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The Origins of Mathematical Knowledge:

Spontaneous Abilities in Rhesus Macaques

An Honors Thesis presented

Gregory Michael Sulkowski

The Department of Psychology and

the Concentration in Biology

in Partial Fulfillment of the Requirements

for the Degree of Bachelor of Arts

with Honors in the Subjects of

Psychology and Biology

Harvard College

Cambridge, Massachusetts

March 20, 2000

Acknowledgements

I could not have run all of these experiments, nor come close to synthesizing the results, without the generous help, input, and advice of a number of individuals. I wish to express my gratitude to the following people, without whom this thesis would not exist:

Dr. Marc D. Hauser, my advisor, for his continuous support and direction over the course of nearly two and a half years in his lab. I cannot thank him enough for the opportunity of working with him.
Dr. Mark G. Baxter and Dr. Naomi E. Pierce, my readers, for their time and advice.
Laurie Santos, Cory Miller, Damian Moskovitz, and Sunana Sohi, for helping me run the experiments in Cayo Santiago, reading drafts of this thesis, and offering their much-appreciated advice.
David "Muck" Goldenberg and Geertrui Spaepen, for their help in running the experiments in Cayo Santiago and keeping the lab up and running.
Dr. Fritz Tsao, Connie Kim, and Michael Tringe, for helping me run the tamarin experiments, despite the frustrating performance of the monkeys.
Erin Driver-Linn, for her much appreciated comments and advice on writing this up.
The entire Primate Cognitive Neuroscience Laboratory, but especially Dr. Jerald Kralik, Dr. W. Tecumseh Fitch, Dan Weiss, Amy Deipolyi, and Matthew Warburton, for their advice and feedback.
The Harvard College Research Program and Mind/Brain/Behavior Research Program, for their generous financial support of my travels and research in Puerto Rico.
The Carribean Primate Research Center, but especially the Boatmen (Julio, Hector, William, and others) for providing the access to the rhesus colony in Cayo Santiago.
The rhesus monkeys, but especially Leaf Boy, Gump, and Puss-head, for showing off their mathematical abilities.

Table of Contents

Title Page

Acknowledgements

Table of Contents

Abstract 1

Chapter 1: Introduction

General Introduction 2

Defining "Mathematical Knowledge" 3

The Logic of Comparative Cognition 5

The Nature of Numerical Representations 7

A Brief Comparative Review of Number Research 10

Summary and Aims 19

Chapter 2: General Methods

Subjects 20

Searching Time Paradigm 23

Choice Paradigm 26

Chapter 3: Great Numerical Expectations

Introduction 30

Experiment 3.1: Addition Task 31

Experiment 3.2: Subtraction Task, Control for Actions 36

Experiment 3.3: Control for Volume 41

Experiment 3.4: Property/Kind Task 46

Chapter Summary 55

Chapter 4: Picking up on Subtraction

Introduction 56

Experiment 4.1: Basic Subtraction Task 57

Experiment 4.2: Control for Manipulation 60

Experiment 4.3: Control for Object Subtraction 63

Experiment 4.4: Control for Food Subtraction 65

Experiment 4.5: Control for Initial Object Numbers 67

Experiment 4.6: Test for "Initial Food Quantities" Explanation 69

Experiment 4.7: Test for "Food Subtraction Avoidance" 71

Experiment 4.8: Incremented Numbers Task 74

Experiment 4.9: Test for Representation of Zero 77

Chapter Summary 82

Chapter 5: The Effect of Updating

Introduction 83

Experiment 5.1: Basic Updating Task 85

Experiment 5.2: Test for "First Food Addition" Explanation 87

Experiment 5.3: Test for "Last Object Addition" Explanation 88

Experiment 5.4: Test for "Last Food Addition" Explanation 89

Experiment 5.5: Test for Recency Effect 91

Experiment 5.6: Test for Object Specificity of Recency Effect 94

Experiment 5.7: Test for Interaction of Initial Quantities with Recency 96

Experiment 5.8: Test for Recency in Analogue of Prior Studies 98

Chapter Summary 101

Chapter 6: General Discussion

Limitations 102

Comparative Implications 104

Methodological Implications 109

Implications for the Nature of Numerical Representation 109

Future Directions 111

References 112