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Endnotes: Abstract Math and its Implications

Endnotes: Abstract Math and its Implications

Back to Topics │Abstract Senses│ Start: Relativity & Reaction
– Nerd Cheat Sheet: Abstract Math and its Implications

Abstract Math explores how humans developed the ability to move from “few and many” to symbolic numbers, and how similar abilities appear in animals and infants. These references underpin the data used in:

Nerd Cheat Sheet: Abstract Math and its Implications

(1) Historical Context

  • Elizabethan literacy: ~20–30% of men, ~10% of women literate; highly variable by region and class (Cressy, Literacy and the Social Order, 1980).
  • Numeracy: depended on social position; peasants relied on tally sticks, trade accounts, and oral reckoning.
  • Tally sticks: widely used for accounts until 19th century; famously stored in UK Exchequer (UK Parliament archives).

(2) Animal Number Sense

  • General review: “Numerical Abilities in Animals.” Biological Reviews (Pongrácz et al., 2014).
  • Cats & dogs: small-number discrimination (1–3 or 4 items), performance drops beyond 4 (summarised in Pongrácz review).
  • Birds:
    • Ravens and crows: discriminate up to 4–5 objects (Science, 2005).
    • Parrots: Alex the African Grey learned labels for numbers up to 6+ (The Alex Studies, Pepperberg, 1999).
  • Fish: Guppies and angelfish reliably distinguish shoal sizes up to ~4 (Agrillo et al., PNAS, 2012).
  • Primates:
    • Chimpanzees and rhesus monkeys can subitize up to 3–4 and learn symbols up to 7–9 (Hauser & Carey, Science, 1998).
    • Gorillas trained for basic symbolic arithmetic (Science reports, 2009).

(3) Human Infants & Early Cognition

  • Wynn, K. (1992). “Addition and subtraction by human infants.” Nature, 358: 749–750. Infants as young as 6 months show surprise when outcomes defy “1 + 1 = 2”.
  • Xu, F., & Spelke, E. (2000). “Large number discrimination in 6-month-old infants.” Cognition, 74: B1–B11. Infants can distinguish larger sets when ratios are big enough (e.g., 8 vs. 16).

(4) Theoretical Frameworks

  • Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics (Oxford University Press). Key framework on subitizing, approximate number systems, and symbolic math.
  • Boyd, R. & Richerson, P. (1985). Culture and the Evolutionary Process (University of Chicago Press). Influence of cultural learning in extending abstract senses.

Back to Topics │Abstract Senses│ Start: Relativity & Reaction
– Nerd Cheat Sheet: Abstract Math and its Implications

📖 Series Roadmap

  1. Forward: A Little Background
  2. Introduction: Action, Reaction, and the Human Paradox (16.09.2025)
  3. Looking Back in Time: The Development of the Human Brain (23.09.2025)
  4. Abstract Senses: Enhancing the way we see the world outside (30.09.2025)
  5. Bias as a Concept & Climbing the Stairs: Pattern Recognition & Everyday Tasks (07.10.2025)
  6. Abstract Feelings and Abstract Senses (14.10.2025)
  7. Motivation (04.11.2025)
  8. The Social Knowledge Base (11.11.2025)
  9. Potential (18.11.2025)
  10. The Subliminal Way We Go Through Life (26.11.2025)
  11. Taking Responsibility (02.12.2025)
  12. Fishing for Complements (22.12.2025)
  13. Peter and Fermi (22.12.2025)

🔗 R&R Navigation

Back to Topics │Abstract Senses│ Start: Relativity & Reaction
– Nerd Cheat Sheet: Abstract Math and its Implications

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