Arithmetic has a biological origin – it's an expression in symbols of the 'deep structure' of our perception

Abstraction: Four perceptual axioms uniquely derive arithmetic from biological first principles

Key points:

• Randolph Grace and colleagues prove that four qualitative assumptions — monotonicity, convexity, continuity, and isomorphism — are jointly sufficient to uniquely identify arithmetic (addition and multiplication over the reals) from all possible algebraic systems
• These four conditions are posited as principles of perceptual organisation shared across animals, forming a biological "deep structure" shaped by natural selection
• Supporting evidence: bees navigate by computing the most direct return path from a meandering outbound journey — a non-symbolic algebraic operation likely precursor to arithmetic, achieved with ~960,000 neurons
• Over 100 distinct numeral systems across human civilisations all converge on addition and multiplication as fundamental operations, suggesting arithmetic is a universal rediscovery rather than a cultural invention
• The result implies mathematics is simultaneously invented (uniquely symbolised by humans) and discovered (biologically grounded), potentially resolving the "unreasonable effectiveness of mathematics" puzzle
• The authors connect their framework to non-dualist philosophies (Taoism, Buddhism, Māori mātauranga Māori), arguing mind and world share a common unity

Connections: Philosophy Of Mathematics · Cognitive Science · Perception · Evolutionary Biology

Source: https://theconversation.com/arithmetic-has-a-biological-origin-its-an-expression-in-symbols-of-the-deep-structure-of-our-perception-211337