My first and greatest debt is to the thousands of informants who patiently answered my questions or questionnaires and who provided most of the data for this study. While the majority of these were students at the Papua New Guinea University of Technology in Lae, there were also students at each of the four National High Schools at Keravat, Passam, Aiyura, and Sogeri. Headmasters at some 300 Community Schools also assisted in the completion of questionnaires. To all of these I am grateful for taking the time to share their knowledge with me. To the informants in 35 villages my special thanks for their hospitality as well as their time and patience.

In 1976, the Indigenous Mathematics Project (IMP) was established by the PNG Department of Education under the directorship of Dr. D.F. Lancy. Within the duration of the IMP, a good deal of data were collected on vernacular counting systems by various anthropologists and linguists working at field sites within the country and some of this information has been published. There was, however, a quantity of useful data that remained unpublished and I am grateful to David Lancy for making that material available to me for this study.

On various occasions from 1984 to 1986 I visited the Summer Institute of Linguistics (SIL) at Ukarumpa in the Eastern Highlands Province (PNG). I was given access to the survey word lists of various PNG languages, as well as other material, held at the SIL library and was thus able to obtain a considerable amount of unpublished number data. I wish to express my gratitude to the Director of the Institute for giving me permission to make use of the library facilities.

I have received practical and financial assistance from two universities. First, from the Research Committee at the PNG University of Technology which provided funds for travel and for facilities which enabled my manuscripts to be typed. Second, I was granted leave by Deakin University which has enabled me to have a period of time devoted entirely to writing, uninterrupted by my other usual responsibilities. The libraries at each institution provide an inter-library loans service which was indispensable in obtaining often difficult-to-get materials. I am immensely grateful to both universities for their assistance.

I have a special debt to Professor Alan Bishop who has been my Supervisor for this project since its inception. Alan's continued encouragement and patience has ensured that the material that follows has actually seen the the light of day when it might well have remained in my head and dozens of mildewed box files.

There are various other friends and colleagues who have provided advice, encouragement, or practical assistance and to whom I am grateful Professors Ken Clements, Peter Jones, Nerida Ellerton and Kathleen Collard. Ken read through the entire manuscript with his usual meticulous attention, thereby eliminating errors of various kinds.

Data for this study were collected over two decades, beginning early in 1968. It has had such a lengthy gestation period that it is inevitable that I have forgotten many of the people who have helped me in one way or another. There are others whose names, in any case, I did not know but who offered their assistance at some crucial moment in trying to get from one island to the next, or while waiting the hundreds of hours beside airstrips for planes that never arrived on time, or when food or antimalarials or patience ran out. Finally, there are the many wantoks and friends that I made during my twenty-two years in Papua New Guinea; to all of you, my thanks. Go I must, but I go grateful, to quote my favourite poet, Wystan Auden, in his Goodbye to the Mezzogiorno,