We are wanderers: Abstract geometry reflects spatial navigation

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.