Lion's pride in arithmetic
by Brian Butterworth
The Guardian: Thursday May 6, 1999.
Animals can put two and two together and make four - but how? Brian
Butterworth sums up the theories
In the Serengeti National Park in Tanzania, a lioness is returning at dusk
to her pride. Eighteen females, one adult male and seven cubs are waiting
a mile away. She hears a roar, one she does not recognise.
It must be an intruder into her territory. Her cubs are safely with her
sisters and she is all alone. She hears the roar again. It's the same
lion. Should she try to drive off the intruder? It would be an even match
- one against one - and it could turn into a real fight. With lions, that
could be fatal. Dusk becomes the inky black of night, and she returns
silently to the pride.
The following week, again at dusk, she hears roaring 500 metres away: one
unfamiliar voice, then a chorus of roars, one overlapping the next, and
none of them the familiar voices. There are three intruders. This time she
is with four of her sisters from the pride. Three of them, five of us.
Their ears prick. The roaring is coming from a stand of trees over to
their left. They wait, they peer into the night, and at each other. One of
them, the leader, approaches the roaring cautiously at first, as the
others join, more quickly, until they are charging headlong into the trees.
By the time they reach the trees, the roaring has stopped and there is no
sign of the intruding lions. The roaring was from a loudspeaker set up by
Karen McComb of the University of Sussex and her colleagues. She was
testing a theory about the way lions make a numerical assessment of the
threat from intruders and the strength of the defence forces.
The theory predicts that lions (like many other animals where fighting
would be costly) will contest resources only when they are very likely to
win; otherwise they will withdraw. The one exception is when a lioness is
with her cub. Then she will always attack an intruder. The lions' decision
to attack depends on the number of intruders - in this experiment one or
three - and how many adult defenders there are. The lioness leader
identifies roaring as coming from individuals who are not members of the
pride; she will also represent the defenders as known individuals. The
best explanation of her decision is that she enumerates the number of
distinguishable roarers and the number of her sisters and compares the two
Only when the number of defenders is greater than the number of intruders,
will she launch the attack. This is remarkable because the number of
intruders comes from the sound they make (they are not visible), while the
number of defenders comes from another sense or other senses, vision
probably, and is stored in the lioness's memory. Thus she has to abstract
the number of the two collections - intruders and defenders - away from
the sense in which they were experienced then compare these abstracted
Research on animal counting is helping us understand how we humans
understand numbers, one of the key abilities that has taken us from the
stone age to the phone age. We process about 16,000 separate numbers a day
- dates, times, page numbers, calculations, government statistics, prices,
addresses, and phone numbers. That's if we don't work in a bank or a shop,
or in a lab. Then of course, we will process vastly more.
Where does this ability come from? Is it just another thing we learn, or
fail to learn, at school? One very influential idea comes from the Swiss
psychologist Jean Piaget. He argued that our very idea of number is
constructed out of previously developed logical abilities. One of these
was transitive reasoning: if A is bigger than B, and C is smaller than B,
which is the biggest? If you can't figure that our correctly, then you
won't be able to put the numbers in order, he claimed. But these logical
abilities don't develop until at least four years of age, and are not
functioning in their most abstract form until the teens. The Serengeti
lions pose a problem here: they certainly cannot reason as well as four
year old humans, and yet they can order two numbers as if their lives
depended on it.
In the laboratory, where it's possible to ensure that number is the
critical variable, all kinds of animals can be trained to make choices
based on numbers. Last year two American scientists, Elizabeth Brannon and
Herb Terrace, showed that it was possible to train a rhesus monkey to
select one of two pictures according to which had the most coloured shapes
in it. Back in the forties, the great German ethologist, Otto Koehler,
successfully trained a raven called Jakob to open boxes and eat the seeds
contained in them until a precise number of seeds had been eaten, and then
These studies suggest that animals are born with numerical abilities, that
can be detected reliably in the lab, and serve a useful purpose in the
wild. If we have inherited these abilities from our non-human ancestors,
then there should be some evidence of it in children much younger than
Piaget's four year olds. Indeed there is. Babies, even newborns, look
longer at a display when the number of things in it changes.
Of course, they may be responding to something other than number, but many
experiments have now shown that change of number alone can trigger
increased looking, and is in fact a more powerful trigger than changing
the colour or shape of the objects.
Many different types of evidence are beginning to converge on the theory
that we humans are born with brain circuits specialised for numbers. We
even have a good idea of where these circuits are in the brain. Have we
inherited these brain circuits from our non-human ancestors? Do our genes
carry a code for building the same kinds of circuits as the lions, the
monkeys and birds use, but perhaps a bit bigger and more advanced? To
answer that question, we need to know which parts of their brains these
animals use; and we don't yet know that.