Time and Number Basics

• Time and number are cognitive processes aiding animal survival.
• Animals need to determine the number of approaching predators.
• Animals must establish how long it has been since they last located food.
• Underlying cognitive processes for time and number are similar, despite different study methods.

Numerical Discrimination

• True counting and arithmetic are uniquely human skills.
• Humans and non-human animals possess a non-verbal means of discriminating numerical magnitude.
• Numerical discrimination is seen across species, including apes, monkeys, dogs, and birds.
• Numerical discrimination can be important for counting offspring, food, and predators.
• Lions respond differently to recordings of approaching lions (Ogutu & Dublin, 1998).

Types of Number

• Cardinal numbers indicate quantity e.g., how many?
• Ordinal numbers indicate ranking e.g., what ranking?
• Nominal numbers are assigned e.g., assigned number

Approximate Number System (ANS)

• The ANS is an evolutionary number system existing without culture or language.
• The ANS is shared by humans and non-human animals.
• Even human tribes without formal number systems can discriminate numerosity using the ANS e.g., the Pirahã and the Mundurukú (Gordon, 2004; Pica, Lemer, Izard, & Dehaene, 2004).
• Numbers become discreet representations in human language when number symbols are mapped onto magnitudes through learning in childhood using fast mapping.
• Numbers are represented internally and continuously as an approximate magnitude on a mental number line.
• According to the ANS, numbers are internally represented on a continuous, linear number line, which allows both humans and non-human animals to discriminate approximate magnitudes.
• The ANS has no upper limit, but it becomes systematically less precise as the number increases.
• The ANS operates according to Weber's law.

Weber's Law

• Weber's law states that the change in stimulus intensity needed for an organism to detect a change is a constant proportion of the original stimulus intensity, rather than a set amount.
• Important effects are the distance and magnitude effects
• Distance Effect: The farther apart two numbers are, the easier they are to discriminate.
• Magnitude Effect: When distance is held constant, smaller numbers are easier to discriminate than larger numbers.
• 1 vs 8 easier to discriminate than 1 vs 2. (0.12 vs. 0.5)
• 1vs 2 easier to discriminate than 8 vs 9. (0.5 vs. 0.88)

Object File System (Subitizing)

• Object File System deals with small numbers only, specifically the numbers 1-4.
• These numbers are thought to be mapped discreetly in a one-to-one representation, making them instantly accessible.
• For instance, people immediately recognize four dots on a screen without systematically counting them.

Hauser, Carey, & Hauser - Monkey Experiment

• Wild, untrained monkeys successfully chose a larger number of food items over a smaller number of food items.
• Over 200 semi-free-ranging rhesus monkeys watched as experimenters placed pieces of apple into each of two containers.
• When the containers contained 1 vs 2, 2 vs 3, or 3 vs 4 slices of apple, the monkeys chose the container with the greater quantity of food.
• When ratios exceeded 4 (e.g., 4 vs 5, 4 vs 6, 4 vs 8, or 3 vs 8), the monkeys were unable to reliably choose the container with the most food

Object File System: Is it a thing?

• Hauser et al. suggested the breakdown in monkeys’ performance beyond four items indicates the use of a spontaneous number system (object file system) rather than the ANS.
• Other research (Beran, 2001; Beran & Beran, 2004) saw chimps discriminating magnitude beyond four items, up to 10 items.
• The chimps watched as an experimenter sequentially dropped food (M&Ms or fruit) into two bowls.
• The chimp was then allowed to choose one of the two bowls and consume its contents.

Brannon & Terrace - Monkey criticism

• One criticism of laboratory monkeys in counting tasks is based on training effects where, with repetition, they learn to solve the counting task
• Brannon and Terrace resolved this issue by spontaneously testing their monkeys on new ratios which they have never encountered before.
• Monkeys still perform highly successfully even with new ratios.

Can Dogs "Count?" Sequential Presentation

• Modality of Presentation
• Nieder, Diester, & Tuduscius, 2006: Monkeys could do sequential task, but better at simultaneous task.

Can Dogs "Count?" Simultaneous Presentation

• Sedona's performance was significantly above chance on all ratios except the most difficult one, 8 vs 9.
• Sedona's percentage correct was highly and negatively correlated, r(7) = -.862, p < .01, with the S/L ratio, indicating consistency with Weber's law.

Addition and Subtraction in Animals

• Evidence of addition and subtraction found in human infants (Wynn, 1992) and some non-human animals using looking time tasks with impossible outcomes (e.g., 1 + 1 = 3, 2 − 1 = 2).
• Alex, the grey parrot (Pepperburg, 2006), was taught Arabic numerals and could respond correctly when asked "which bigger".
• Sheba, a chimp (Boysen, 1993) could search a room for objects and report how many she found by touching the corresponding numeral.
• Chimps could not learn to choose the smaller of two quantities of candy, but when the candy was replaced by numerals, they could.

Single Cell Recording -The Brain and Numerical Processing

• Single-cell recordings implicate the intraparietal sulcus (IPS) as the primary brain structure involved in numerical processing.
• Although it was originally thought that the IPS might contain a module for specific numbers, evidence now suggests the IPS serves a "patchwork" of different functions (Ansari, 2008).
• The prefrontal cortex (PFC) is also involved in numerical processing.
• Response latencies are faster in the IPS than in the PFC
• The IPS extracts numerical information which is then sent to the PFC for processing (Nieder & Dehaene, 2009).

Nieder & Miller - The Brain and Delayed tasks

• In a delayed matching to sample task (Nieder & Miller, 2004), monkeys were shown an array of 1-5 items and subsequently determined if a sample array matched this number
• Single-cell recordings showed that monkeys had numerosity selective neurons, which fired preferentially to a "preferred" numerosity and Neurons appear to be "tuned” for specific numerosities.
• Tuning curves are imprecise, so a neuron with a "preference" for 4 will also fire for 3 and 5.

ANS Tuning Curves Explained

• Tuning curves explain the distance and magnitude effects in the analogue magnitude system.
• When two numbers are farther apart, their tuning curves overlap less, making them easier to discriminate.
• As numerical magnitude increases, tuning curves widen and become less precise with sharper curves, meaning more precision

Scalar vs.Logarithmic Models

• In the ANS hypothesize, the mental number line is hypothesized to be linear/scalar.
• Other models suggest number lines could be logarithmic.

Summary

• While true counting is unique to humans, there is a shared, non-verbal ability to discriminate number in humans and non-human animals..
• Suggests evolutionary ancient origin of this ability
• Two main systems have been proposed
• ANS (widely accepted)
• Object File (support more mixed)
• Time and number are closely linked (next lecture!)

Timing

• Timing is relevant to all aspects of behavior.
• Occurrences exist across a time-some events are close and others have longer separating intervals.
• Many topics e.g., sensitization, habituation, and associative learning depend upon timing.
• Temporal control of behavior has been researched rigorously in animal cognition over the past 40 years.

Circadian/Periodic Timing

• Timing in a 24-hour day-night cycle
• Circadian/Periodic Timing regulates sleep/wakefulness.
• Components include the Suprachiasmic nucleus and Pineal gland/melatonin.
• Crucial in migratory species and their migratory patterns
• Zugunruhe/photoperiod in migratory birds

Interval Timing

• It allows animals to respond after a specific interval has elapsed since an event.
• Important to know how often to scan for predators.

Methods for the study of interval timing

• Duration estimation (Fixed Interval): Participants learn to respond after a set time from the stimulus or the start of a trial.
• Peak Procedure: A discrete-trial variation of a fixed interval schedule to study timing in animals.
• Animal receives fixed interval training before occasional random, nonreinforced trials during which stimulus extends past the usual time of reinforcement.
• Responses exhibited during test trials show a peak at the fixed interval value of the training schedule.

Scalar Expectancy Theory (SET)

• Gibbon and Church (1984).
• It serves as the standard model in timing research.
• Incorporates scalar invariance (or scalar property), where animals respond to relative values rather than absolute values.

Scalar Expectancy Theory (SET) Components

• Clock: Provides information about how much time has elapsed.
• Achieved with the Pacemaker providing pulses.
• Switch opens before an event to be timed and pulses collected by an Accumulator.
• Memory: Number of accumulated pulses and Event duration are stored in working memory.
• Decision: Comparison working and reference memory.
• Determines weather working memory matches reference memory in task.

Henderson et al (Humming Bird)

• Wild hummingbirds forage on artificial flowers
• Birds visit flowers at intervals matching refill rates - e.g., Red=10 mins, Green=20mins
• Demonstrates Scalar invariance

Temporal Bisection Task

• Church & Deluty (1977) tested Temporal Bisection Task with rats
• 2s vs 8s light/tone Training Trials
• Used Probe Trials of 3s, 4s, 5s, 6s, 7s
• Evaluated Arithmetic mean (5) vs. Geometric mean (4)

Recalling Differences in Discriminative Ability

• We can't take the point where the comparison stimulus is considered "lighter" half the time and heavier half the time as a threshold that is the point where the weights are judged to be the same
• (0.5 on y axis = 99g)...point of subjective equality (PSE).
• Instead, we are interested in the point where heavier/lighter can be distinguished from the PSE...
• Point of subjective equality (0.25 and 0.75 on y axis).

Behavioural Theory Of Time

• Killeen and Fetterman (1993) Characterizes timing in more behavioural terms.
• Uses pacemaker, decision and memory (but differently from SET).
• Adjunctive behvaiours are systematic responses that occur when reinforcers are delivered at fixed intervals.
• Different behaviours occur at different intervals - post food focal search, general search, pre food focal search etc
• Subjects use temporally organized behvaiours to track time.

Oscillator Model of Time

• Crystal 2012; Cheng & Crystal 2008. (Alternative to SET).
• The Vector and matrix based model.
• Instead of using a pacemaker emiting pulses, this model uses multiple oscillators which each oscillate for different time amounts.
• Oscillator (pendulum) and pacemaker (hourglass)
• Oscillator cycles through predictable sequences of events over & over again .Different time points become associated with different oscillators.

Link between Time/Number

• The same brain regions activated when thinking about time, are also activated in the same way when thinking about time.

Conclusions

• Time and number are fundamental components of cognition in both human and non-human animals.
• Time and number are readily studied both in laboratory and natural settings.
• Both time and number are ratio-dependent, and operate in accordance with Weber's law with Magnitude/Distance Effects and Scalar Invariance.
• Comparative study of time and number in non-human animals has contributed to advances in the understanding of cognitive and neural mechanisms.