Clever Hans's gift was just too good to be true. The Arabian stallion wowed the crowds in early 20th-century Europe with his apparent ability to stomp out the answers to simple mathematical problems, such as 123=9. He could even add fractions and factorise small numbers. Then in 1907, a German psychologist, Oskar Pfungst, proved that Hans was no animal savant. In a scientific trial of sorts, Pfungst demonstrated that Hans could do arithmetic only when his owner, a maths teacher, or another questioner provided unconscious body cues hinting that Hans had reached the correct answer. With blinkers on or with the questioner hidden, Hans's abilities vanished. So, too, did the notion that animals could count.
Much has changed, however, in the century since Clever Hans's ignominious exposure. Few now doubt that primates have a sense of number, and even distantly related animals, including salamanders, honeybees and newly hatched chicks, seem to have the knack, with some able to perform basic arithmetic. What's more, the skills of this growing mathematical menagerie resemble our own innate abilities. Could basic mathematics have evolved hundreds of millions of years ago?
"The ability to represent time and space and number is a precondition for having any experience whatsoever," says Randy Gallistel, a psychologist at Rutgers University in Piscataway, New Jersey. Of course, without language or a precise symbolic system to represent numbers, animal numerical abilities will never reach human levels. No chimpanzee will ever learn long division, but with enough practice almost any human can master the challenge. So to put humans and animals on an equal footing, we need to look at more basic numerical faculties. Prime among those is the ability to distinguish between a larger and a smaller number, says Elizabeth Brannon, a psychologist at Duke University in Durham, North Carolina. Humans can do this with ease - providing the ratio is big enough - but do other animals share this ability?
In one experiment, rhesus monkeys and university students had to choose the bigger of two sets of geometrical objects that appeared briefly on a computer monitor. Both groups performed successfully. Importantly, Prof Brannon's team found that monkeys, like humans, make more errors when the ratio between the two groups is smaller. Primates are not the only animals whose numerical capacities rely on ratio, however. While at the University of Louisiana in Lafayette, Claudia Uller, a psychologist now at the University of Essex in the UK, wondered whether our more distant relatives could also distinguish large numbers from small.
To investigate, her team tempted local red-backed salamanders (Plethodon cinereus) with two sets of fruit flies held in clear tubes. In a series of trials, the researchers noted which tube the amphibians scampered towards, reasoning that if they had a capacity to recognise number, they would head for the larger number of tasty snacks. At rates well above chance, the salamanders successfully discriminated between tubes containing eight and 16 flies, for example, but not between three and four, four and six, and eight and 12. So it seems that for the salamanders to discriminate between two big numbers, the largest must be at least twice as big as the smallest.
That was not the case, however, for numbers up to and including three. The salamanders could differentiate between two and three flies just as well as one and two flies, suggesting they recognise small numbers in a different way to larger numbers. This chimes with studies showing that adults, infants and primates can also differentiate precisely between small numbers, irrespective of the ratios between the quantities.
Together, the results suggest that the two abilities - to precisely identify small numbers and to estimate the relative size of large numbers - have deep roots in our evolutionary history. "There's a good chance that this thing goes way back," says Marc Hauser, a psychologist at Harvard University, who led many of the primate studies. Further support for this theory comes from studies of mosquitofish (Gambusia holbrooki), a freshwater species native to the south-eastern US which instinctively join the biggest shoal they can. A team led by Christian Agrillo at the University of Padua, Italy, found that mosquitofish can discriminate between numbers up to 16, but only if the ratio between the fish in each shoal was greater than 2:1.
This ability may date back to even more primitive organisms than fish. Jürgen Tautz, an entomologist at the University of Würzburg in Germany, and colleagues sent a group of bees down a corridor, at the end of which lay two chambers - one with a sugar water reward, the other with nothing. To test the bees' numeracy, the team marked each chamber with a "room number" consisting of two to six shapes. A similar sign at the beginning of the corridor indicated which room would contain the reward. The bees quickly learnt to match the number at the entrance with the correct room number. Like the salamanders and fish, there was a limit to the bees' mathematical prowess - they could differentiate up to four shapes, but failed with five or six shapes. So it seems that even our most distant relatives have some concept of number.
Numerical ability might emerge in any sufficiently advanced nervous system faced with an environment in which numeracy would prove an advantage. Just as bat and bird wings evolved separately yet work using the same fundamental principles, numerical representation may have developed in many separate instances. Unlike bony wings, number-crunching brains leave little trace in the fossil record. Only by studying the numerical abilities of more and more creatures using standardised procedures can we hope to understand the basic preconditions for the evolution of number.
Working towards that end, Dr Uller and her team have now returned horses to the counting club. They found that horses can distinguish two apples from one, three from two, and six from four. When presented with two smaller apples similar in volume to one larger apple, horses still go for the larger number. Her experiments are not a validation of Clever Hans and his believers, but they might do something to restore his good name.
