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