Not Good at Math? Blame Your Inner Fish

New research suggests that female mosquitofish can count, but only up to four with any precision. No word on how high male mosquitofish can count. The research design is quite clever:

When males bother females, the females try to flee to the biggest group of nearby females. When given the choice between two groups — one with three other fish and another with four — the females consistently choose the group with four. When the choice is six vs. seven, they act like they can’t tell the difference. (Although maybe they count that high and they just don’t care about six vs. seven.)

They do, however, distinguish between groups that are twice as big as other groups even when the numbers are big (e.g. eight vs. sixteen). According to the article, this puts the mosquitofish on par with young children, and apparently, any human who does not have access to language as a way of helping with the counting.

As an example, Christian Agrillo, an experimental psychologist at the University of Padua in Italy, claims that the indigenous people who speak Munduruku in the Amazon don’t have words for any number higher than five, and these folks don’t count much better than the fish.

One needs to be a little careful with the direction of causality here, however. Perhaps the fact that the Munduruku don’t bother with numbers higher than five is an indicator that math isn’t really their thing to start with. (Hat tip to the always-interesting folks at Spectre.)

The similarity between fish and humans caught my attention because I’ve been reading a delightful little book by my University of Chicago colleague (who I don’t think I have ever met), Neil Shubin, entitled Your Inner Fish.

Shubin, a paleontologist, makes a convincing case for us being very fish-like physically and anatomically:

The same bones that make up fish fins are in our hands. Early on, human embryos and shark embryos look a whole lot alike.

There are dozens of examples. Perhaps this should not be surprising given that we evolved from fish, but I had never really thought about the details before. The best thing about the book is that Shubin absolutely loves what he does with the sort of child-like innocence that often typifies the best scientists. His enthusiasm is infectious.

Joshua Zucker

Re: "Counting isn't math" - sure it is!

But what the mosquitoes are doing is probably not counting.

Counting involves putting things into a one-to-one correspondence with other things ... and even that's only just barely counting.

The mosquitoes are just judging which group looks bigger.

I think five is just about the right size for that: for me, if I see a bunch of dots, if it's up to about 5 then I can immediately see how many it is WITHOUT counting, whereas if it's more than about 5 then I need to count to find out how many there are (or mentally split it into groups smaller than about 5, see each group's size, and then add).


Good call on "Your Inner Fish." The central premise of that book is incredibly powerful -- that we can essentially read through the history of life in our own bodies.

BTW, after reading about your experience on the Colbert Report, I figured it's only fair to show Neil Shubin going mano-a-mano with Colbert:


I agree that this isn't really counting, but I think being able to judge different sizes is probably a better survival skill for fish.

If a female fish wants to escape to the largest group, the difference is going to be more obvious, and more important in smaller numbers.

In a way though, isn't differentiating between different sizes still a math skill? After all, the fish are making a distinction between greater and lesser area. I don't have kids so I don't know: how old is a human child before they can understand "bigger" and "smaller" concepts?

Troy Camplin, Ph.D.

We forget, too, that in the case of those tribes that don't have words for numbers above 3-5 or so, that there is little need for large numbers for the vast majority of people throughout the vast majority of history. You really only need to know what 10% of 15,000 is if you're buying a car at a 10% off sale -- and even then, they typically do the math for you.


Interestingly enough, even people seem to simply measure things out in their heads as number sizes. There is a small, but measurable difference in the speed at which we judge 7


I agree with those who have brought up the possibility that the fish are possibly not discretely counting, but instead are just comparing size. 4 fish are 33% "larger" than 3 fish and is easier to see right away than 7 versus 6 fish, which is just 16.67% larger.


Joshua Zucker: That's called subitizing!
I think you're right about even that not happening; do we know it's not just group-size comparison?


Perhaps the fact that the Munduruku don't bother with numbers higher than five is an indicator that math isn't really their thing to start with. (Hat tip to the always-interesting folks at Spectre.)

Do the always-interesting folks at Spectre speculate on a reason why one tribal group of humans might have so much less mental capacity than the rest of the species that they can't count to six?

I'll give you odds of a million to one that if a Munduruku child was taught a language that included names for numbers higher than five, they'd have no problems with it.

Not mistaking correlation for causation is a fine thing, but it can be taken too far.


wintermute - the Munduruku study is based on culture, not on biology. When a child is "taught a language that included the names for numbers higher than five," you've removed them from the context of their culture. You're not comparing apples to apples.

The claim from Spectre does not make a statement about biology - it makes a statement about cultural learning. The relationship between culture and biology falls apart when looking at fish (no culture present), but in humans, culture can run parallel biology. Our base10 counting system is likely based on our 10 fingers -- that's an example of culture built around our biology.

That the Munduruku count to five is a matter of culture, which happens to be similar to the biology of the counting fish.


Neil Shubin was on Bloggingheads TV with Carl Zimmer. For something a bit more in depth than the Colbert Report, head over to:

Shubin's enthusiasm for his subject and for science really comes through. With movies like "Expelled" coming out, we need scientists to get out there and counter the know nothings.

BTW, Prof. Levitt is probably the most requested person to appear on BHtv in the forums. When will he adopt the latest media technology?


Perhaps the fact that the Munduruku don't bother with numbers higher than five is an indicator that math isn't really their thing to start with. (Hat tip to the always-interesting folks at Spectre.)

Or maybe they simply are not in situations where they need to count higher than about five. I would imagine that counting accurately higher than 5 or so is not necessary until you start doing advanced trading or architecture. Kind of like the adage "if you don't use it you lose it."


It's tough being a pedant...

When I saw this reported earlier, my immediate reaction was: Math? Counting isn't "math". It's barely arithmetic.


Does a fish really need to be able to count, as one would when following the lead of Big Bird, to be able to differentiate which group is larger? Presumeably the larger group would take up more space and would be easy to separate from the smaller group without counting. Unless... the fish tended to shrink when in close proximity to one another like font resizing in a text box in PPT - what a cool feature that would be. Beyond a certain size of group the incremental probability of losing the pesky male would diminish into insignificance so the size would no longer matter. I should have read the article before commenting, but hey; I didn't want to.