• Represented system
• Representing system
• e.g., environment (represented) and brain (representing)

• Common to all mobile animals
• Navigation
• e.g., Foraging and predation, shelter, mating, migration, etc.
• Brain structures linked to spatial representation
• Path integration (dead reckoning)
• Piloting
• Cognitive maps

• Necessary in navigation
• Other behavioural processes
• e.g., Feeding, mating, resting, etc.
• Exogenous clocks
• e.g., Sun, moon, seasons
• Endogenous clocks
• Internal clocks; circadian rhythms

• Nervous system
• Computes and stores aspects of the environment
• Internal world represents external world

• Varying degrees of representations
• Depends on extensiveness of correspondence between represented and representing systems

• Objects have mass
• Weigh object
• Scale
• Produces numerical value

• Mass = represented system
• Numerical value = representing system
• Can apply mathematical functions
• e.g., +, -, >, <, =
• A "rich" representation
• Makes valid use of all the arithmetic operators and relations

• String of numbers
• e.g., <x,y>
• Vector addition

• Vector subtraction

• Many map systems
• Latitude
• North/south
• Longitude
• East/west

• Edmonton
• 54° latitude
• 114° longitude
• (54, 114)

• Edmonton (54,114) and London (51,0)
• Change in position?
• New position minus old position

• Process of determining and maintaining a course from one place to another
• Two basic forms
• Path integration
• Piloting

• Determining change in position by integrating velocity with respect to time
• Velocity: speed and direction
• Velocity on a plane is a 2-dimensional vector
• e.g., <10, 3> = 10 m/s North and 3 m/s East

Path Integration

• Need distance and angular information

• Overall velocity may not be due to animal’s locomotion alone
• e.g., crosswind, current, moving sidewalks, etc.
• To determine course
• Add animal’s movement vector to additional vectors

• Brain function
• Dedicated neural structure
• Innate process
• Nervous system "does the math"

• Navigational tasks requiring "complex" mathematical descriptions aren’t necessarily neuronally complex
• Mathematics is a human notational system
• A representation of the world
• Natural selection
• Selects for adaptive, functional system

• Uses landmarks
• Terrestrial, celestial, olfactory, etc.
• Need to determine position and heading
• Position: coordinates on a map
• Heading: orientation on the map
• Angular distance between grid north and egocentric north

• Grid north
• Top of the map
• Egocentric north
• Direction you are facing
• True north
• Northern end of earth’s axis of rotation
• Local magnetic north
• Direction of magnetic field at a given place
• Can vary from place to place

Egocentric and Geocentric Coordinates

• Egocentric
• In relation to self

• 1. Displacement of the mapping
• Where something is on the map?
• 2. Scale of the mapping
• Units of measure?
• 3. Orientation of the mapping
• Which way is north?

Navigation by Aplysia

• Straight line navigation
• Visual navigation
• Disabled eyes
• Near shore
• Turns off shore
• Hydrodynamics, wave surge
• Off shore
• Erratic route

• Conditions
• 12 Aplysia
• Daylight
• Florida
• 475+ m off shore in 20-60 cm deep water

• Start from bottom
• Direction at T = 15, 30, 45 sec
• Deflection of 180°
• Direction at T = 60, 75 sec
• Results
• Recovered pre deflection direction, +/- 7°

• Conditions
• 17 Aplysia
• Daylight
• Florida
• On shore
• 82.5 cm diameter arena

• Start from centre of arena
• Direction at T = 45 sec
• Move to second arena with
• 1. no cover
• 2. clear plastic cover
• 88-91% of 400-600 nm light
• 3. opaque plastic cover
• 5-7% of 400-600 nm light
• Direction at 15 sec intervals for 5 min

• Results
• Conditions 1 and 2
• Maintained pre-move direction for 3 min
• Condition 3
• Random direction

• Visual system provides directional information
• Less surface scattering of light
• Aplysia maximally sensitive to 500 nm

URL: www.psych.ualberta.ca/~msnyder/p486/notes/n01.html
Page created: 8 Sept. 2002 --- Last modified: 8 Sept. 2002