Timing and Number Cognition Study Notes

Due Date: February 23, 2026, on OWL Brightspace.
Weight: $5\%$ of the final grade.
Requirements: Informal commentary, maximum $300$ words, based on topics from Weeks 1-6 (History, Sensory Systems, Memory, Associative Learning, Orientation/Navigation, Timing/Number).
Rubric: Evaluates critique of existing knowledge, connection to research, and language use.

Periodic Timing: Relates to cyclical activity on a $24\,hour$ scale (Circadian rhythm). * Entrainment: Synchronizing the internal clock with the day/night cycle. * Free-running rhythm: Circadian cycles occurring without environmental cues, typically close to but not exactly $24\,hours$ . * Clock Anatomy: The Suprachiasmatic nucleus (SCN) is the master mammalian clock. Information flows: $Light \rightarrow photoreceptors \rightarrow melanopsin \rightarrow SCN \rightarrow pineal \rightarrow melatonin$ .
Interval Timing: Timing short durations since a specific event; critical for associative learning and foraging.

Peak Procedure: A method where animals are trained on a Fixed Interval schedule. On random non-reinforced probe trials, response rates peak at the originally trained interval duration.
Scalar Property: The variability of timing curves is proportional to the length of the interval (related to Weber’s Law).
Information Processing Model (Scalar Expectancy Theory - SET): Proposes a Pacemaker (generates pulses), a Switch (opens to collect pulses), an Accumulator, Memory (Working and Reference), and a Decision mechanism.
Oscillator Model: Uses multiple oscillators (like pendulums) cycling at different scales rather than a single pacemaker.
Behavioural Models: Suggest timing is tracked via sequential behaviors or the strength of memory decay.

Approximate Number System (ANS): An evolutionary, non-verbal system handling approximate magnitudes on a continuous mental number line. It exists in infants, animals, and cultures without formal number language (e.g., Pirahã and Mundurukú).
Object File System: A discrete tracking system limited to small quantities ( $1-4$ ). It is characterized by the "Set Size Signature."
Weber’s Law in Number: * Distance Effect: Discrimination is easier when two numbers are farther apart. * Magnitude Effect: For a constant difference, smaller numbers are easier to discriminate than larger ones.

Operations: Addition and subtraction are not dependent on language. Demonstrated in human babies, monkeys, and chicks (Rugani et al. 2009).
Ordinality: The ability to rank numbers by magnitude. Rhesus macaques show accuracy in ordinal judgments with novel stimuli (Brannon & Terrace).
Nominal Numbers: Arabic numerals used as labels. Successfully taught to chimpanzees (Sheba) and grey parrots (Alex).
Language Influence: While ANS is universal, precise arithmetic for numbers larger than $5$ typically requires specific number language.

Intraparietal Sulcus (IPS): The primary brain structure for numerical and magnitude processing. It shows shorter response latencies than the Prefrontal Cortex.
Prefrontal Cortex (PFC): Also contains numerosity-selective neurons tuned to specific values.
Tuning Curves: These neural responses explain distance and magnitude effects; curves for larger numbers are broader and overlap more (creating more "noise").

Commonality: Both are fundamental cognitive processes for survival (e.g., counting predators vs. timing predator scans).
Unified System: Both rely on ratio-dependent discrimination, follow Weber’s Law, and show overlapping activation in the Parietal Cortex and IPS.
Scalar Invariance: Both processes demonstrate variability proportional to the magnitude being judged.