Upload
arabella-douglas
View
219
Download
1
Embed Size (px)
DESCRIPTION
Number Systems Accumulator Model –Larger Number = harder to keep track Scalar Variability
Citation preview
Primate Number AbilitiesPrimate Number Abilities
Can Rhesus Monkeys Can Rhesus Monkeys Spontaneously Subtract?Spontaneously Subtract?
Gregory M. Sulkowski & Mark D. HauserGregory M. Sulkowski & Mark D. Hauser
Number SystemsNumber Systems
Object File ModelObject File Model– Instant recognition of small numbersInstant recognition of small numbers
Number SystemsNumber Systems
Accumulator ModelAccumulator Model– Larger Number = harder to keep trackLarger Number = harder to keep track
Scalar VariabilityScalar Variability
Why Test Primate Number Why Test Primate Number Abilities?Abilities?
Can counting exist without language?Can counting exist without language?– Animal vs Human number learning Animal vs Human number learning
fundamentally differentfundamentally differentBrute MemorizationBrute Memorization
– 1 = 1, 2 = > 1; 1 = 1, 2 = 2, 3 = > 2 …1 = 1, 2 = > 1; 1 = 1, 2 = 2, 3 = > 2 …– The chimpanzee AiThe chimpanzee Ai
VSVS Successor FunctionSuccessor Function
– S(n) = n + 1 S(n) = n + 1 SS(1)=1+1=2, (1)=1+1=2, SS((SS(1))=2+1=3, ...(1))=2+1=3, ...
Why Rhesus Monkeys?Why Rhesus Monkeys?Other animals have been Other animals have been tested…with trainingtested…with training– Pigeons, Parrots Pigeons, Parrots
Raccoons, Ferrets, RatsRaccoons, Ferrets, Rats
Why not other animals?Why not other animals?– Rhesus can accomplish Rhesus can accomplish
without trainingwithout training– Population ready to work Population ready to work
withwith
Experiment 1Experiment 1
1 1 versusversus 1-1, Single 1-1, Single SubtractionSubtraction– Monkeys could be Monkeys could be
avoiding the side that avoiding the side that was affectedwas affected
Experiment 2Experiment 2
1 1 versusversus 3-1, Single 3-1, Single SubtractionSubtraction– Only action on one of Only action on one of
the two sidesthe two sides
Experiment 3Experiment 3
2-0 2-0 versusversus 2-1, 2-1, Double ActionDouble Action– Monkeys could be Monkeys could be
avoiding the side avoiding the side associated with object associated with object removalremoval
Experiment 4Experiment 4
2-1 2-1 versusversus 1-1, 1-1, Double SubtractionDouble Subtraction– Nothing but food on Nothing but food on
platforms, no identity platforms, no identity to trackto track
Experiment 5Experiment 5
2-1 food 2-1 food versusversus 2-1 2-1 non-food, Double non-food, Double Subtraction and Subtraction and Object IdentityObject Identity– Removed different Removed different
objects from each objects from each side, could make side, could make monkey think only monkey think only metal on one side metal on one side while food on the otherwhile food on the other
Experiment 6Experiment 6
2-1 food versus 2-1 2-1 food versus 2-1 non food, double non food, double subtraction and object subtraction and object identityidentity– Thus far, number of Thus far, number of
objects has been objects has been minimalminimal
Experiment 7Experiment 7
3-1 food 3-1 food versusversus 2-1 2-1 non-food, Double non-food, Double Subtraction and Subtraction and Object IdentityObject Identity– Might have avoided Might have avoided
one side by ignoring one side by ignoring non-food itemnon-food item
Experiment 8Experiment 8
3-1 food 3-1 food versusversus 2-1 2-1 food, Double food, Double subtraction and subtraction and Object IdentityObject Identity– Only tested one Only tested one
aspect of subtractionaspect of subtraction
Experiment 9Experiment 9
2-1 2-1 versusversus 1+1, 1+1, Subtraction and Subtraction and Addition Without Addition Without Changing Initial Changing Initial Object NumberObject Number– Equality has yet to be Equality has yet to be
testedtested
Experiment 10Experiment 10
3-1 3-1 versusversus 1+1, 1+1, Subtraction and Subtraction and Addition Leading to Addition Leading to EqualityEquality– Never represented Never represented
zero in the presence of zero in the presence of addition and addition and subtractionsubtraction
Experiment 11Experiment 11
0+1 0+1 versusversus 1-1, 1-1, Subtraction and Subtraction and Addition and the Addition and the Representation of Representation of ZeroZero
Conclusive ResultsConclusive Results
ConclusiveConclusive– Represent zeroRepresent zero
Something even human infants can not doSomething even human infants can not do– Identify object properties separately of Identify object properties separately of
computationscomputationsModifies what is known of object file modelModifies what is known of object file model
Inconclusive ResultsInconclusive Results
Inconclusive Inconclusive – Numbering model utilizedNumbering model utilized
Data explainable by both modelsData explainable by both models– How zero was representedHow zero was represented
Still uncertain how zero is represented in either Still uncertain how zero is represented in either modelmodel
– Likely combination of both modelsLikely combination of both models