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We are wanderers: Abstract geometry reflects spatial navigation.

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Abstract geometry mirrors spatial navigation geometry in humans and animals. Language can isolate ancient spatial representations, suggesting abstract geometry originates from physical world navigation.

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Area of Science:

  • Cognitive Science
  • Psychology
  • Philosophy of Mathematics

Background:

  • Historically, the relationship between abstract mathematical geometry and real-world physical geometry has been a subject of philosophical debate.
  • Understanding how humans and animals perceive and represent geometric information is crucial for cognitive science and psychology.

Purpose of the Study:

  • To investigate whether abstract geometry aligns with the spatial navigation geometry used by humans and nonhuman animals.
  • To explore the influence of language in isolating and eliciting specific geometric representations.

Main Methods:

  • Two preregistered experiments were conducted with educated adults.
  • Participants viewed short videos of simple geometric figures and were prompted to click in specific conditions (anywhere, triangle, object, navigation, abstract).
  • Responses were analyzed to identify the geometric representations elicited by different spatial contexts and language cues.

Main Results:

  • Participants' responses revealed distinct geometric representations based on the task context.
  • Navigation and abstract conditions showed similar elicited geometries, preserving distance and direction for open paths.
  • Object completion tasks preserved length and angle for closed shapes, differing from navigation-based responses.

Conclusions:

  • Human language can isolate phylogenetically ancient geometric representations crucial for spatial navigation and object recognition.
  • The cognitive origins of human abstract geometry may be rooted in the representations used for navigating the physical world.
  • This research bridges formal mathematics, cognitive psychology, and evolutionary biology by linking abstract thought to embodied experience.