Can fish count?

Ken writes:

There is a story in the Guardian today reporting a study that allegedly shows that certain fish can count to four. My normal first reaction to this sort of wildly implausible claim is that the journalists have gotten the details wrong, but this time they quote a researcher apparently making that wildly implausible claim:

Their numerical ability is on a par with that of monkeys, dolphins and children aged between six months and 12 months. “We have provided the first evidence that fish exhibit rudimentary mathematical abilities,” said experimental psychologist Christian Agrillo, of the University of Padova in Italy.

OK, the researcher only says, or in translation says(?), that their study is evidence of “rudimentary mathematical abilities”, which is much less specific and less mentalistic than “able to count to four” as the Guardian’s James Randerson reports

Fish are able to count to four, according to experiments which involved giving them the option of joining shoals of different sizes.

Call me a pedant, but the experiment does not show that fish can count to four! It shows they exhibit behaviour that can be quantified in various ways. It shows they can be predicted to move to the biggest group of fish when the groups have sizes up to four after which point they are unpredicatable, but those conclusions exploit our mathematical ability not the fish’s. You might just as well say my DNA can count to four because it stops giving me limbs at four, or can count to five because it stops giving me fingers at five. The inference that they are counting is drawn on the basis of a change in their behaviour after a certain point, but the change could be triggered by purely physical causes. Do we say a thermostat can count because it switches the boiler off at a certain temperature? I don’t know what is responsible for the fish’s responding in this way, but I’m pretty confident it’s not a matter of counting anything. Four is a mathematical concept with necessary connections to other numbers and mathematical operations. Only something whose behaviour exhibits a sensitivity to these interrelations with other mathematical terms can be taken to deploy a genuine mathematical concept.

Misunderstandings of this sort show why one or two philosophy courses should be compulsory for psychologists (if the mistake is the researcher’s), or journalists. It is important because stories of this sort feed into the debates about what is so special about humans and what our place in nature is. The latter debates are too important to be choked up with muddled thinking from researchers and lay people.

P.S. The most important science related story in the Guardian today is not this one, of course, but this one.


8 thoughts on “Can fish count?

  1. Dot

    I don’t think being able to count to four and having a mathematical concept of four are the same thing. A child when s/he learns to count starts by interacting with objects (say, lining up toy bricks) and performing a verbal ritual of counting, ‘one, two, three, four…’ Only later does this translate into an abstract notion of four that can be handled without the things. Now the fish clearly doesn’t say ‘one, two, three, four’, but it does do something closer to the lining up of bricks: it detects a difference between three things and four things and behaves accordingly.

  2. ken

    I concede that counting to four and having a concept of four are different things. Judging that something can count to four deploys the concept the counter doesn’t necessarily have yet. But there’s clear water between the concrete practice of a child and the behaviour of the mosquito fish. I need to think of a better reason to distiinguish them, but the mere responsiveness to the difference between three things and four things seems insufficient to count as counting (or else thermostats and DNA ought to count as counters -and you didn’t challenge that)

  3. Geoff

    If there was a group of three and a group of four in front of me I would tend to join the group of three to even things up.

    Maybe this experiment just shows that fish don’t have much of a sense of fair play.

    After all, when did you last see a fish give any spare change to a homeless scallop?

  4. fergus

    The experiment would seem to warrant at most the conclusion that the fish can discriminate (by some unexplained mechanism) between fish shoals of different sizes within certain parameters defined by a minimum ratio. The minimum ratio in the experiment was discovered to be 4/3. For lesser ratios eg 5/4 the fish do not discriminate. Although the experimenters interpret the ratio numerically it is not warranted to conclude that the fish also discriminate on the basis of a numerical ratio. If the experiment claims that the fish can count to four but no higher and that they can discriminate between two shoals of larger sizes than 4 as long as there is a sufficient difference in size between the populations and further if they posit only one discriminatory mechanism then their findings are inconsistent. Either the fish have one (counting) mechanism for shoals four and less and another (noncounting) mechanism for shoals greater than four or they can count to more than four after all or they do not count at all whatever the shoal size. The final option is the most plausible. Fish might discriminate on the basis of detecting (nonmentally) a relation of ‘greater than’ existing between particular shoals of fish. In the same way humans can determine that one collection of objects is larger than another without knowing or needing to know the number of objects in each collection nor obviously the numerical ratio of objects in any collection compared to another. Also the human need not be numerate in order to make such discriminations. It is also notable that our own powers of size discrimination between objects is limited by some minimum degree of size difference. This minimum is presumably expressible as a numerical ratio but that ratio indicates nothing about our ability to perceptually recognise that ratio AS a ratio.

  5. laura

    Since you mention it briefly, I want to comment on the other article. I read that yesterday, too. What the Guardian didn’t report (and perhaps the study hadn’t included) is that fact that a great many people get MAOI and similar prescriptions for “off-lable” use. Which is not to say, these are used as recreational drugs, but psychotropics may have multiple possible effects. So for example, I’ve read that Prozac is widely prescribed as an anxiolytic, and some anti-psychotics are prescribed to children to “help with depression.” As docs put people on a drug for disorders other than the drug’s intended purpose, you begin to believe (as my friend the psychopharmacologist says) the whole field of psychiatry involves guess work – trial and error – more than anything else. And guess who gets to be in the trial. I just want to know how it takes years for this data (or absence thereof) to reach the public.

  6. fergus

    I’ve just read that the research team said that the mosquitofish use 2 distinct systems for quantity discrimination so that blows my previous comment out of the water!

  7. kenanddot

    Fergus, thanks for the comment. I’m completely in sympathy with it, even their postulating two systems means your inconsistency objection doesn’t go through.

    Laura, I agree with your concerns about issues thrown up by the prozac study. It also worries me to think how many other drugs the criticisms might apply to. How many other drugs got through the approvals process because negative or inconclusive studies were sat on by drugs companies?

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