researchers left one combination out of the initial experiments. They wanted to know if the fish could perform the same arithmetic on a number combination they hadn’t seen during training: specifically, “3+1” and “3-1.”

    Once the training was complete, the fish were tested for three yellow or blue geometric shapes in the first group, and then shown a choice of two and four shapes. Most of the time, they still chose the correct answer, according to the paper, published last month in Scientific Reports. Cognition researcher Vera Schluessel led the work.

    A critical question the team posed was whether the fish were actually adding or subtracting by one, or if they were viewing subsequent groups as being just an increase or decrease of shapes. So they repeated the experiment, but with a twist. The fish started with a group of three blue shapes and saw two choices afterward: one choice had four shapes, and the other had five shapes. The fish still chose the group with four shapes, indicating that they had learned that blue means “add one,” not “add more.”

    Examples of two tasks given to the fish. The animals usually swam to the correct solution after successful training.

    Esther Schmidt

    Types and sizes of shapes didn’t throw the fish off course in their quest for a nibble, either. Instead of presenting the same shape consistently, the team tried to confuse the fish with combinations of different shapes and sizes in the same experiment. For instance, a group of five objects could include squares, triangles, and circles in an earlier part of the task, and then it could be composed of just triangles of different sizes.

    That means the fish were keeping both the color and number of shapes in their memory, and not getting distracted by the sizes and types of shapes, the researchers write in the study. The animals proved they could perform the simple (but precise) operation of distinguishing between objects that just differed by one.

    The scientists don’t know why these fish can calculate, since none of their hunting, mating, or reproductive behaviors indicate a need for this ability.

    stingrays and cichlids in study

    Stingrays (left) and cichlids (right) demonstrated the ability to add and subtract when shown small groups of objects.

    Dr. Vera Schlüssel/University of Bonn

    However, simple arithmetic skills have been well-documented among a variety of animals, the authors say: pigeons, African gray parrots, bees, chimpanzees, orangutans, and other animals have all demonstrated practical counting ability. Other studies show that these animals can distinguish among groups of items that contain more or less, as long as the number of items is small. Some animals can even demonstrate specific counting abilities. For example, rats could be trained to press a lever a specific number of times between four and 16.

    Researchers have known for some time that fish are able to track and compare groups of objects, Calum Brown, a fish behavior researcher not involved in the experiment, tells Popular Mechanics in an email. In this ability, they’re the same as some terrestrial vertebrates, such as primates and dogs, says Brown, whose research at Macquarie University in Sydney, Australia focuses on fish cognition and behavior. “The fact that we know that fish have an object-tracking system (literally counting objects), it should not be surprising that they should be able to add or subtract 1, so long as the number falls within the tracking range,” he says.

    Brown notes that the authors’ approach to the study is elegant. He appreciates their extra effort to make sure the fish were counting by trying to trick them with two or more objects. “It would have been tempting for the fish to follow a simple rule—choose the bigger or smaller group—but they didn’t do that. The fish still stuck with the +1 or -1 rule,” he says.

    Brown adds that it’s interesting to observe that the fish could add more easily than they could subtract, since we see that tendency in children solving math problems, too.

    As for which sea creature was better at math? “While cichlids learned faster than stingrays, and more cichlids than stingrays learned the task, individual performance of stingrays exceeded that of cichlids,” the study concludes. Better do more practice problems then, cichlids.

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