Thank Me With TEA!

Numerosity

Resources

Contours of time: Topographic construals of past, present, and future in the Yupno valley of Papua New Guinea (Núñez et al., 2012)

This study investigated how the Yupno, an indigenous group from Papua New Guinea who heavily rely on allocentric topographic (uphill/downhill) spatial terms, construe deictic time (past, present, future). The findings showed that the Yupno spontaneously structure time based on allocentric topography: the present is co-located with the speaker, the past is downhill, and the future is uphill. This spatial construal is not linear but exhibits a specific, bent geometry that appears to reflect the local terrain of the Upper Yupno valley.

Decision making, impulsivity and time perception (Wittmann & Paulus)

This article explores the hypothesis that impulsive individuals experience time differently—with a higher cost to delay—which explains why they discount the value of delayed rewards more strongly than self-controlled individuals. Impulsive subjects tend to overestimate the duration of time intervals. This altered sense of subjective time is linked to cognitive models of time perception, suggesting it could be caused by either increased attention to time or an arousal-related increase in the rate of the internal pacemaker (a faster internal clock rate).

Important

  • Numerical competence – This ability is widespread across the animal kingdom.
  • Methodological problem in numerosity research – Researchers must ensure that animals respond to quantity as opposed to other non-numerical features, such as the overall amount of space covered, color, or shape [45, 11:48].
  • Weber’s law – The Approximate Number System (ANS) is said to follow this law [12, 30:07].
  • Symbolic reference gap – This concept represents the idea that non-symbolic mathematical skills cannot simply scale up to allow for the development of symbolic mathematical skills.

Core concepts

  • Numerical competence – The ability to discriminate the number of elements in a set, known as numerosity, is widespread across diverse zoological groups, including insects, spiders, fish, birds, primates, and other mammals [1, 33:56].
  • Approximate Number System (ANS) – A cognitive system, often called the “number sense,” that allows for the estimation of numerical quantity without relying on symbols or language. It is ubiquitous, existing across different cultures, ages, and animal species.
  • Early Numerical Competence – Research indicates that human infants possess hardwired numerical abilities, as 6-month-old infants preferentially attend to image streams where the number of dots changes, even when controlling for spacing, location, and size [10, 56:00].
  • Evolutionary benefits of numerosity perception – Numerical competence is adaptive, providing advantages in several areas:
    • Foraging: Identifying a food patch with a greater number of items [8, 52:00].
    • Navigating: Enumerating landmarks to estimate travel distance (e.g., honeybees counting landmarks) [8, 34:00].
    • Predation avoidance: Seeking shelter within large groups of companions.
    • Social territory defense: Assessing the strength or number of opponents before fighting.
    • Reproductive activities: Tracking competitor numbers or possessions (like a shrike collecting bugs) in the context of mating competition [10, 55:00].
  • Ratio-Dependency Effects (Weber’s Law in ANS) – ANS performance reflects Weber’s law, leading to two observable phenomena related to the ratio between quantities [14, 15, 68:00]:
    • Numerical distance effect: Similar numerical values are more difficult to discriminate; greater distance yields better performance (e.g., a frog distinguishing 3 vs 6 is easier than 3 vs 4) [14, 69:10].
    • Numerical size effect: Discrimination precision decreases systematically as the absolute magnitude of the numbers increases, even if the absolute difference is constant (e.g., discriminating 2 vs 4 is easier than 4 vs 6) [14, 70:00].
  • Object Tracking System (OTS) / Subitizing – A proposed non-symbolic system for the exact and fast quantification of small sets (1 to 4 items) without counting [18, 91:06]. Quantification of larger numerosities is handled by the Approximate Number System (ANS) [18, 92:00].
  • Cross-Modal Perception – Monkeys demonstrate the ability to match and tally quantities across senses, such as matching the number of voices they hear to the number of faces they see, with cross-modal accuracy being equal to accuracy obtained within a single modality [6, 7, 47:00, 49:00].
  • Arithmetic Abilities in Animals – Newborn chicks appear to possess some arithmetic abilities, systematically picking a hidden set that contains more items after objects have been moved and hidden under covers, suggesting they keep track of quantities [3, 38:49].
  • Empty Sets – Monkeys (rhesus macaques) were able to accurately match empty sets, demonstrating a conceptual precursor to the zero concept, independent of background area or color [8, 51:00].

Theories and Frameworks

  • Weber’s law – A law of psychophysics defining the relationship between the physical properties of a stimulus and the resulting perceptual experience [64:00, 65:00]. It states that the difference threshold (DL)—the minimal difference between two stimuli required for them to be barely distinguishable—is proportional to the value of the standard stimulus (S) [12, 13, 67:00].
  • ANS Neural Loci – Convergent findings suggest that the ANS is located in the posterior parietal cortex (PPC), specifically the intraparietal sulcus (IPS). Researchers have shown that neural populations tuned to small numerosities in the human parietal cortex are organized topographically, forming a numerosity map [16, 17, 77:00].
  • Numerical Competence Conceptualization (Núñez) – Numerical abilities are typically divided into non-symbolic (ANS, OTS/Subitizing) and symbolic types, though the relationship between them remains debated [17, 89:00]. Symbolic abilities may require cultural tools such as counting words, oral language, or written numerals [20, 90:00].

Notable Individuals

  • Dr. Nadiya Slobodenyuk: Course instructor/presenter of the lecture material on Numerosity Perception.
  • Ernst Heinrich Weber: German physician known for his work in psychophysics, establishing the principle known as Weber’s law regarding the constancy of the difference threshold ratio [12, 64:00].
  • Elizabeth Brannon: Her laboratory conducted key research demonstrating that 6-month-old human infants display early numerical competence, attending to numerically changing stimuli [10, 58:09].
  • Rafael E. Núñez: Conceptualized numerical abilities as divided into symbolic and non-symbolic systems and argues that counting requires cultural tools, such as counting words.
  • Jean Piaget: Early developmental psychologist who believed that the acquisition of counting words plays little to no role in the development of the concept of cardinal number [20, 96:00].
  • Brian Butterworth: Conducted studies suggesting that counting words above four are not necessary for children to count small quantities, based on research with Indigenous Australian children using restricted number vocabularies [23, 107:00].