Mathematical Modeling of Generic Spatial Representation Systems
How humans and other animals remember places and navigate in their environments has been an important topic in cognitive science. Various theories have been proposed regarding whether locations are specified relative to the animal itself (egocentric coding) or relative to something in the environment (allocentric coding); how an animal keeps track of its relationship with the environment as it moves around (spatial updating); how an animal determines its location and direction after getting lost (reorientation); and so on. Because existing theories are schematic, descriptive, and qualitative in nature, it is difficult to make concrete, consistent predictions from them, and this has caused much confusion in the literature when researchers have attempted to test and compare theories. During her Center appointment, Professor Wang proposes to develop a generic mathematical formalization of the main classes of theories in spatial representations.
First, she will construct the basic mathematical expressions of different types of spatial representation, following a flexible architecture that encompasses the reference frame (egocentric or allocentric), coordinate system (e.g., Polar, Cartesian), and type of spatial relations coded (e.g., location and orientation of a single target, inter-object distance and direction). Then she will develop a set of mathematical operations for five basic units: conversion between coding systems, spatial updating and perspective change, place recognition, reorientation, and spatial learning from navigation. The representations and the operators together capture the elements that allow an animal to perform basic navigation tasks, build mental maps about the environment, and retrieve hidden targets.
The next step is to implement the mathematical models in a computer program that allows the user to set parameters to simulate various experimental conditions. The results will provide a concrete illustration of how different theories approach spatial tasks, determine whether they can be teased apart using a given task, and clarify many of the theoretical misunderstandings as to what different types of spatial representations can and cannot do.