Neurophilosophy

OUR ability to use and manipulate numbers is integral to everyday life – we use them to label, rank, count and measure almost everything we encounter. It was long thought that numerical competence is dependent on language and, therefore, that numerosity is restricted to our species. Although the symbolic representation of numbers, using numerals and words, is indeed unique to humans, we now know that animals are also capable of manipulating numerical information.

One study published in 1998, for example, showed that rhesus monkeys can form spontaneous representations of small numbers and use them to choose containers with more pieces of fruit. More recently, it was found that monkeys can perform basic arithmetic on a par with college students. Now, German researchers report that not only do rhesus monkeys understand simple mathematical rules, but also that these rules are encoded by single neurons in the rhesus prefrontal.

Animal experiments and neuroimaging studies performed with humans have implicated the prefrontal cortex (PFC) in the processing and execution of numerical operations. In humans, this part of the brain is engaged during tasks involving mathematical rules, and it has long been known that damage to the PFC can lead to impaired quantitative reasoning. Sylvia Bongard and Andreas Nieder of the Institute of Neurobiology at the University of Tubingen therefore hypothesized that PFC neurons are involved in encoding aspects of numerosity, and designed a numerical task based on simple numerical rules to test this.

Two rhesus monkeys were shown pairs of visual stimuli consisting of sets of dots and trained to compare them by applying two simple mathematical rules. In each trial, they were shown a sample set of dots followed, after a short delay, by a test set with a different number of dots. The ‘greater than’ rule required the monkeys to release a lever if the test set contained more dots than the sample set, whereas the ‘less than’ rule required them to release the lever if it contained fewer dots. During the interval between each pair of stimuli, a cue was presented, indicating which of the two rules should be applied.

While the monkeys performed this task, microelectrodes were used to record the activity of approximately 500 individual and randomly selected PFC neurons. The response of each cell was determined during four different time periods in each trial: the time during which the sample set of dots was displayed, the delay between the sample and the cue indicating which rule to apply, the time during which thecue was displayed, and the delay between presentation of the rule-related cue and the monkeys’ response to it.

Significantly, the monkeys immediately applied the mathematical rules to all the stimuli pairs they were shown, even when the sample sets contained numerosities that had not been previously presented. Selective responses were recorded during the interval between the cue and the response. 90 rule-selective neurons (~19% of the total from which recordings were made) were detected, which fired independently of the number of dots presented or the sensory properties of the rule-related cue. Of these, 50 fired exclusively when the monkeys produced ‘greater than’ responses, and the remaining 40 fired exclusively when they produced ‘less than’ responses. Rule selectivity was not encoded immediately, but emerged in the cells after a short period of time.

Across hundreds of trials, the monkeys had a minimum success rate of 83%. The researchers compared the neuronal responses of individual rule-selective neurons during trials in which the monkeys gave correct responses with trials in which they made errors. The firing rates were found to decrease significantly when the monkeys made the wrong choices. The selectivity of the responses also enabled the reearchers to predict which rule the monkeys were applying during each trial, from the cellular activity they recorded.

Thus, single neurons in the lateral PFC of the rhesus monkey can flexibly encode abstract mathematical rules which guide greater than/ less than decisions. Each session involved large numbers of unique trials, so it was impossible for the monkeys to solve the task by learning. Instead, they were required to understand relationships between numerosities in each pair of stimuli, and to apply these principles to make their decisions. These findings are consistent with a model which proposes that the PFC contains a network of distinct rule-coding neuron clusters, each of which receives input from a corresponding internal memory cluster and sends its output to a dedicated downstream cluster. The findings also add to a body of evidence suggesting that humans and other primates process numbers using common cognitive skills with a shared evolutionary origin.


Bongard, S. & Nieder, A. (2010). Basic mathematical rules are encoded by primate prefrontal cortex neurons Proc. Nat. Acad. Sci. DOI: 10.1073/pnas.0909180107.

Cantlon, J. F. & Brannon, E. M. (2006). Basic math in monkeys and college students [Full text]

Hauser M. D., et al. (2000). Spontaneous number representation in semifree-ranging rhesus monkeys. Proc. R. Soc. Lond. B Biol. Sci. 267:829-33 [PDF]

Comments

  1. #1 Jacob Mack
    January 21, 2010

    Good read. Once again our evolutionary relationship to other organisms is well evidenced.

  2. #2 SteveP
    January 21, 2010

    I might have to read the papers to get the full gist, but at the moment, I dont understand how you get from the observation that

    particular neurons (out of a tiny subset of all neurons in the PFC, let alone the brain) fire exclusively when a greater than rule is applied, and other fire exclusively when a less than rule is applied,

    to the conclusion that

    “…single neurons in the lateral PFC of the rhesus monkey can flexibly encode abstract mathematical rules which guide greater than/ less than decisions.”

    Identifying some neurons involved in a process doesn’t necessarily imply that these neurons are encoding the entire process/concept. Surely the relationship between these neurons and possibly countless other neurons around the brain doing their thing is important, and you can’t just say that firing of neuron set A in isolation encodes an abstract mathematical rule.

  3. #3 Brandon
    January 21, 2010

    As an undergraduate who has a variety of interests mainly surrounding biology/neuroscience/philosophy this had proved a great site for leisure and challenging reading. Keep it up please.

  4. #4 Mo
    January 22, 2010

    @SteveP: Quite right – the cells could be part of a wider diffuse network, and almost certainly rely on inputs from other neurons involved in numerical processing. But that doesn’t exclude the possibility that they are the only cells in this hypothetical network that respond to/ encode greater than/ less than rules. I was merely describing the authors’ conclusion – let me know if you want me to send you the PNAS paper.

    @Brandon: Thanks. I will keep it up, and hope you continue to enjoy reading.

  5. #5 AK
    January 22, 2010

    Significantly, the monkeys immediately applied the mathematical rules to all the stimuli pairs they wer shown

    S/B “Significantly, the monkeys immediately applied the mathematical rules to all the stimuli pairs they were shown”

    Also, could you send me the paper? Thanks.

  6. #6 ianam
    January 22, 2010

    “More recently, it was found that monkeys can perform basic arithmetic on a par with college students. ”

    This is misleadingly stated. The tasks involved are “approximate” addition of 1+1, 2+2, and 4+4 — not exactly college level arithmetic.

  7. #7 Scientific Chick
    January 23, 2010

    Interesting read. I wonder if the same part of the brain (same neurons, possibly) would be involved in a similar task but with a real-life application (such as the fruits in the bucket idea)? I’m always curious about these studies involving monkeys interacting with a screen.