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Do baboons understand numbers?

If you look at the news headlines over at Science Daily for May 3, 2013, you’ll immediately see that their top story is: “Monkey Math: Baboons Understand Numbers.” Which, to put it quite bluntly, is pure poppycock.

The full title of the story linked to reads: Monkey Math: Baboons Show Brain’s Ability to Understand Numbers, which is equally misleading. The Science Daily news story is reprinted from a press release provided by the University of Rochester, a private research university in Rochester, New York, USA. The story’s opening paragraph makes the sensationalistic claim that olive baboons possess “the ability to understand numbers”:

Opposing thumbs, expressive faces, complex social systems: it’s hard to miss the similarities between apes and humans. Now a new study with a troop of zoo baboons and lots of peanuts shows that a less obvious trait — the ability to understand numbers — also is shared by humans and their primate cousins.

(For those who are interested, the citation for the study is:
Barnard A.M., Hughes K.D., Gerhardt R.R., DiVincenti L. Jr., Bovee J.M. and Cantlon J.F. (2013). Inherently analog quantity representations in olive baboons (Papio anubis). Frontiers in Comparative Psychology 4:253. doi: 10.3389/fpsyg.2013.00253.)

What can the baboons really do?

But if you actually read the story, you’ll find that all it says is that:

(i) Baboons can, without any prior training, discriminate between two cups containing different numbers of items (e.g. peanuts) and pick the cup that contains more items;

(ii) They’re very good at doing this when there’s a large relative difference between the number of items in the two cups (e.g. two peanuts versus seven peanuts), but they’re not so good when there’s a small relative difference (e.g. six versus seven);

(iii) They don’t need to count in order to make this discrimination – instead, they make use of what the researchers call an analog system, which allows them to make “more than” or “less than” discriminations when there’s a large relative difference between the number of items in two groups;

(iv) Young children who haven’t yet learned to count can do this too;

(v) According to the story, animals such as “birds, lemurs, chimpanzees, and even fish” can do this too, but this is the first time that non-human animals have been shown to be able to do it without undergoing any training;

(vi) Even with practice, the baboons don’t get significantly better at discriminating between the relative number of items in the two cups, showing that learning has little or nothing to do with it.

Why understanding numbers isn’t the same thing as making snap “numeric judgments”

What’s wrong with this story is that it confuses the ability to understand numbers with the ability to make numeric judgments, including the perceptual judgment that one set contains more (or fewer) items than another. Judgments of this sort are commonly referred to in the psychological literature as judgments of relative numerosity. The ability to understand numbers, on the other hand, is much more sophisticated. For starters, it presupposes an ability to count: you can’t properly be said to understand the concept of “five” unless you know that it’s the number after four, three, two and one. The baboons in the story above didn’t have to count, in order to judge which cup contained more peanuts: they were able to tell at a glance.

But the ability to understand numbers doesn’t stop with counting. As former Nature editor Stephen Budiansky points out in his best-selling book, If a Lion Could Talk: Animal Intelligence and the Evolution of Consciousness (The Free Press, New York, 1998), it also involves the ability to make judgments of a more general nature. “A seven-year-old child can tell you whether 173 is bigger than 142 without having to count from 1,” he writes, adding: “Older children implicitly grasp the notion that counting involves the possibility of extending the process indefinitely, but even young children do not need to be taught each number separately: a child who can count to 24 doesn’t need to be taught that there are numbers called 25 and 26″ (p. 97).

Can any non-human animals count?

It has been widely alleged that Alex, the late African grey parrot trained by Dr. Irene Pepperberg, was able to count to six. However, this is highly doubtful, for reasons pointed out by science journalist Betty Lindsay in an article published in Nature’s Corner magazine (Issue 012). True counting, she observed, is a complex ability, which requires four things: first, the ability to produce a standard series of number tags (e.g. 1, 2, 3, …); second, the ability to give each item to be counted its own unique number tag; third, the ability to remember which items have already been counted; and finally, the ability to know that the last number tag indicates the total number of items. Lindsay then suggested that for quantities of four or less, Alex may be subitizing: in other words, he may simply perceive the number of objects at a glance, as we do when we count the number of spots on dice. Even Alex’s trainer, Dr. Pepperberg, has acknowledged that Alex need not be able to count: he may have simply been able to quickly and accurately estimate the number of items in a small collection, somewhat more rapidly than humans can. That’s an impressive judgmental ability, to be sure, but counting it ain’t.

Even more absurd is the risible claim, published in Science Daily back in 2005, that Alex has “a zero-like concept” – despite his trainer’s admission that he had never been taught the concept of zero as a quantity. Apparently, what Alex was able to do was call out the word “None,” when he was unable to see any group of identically colored objects on a tray, having the same number of items as a number called out by the trainer. Did he have a “null concept”, as his trainer suggested? Or did he simply mean: “Can’t answer that”?

Getting back to the baboons: what the experiment in the study cited above showed was that they are able to make judgments of relative numerosity: they can tell at a glance which set contains more or fewer items. It turns out that this ability is found in a wide variety of animals, including some that are not even conscious! Fish have this ability too: a recent study found that female mosquitofish were able to discriminate between two shoals with a 1:2 numerosity ratio (2 vs. 4, 4 vs. 8 and 8 vs. 16 fish) but were unable to discriminate a 2:3 ratio (8 vs. 12 fish). However, Professor James D. Rose (Department of Zoology and Physiology, University of Wyoming) has concluded on scientific grounds that fish are totally lacking in consciousness: they can respond to events occurring in their surroundings without being consciously aware of anything. In case readers are wondering how Rose arrived at his conclusion that fish are not conscious, here are the references:

(1) The Neurobehavioral Nature of Fishes and the Question of Awareness and Pain (Reviews in Fisheries Science, 10(1): 1-38, 2002).

(2) “Can fish really feel pain?” by J. D. Rose, R. Arlinghaus, S. J. Cooke, B. K. Diggles, W. Sawynok, E. D. Stevens, and C. D. L. Wynne (Fish and Fisheries, published online 20 December 2012, doi: 10.1111/faf.12010).

The neurological basis of animals’ ability to make judgments of relative numerosity is now fairly well understood, and has been described in an recent article by Manuela Piazza and Veronique Izard, entitled, How Humans Count: Numerosity and the Parietal Cortex (The Neuroscientist, Volume 15 Number 3, June 2009 261-273). However, the neurological basis of the human ability to grasp the concept of a number is far more mysterious, as the authors acknowledge:

In humans, during development, with the introduction of symbols for numbers and the implementation of the counting routines, the parietal system undergoes profound (yet still largely mysterious) modifications, such that the neural machinery previously evolved to represent approximate numerosity gets partially “recycled” to support the representation of exact number.

Are baboons really as smart as three-year-old children?

The story about the baboons in Science Daily also claimed, incorrectly, that the baboons’ ability to make “more than” or “less than” discriminations is only found in human children aged three and over, implying that the baboons are as smart as three-year-olds. Study co-author Jenna M. Bovee, described in the story as “the elephant handler at the Seneca Park Zoo who is also the primary keeper for the baboons,” was quoted as saying:

“A lot of people don’t realize how smart these animals are. Baboons can show you that five is more than two. That’s as accurate as a typical three year old, so you have to give them that credit.”

This is simply wrong. Recent research has shown that even 6-month-old infants can successfully discriminate between two sets and identify which one has more items, so long as the ratio of the number of items in the two sets exceeds 2:1 (see here, here). What’s more, this ability holds regardless of how big or small the two sets are, according to recent research (see here). In other words, even a 6-month-old human baby can “show you that five is more than two,” as study co-author Jenna Bovee put it.

Now, Ms. Bovee has a Bachelor’s degree in zoology, but no formal qualifications in psychology (see here). It would be extremely uncharitable to blame her for making factual errors about infants’ cognitive abilities: after all, that’s not her specialty. The real responsibility for the error lies with the University of Rochester, which authorized the press release without bothering to check the accuracy of her assertions about infants’ cognitive abilities. That is extraordinarily careless.


So in conclusion, what are we left with, after all this brouhaha about monkeys that can understand numbers? All the story shows is that untrained baboons are reliably able to judge which of two sets of objects contains more items, so long as the ratio of the number of items in the two sets remains sufficiently large (e.g five items versus two). But it turns out that this ability is found even in fish, which are not even conscious! It’s also found in six-month-old infants – a fact which refutes the claim made by one of the authors of the study, that the baboons accomplished a feat that human children are not capable of until the age of three.

In short: the Science Daily story of baboons that can grasp the concept of a number might best be described as “much ado about nothing.” Methinks it is time for science reporters to show a little more skepticism.

NOTE: News would like to gratefully acknowledge that the picture of an olive baboon shown above was taken by Muhammad Mahdi Karim (www.micro2macro.net). The picture is a Wikipedia image.

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15 Responses to Do baboons understand numbers?

  1. Take 8 peanuts and put them into a large cup so that they only fill it 1/2 way.

    Take 4 peanuts and put them into a smaller cup such that they fill the cup.

    Then see which cup gets chosen the most.

  2. But if Baboons aren’t really that good at math, wouldn’t that explain why neo-Darwinists aren’t good at math either?

    Excerpt: A number of mathematicians, familiar with the biological problems, spoke at that 1966 Wistar Institute,, For example, Murray Eden showed that it would be impossible for even a single ordered pair of genes to be produced by DNA mutations in the bacteria, E. coli,—with 5 billion years in which to produce it! His estimate was based on 5 trillion tons of the bacteria covering the planet to a depth of nearly an inch during that 5 billion years. He then explained that the genes of E. coli contain over a trillion (10^12) bits of data. That is the number 10 followed by 12 zeros. *Eden then showed the mathematical impossibility of protein forming by chance.

    “Darwin’s theory is easily the dumbest idea ever taken seriously by science.”
    Granville Sewell – Professor Of Mathematics – University Of Texas – El Paso

    Dr. David Berlinski: Head Scratching Mathematicians – video

    quote from preceding video:

    “John Von Neumann, one of the great mathematicians of the twentieth century, just laughed at Darwinian theory, he hooted at it!”
    Dr. David Berlinski

    Darwin and the Mathematicians – David Berlinski
    “The formation within geological time of a human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.”
    Kurt Gödel, was a preeminent mathematician who is considered one of the greatest to have ever lived. Of Note: Godel was a Theist!

    In Barrow and Tippler’s book The Anthropic Cosmological Principle, they list ten steps necessary in the course of human evolution, each of which, is so improbable that if left to happen by chance alone, the sun would have ceased to be a main sequence star and would have incinerated the earth. They estimate that the odds of the evolution (by chance) of the human genome is somewhere between 4 to the negative 180th power, to the 110,000th power, and 4 to the negative 360th power, to the 110,000th power. Therefore, if evolution did occur, it literally would have been a miracle and evidence for the existence of God. William Lane Craig

    William Lane Craig – If Human Evolution Did Occur It Was A Miracle – video

  3. Alex the Parrot could count objects presented to him, he also had a theory of mind sufficient to play tricks on other birds while they were trying to count.
    Chaser the Border Collie memorized the names of over a thousand objects, could recognize them by name or appearance, and demonstrated an abstract understanding of the object’s properties by identifying them when their color or size was changed.
    Animals have souls, face it.

  4. She also reported that Alex had the intelligence of a five-year-old human.

    Yeah, whatever. I’m sure the bird could read, write, multiply, divide, memorize long passages, play a musical instrument, tell time, understand the meaning of stories, and so on . . .


    It sounds like Alex was an impressive Parrot and it was definitely an interesting experiment. But I’m afraid the researcher was exaggerating a bit in her assessment.

    I remember reading about the Border Collie a while back. Very interesting.

    Incidentally, I don’t have a problem with the idea of animals having some kind of soul. But the comparisons to human capabilities invariably fall way short.

  5. Hi sigaba,

    Everything that’s alive has a soul. Aristotle said as much.

    Unfortunately, Your Wikipedia link failed to substantiate your claim that Alex played tricks on other birds when they were trying to count, and there are researchers such as Daniel Povinelli who argue that humans are the only animals possessing a theory of mind. (Dian Fossey used to say the same thing about Koko the gorilla, back in the seventies, until Herbert Terrace poured cold water on her claims, as I recall.) You might like to have a look at this article from The New York Times: “A Thinking Bird or Just Another Birdbrain?” at http://www.nytimes.com/1999/10.....abstract=1

    Asked about Alex, Dr. Terrace said he thought that what Alex was doing was “a rote response.” He calls it “a complex discriminative performance.”

    But is Alex thinking? “I would say minimally,” Dr. Terrace responded. “In every situation, there is an external stimulus that guides his response.” Thought, he said, involves the ability to process information that is not right in front of you.

    “It shows Alex is a smart bird,” he said. But if you take away Alex’s ability to vocalize in a way that seems human, he went on, it would not seem as impressive: “The words are responses, are not language.”

    Chase does have a pretty good memory, I admit.

  6. 6

    this yEC welcomes primates or any creatures being able to count or do more advanced math.
    This because man has a soul made in gOds image and animals do not.
    Yet our memory is not in our soul but a part of the material world.
    So animals, though dumb, can or do have memories that are pretty good or close, maybe , to ours.
    So creatures can memorize probably numbers where they have memorizede the numbers mean things.
    child prodigy’s or adults or idiot savants can do great number feats without any claim to high or even any intelligence at all.
    Its just a memory game.
    Creationists should welcome animals having great memories and not see it as any claim on a mutual intellectual origin or likeness.
    Animals are as dumb as they seem.
    Yet there are many cases of creatures memorizing great numbers of facts.
    Numbers can simply be more facts to creatures.
    We should have the option of segregating intelligence vfrom the vcommon ability of the brain to store memory.
    Memory does not equal intelligence.

    This is why , i say, all human problems with intelligence interference like retardation, Autisms, depressions, phobias etc etc can be explained as simply triggering problems with the memory.
    So the Savant great memory reveals the great problem. Can’t remember everything else and so fails in learning.
    the abberation reveals the equation of whats wrong.
    Nothing to do with a thinking human being made with the intelligence , a part, of God.
    Creationism can contribute to healing by questioning presumptions on human intelligence here.
    Welcome and bring on mathy apes.

  7. Notes:

    “But then with me the horrid doubt always arises whether the convictions of man’s mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy. Would any one trust in the convictions of a monkey’s mind, if there are any convictions in such a mind?” –
    Charles Darwin – Letter To William Graham – July 3, 1881

    “Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation.”
    Alfred Russell Wallace, New Thoughts on Evolution, 1910

    Human brain has more switches than all computers on Earth – November 2010
    Excerpt: They found that the brain’s complexity is beyond anything they’d imagined, almost to the point of being beyond belief, says Stephen Smith, a professor of molecular and cellular physiology and senior author of the paper describing the study: …One synapse, by itself, is more like a microprocessor–with both memory-storage and information-processing elements–than a mere on/off switch. In fact, one synapse may contain on the order of 1,000 molecular-scale switches. A single human brain has more switches than all the computers and routers and Internet connections on Earth.

    Excerpt: Although Lennox considered the performance of mental arithmetic as “mental work”, it is not immediately apparent what the nature of that work in the physical sense might be if, indeed, there be any. If no work or energy transformation is involved in the process of thought, then it is not surprising that cerebral oxygen consumption is unaltered during mental arithmetic.

    Has “Evolution” Given Humans Unique Brain Structures? – February 22, 2013
    Excerpt: “We did functional brain scans in humans and rhesus monkeys at rest and while watching a movie to compare both the place and the function of cortical brain networks.,,, we found two networks unique to humans and one unique network in the monkey.”
    “When watching a movie, the cortex processes an enormous amount of visual and auditory information. The human-specific resting state networks react to this stimulation in a totally different way than any part of the monkey brain. This means that they also have a different function than any of the resting state networks found in the monkey. In other words, brain structures that are unique in humans are anatomically absent in the monkey and there no other brain structures in the monkey that have an analogous function.,,

    Geometric Principles Appear Universal in Our Minds – May 2011
    Excerpt: Villagers belonging to an Amazonian group called the Mundurucú intuitively grasp abstract geometric principles despite having no formal math education,,, Mundurucú adults and 7- to 13-year-olds demonstrate as firm an understanding of the properties of points, lines and surfaces as adults and school-age children in the United States and France,,,

    Children Act Like Scientists – October 1, 2012
    Excerpt: New theoretical ideas and empirical research show that very young children’s learning and thinking are strikingly similar to much learning and thinking in science. Preschoolers test hypotheses against data and make causal inferences; they learn from statistics and informal experimentation, and from watching and listening to others. The mathematical framework of probabilistic models and Bayesian inference can describe this learning in precise ways.

    Darwin’s mistake: explaining the discontinuity between human and nonhuman minds. – 2008
    Excerpt: Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as “one of degree and not of kind” (Darwin 1871).,,, To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain,,,

    The Mind Is Not The Brain – Scientific Evidence – Rupert Sheldrake – (Referenced Notes)- video

    Young Children Have Grammar and Chimpanzees Don’t – Apr. 10, 2013
    Excerpt: “When you compare what children should say if they follow grammar against what children do say, you find it to almost indistinguishable,” Yang said. “If you simulate the expected diversity when a child is only repeating what adults say, it produces a diversity much lower than what children actually say.”
    As a comparison, Yang applied the same predictive models to the set of Nim Chimpsky’s signed phrases, the only data set of spontaneous animal language usage publicly available. He found further evidence for what many scientists, including Nim’s own trainers, have contended about Nim: that the sequences of signs Nim put together did not follow from rules like those in human language.
    Nim’s signs show significantly lower diversity than what is expected under a systematic grammar and were similar to the level expected with memorization. This suggests that true language learning is — so far — a uniquely human trait, and that it is present very early in development.
    “The idea that children are only imitating adults’ language is very intuitive, so it’s seen a revival over the last few years,” Yang said. “But this is strong statistical evidence in favor of the idea that children actually know a lot about abstract grammar from an early age.”

    Stark Differences Between Human and Chimp Brains – Brian Thomas, M.S. – Oct. 5, 2012
    Excerpt: The researchers used a new technique to peer in unprecedented detail at the methylation patterns of human and chimp DNA that they harvested from brain tissue of three cadavers of each species. They compared only those DNA sequences already known to have basically the same genes, ignoring the vast majority of DNA. If humans and chimps are close relatives, then they should have similar DNA methylation patterns in the areas of chromosomes that they have in common such as similar gene sequences.2 However, this team found major differences.
    In particular, human and chimp DNA methylation patterns, called “methylomes,” were very different between the two species’ brain tissue. The data statistically indicated that “major principal components separate humans and chimpanzees,” according to their report in American Journal of Human Genetics.1,3
    A second observation is that the very genes that were differently methylated “exhibit striking associations with several disorders, including neurological and psychological disorders and cancers.”1 These data show that methylation patterns in many cases can tolerate very little disruption, thus presenting another impossible hurdle for the evolutionary model to overcome.
    If humans evolved from chimpanzee-like creatures, then some unknown evolutionary process must have altered their methylomes. But since methylomes apparently cannot tolerate that much alteration, then the evolutionary story must be in error.
    Human and chimp species-specific and irreducibly complex methylomes refute human evolution.,,,
    (Zeng, J. et al. 2012. Divergent whole-genome methylation maps of human and chimpanzee brains reveal epigenetic basis of human regulatory evolution. American Journal of Human Genetics. 91 (3):455-465.)

  8. semi OT: although Ian Juby is a YEC, I have to admit that his teaching style is fun to watch and that he does bring a lot of very interesting facts to the table in his videos to keep things interesting.

    Walk like an ape? This is Genesis Week, Episode 34, season 2, with Wazooloo/Ian Juby – video

  9. Do We Have Souls? Lee Strobel interviews Dr. J.P. Moreland – article

    “If atheism is true, it is far from being good news. Learning that we’re alone in the universe, that no one hears or answers our prayers, that humanity is entirely the product of random events, that we have no more intrinsic dignity than non-human and even non-animate clumps of matter, that we face certain annihilation in death, that our sufferings are ultimately pointless, that our lives and loves do not at all matter in a larger sense, that those who commit horrific evils and elude human punishment get away with their crimes scot free — all of this (and much more) is utterly tragic.”
    ~Damon Linker – ‘Must Atheists Be Nihilists?’

  10. I admit I was trolling a bit. I found it interesting, and predictable, that everyone here immediately jumps to implications for religious doctrine.

  11. Yeah, comment 1 was totally about religious doctrine… (imp)

  12. Pascal’s Anthropological Argument – (Christianity is the best explanation for the human condition) – video

  13. sigaba:

    I found it interesting, and predictable, that everyone here immediately jumps to implications for religious doctrine.

    You mean other than Joe’s and News’ and my comments?

    2 out of 5 people constitutes “everyone”?

    I find it interesting, and predictable, that you would think your preconceptions have been verified, notwithstanding the contrary data. :)

  14. Hi Joe,

    You wrote:

    Take 8 peanuts and put them into a large cup so that they only fill it 1/2 way.

    Take 4 peanuts and put them into a smaller cup such that they fill the cup.

    Then see which cup gets chosen the most.

    You made an interesting proposal. However, I think that the baboons would pass this test. Even pigeons can be trained to attend to the relative numerosity of two different sets, irrespective of the size and shape of the items. See this article: “Birds’ Judgments of Number and Quantity” at http://www.pigeon.psy.tufts.ed.....ection%203 by Jacky Emmerton, Department of Psychology, Purdue University. Still, it was a good idea for an experiment.

    The article also reveals that animals can be taught to attend to absolute numerosity, and pick a set containing, say, three items. However, there’s no good evidence to date that non-human animals can count.

  15. Hi News,

    Thanks for the response.

    With the peanuts in the cup the baboons would only know how many if they dumped them out. The smaller cup should appear to them to contain more as it is full. Unless they can reason that the larger cup contains more volume and therefor more peanuts even though it isn’t full.

    But OK, if they were taught and trained that the larger cup contains more then when the selection time came they would nail it.

    Unfortunately I don’t have any baboons to try this on… :)

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