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Before documentation became his primary interest, Robert Fairthorne would conventionally have been described as an applied mathematician. Such a description, however, does not give a true indication of his special abilities. He is, in fact, dedicated to the task of bringing to science and engineering the benefits of mathematics in all its forms, and to him such classifications as ‘pure’ and ‘applied’ were mere irrelevancies.

Aims to review Fairthorne's classic article “Empirical hyperbolic distributions (Bradford‐Zipf‐Mandelbrot) for bibliometric description and prediction” (Journal of Documentation, Vol. 25, pp. 319‐343, 1969), as part of a series marking the Journal of Documentation's 60th anniversary.

Analysis of article content, qualitative evaluation of its subsequent impact, citation analysis, and diffusion analysis.

The content, further developments and influence on the field of informetrics of this landmark paper are explained.

A review is given of the contents of Fairthorne's original article and its influence on the field of informetrics. Its transdisciplinary reception is measured through a diffusion analysis.

Should information science ever succeed in establishing itself as a scientific discipline distinguishable from the other sciences which have already contributed to its presumed field of study, then Robert Fairthorne will be recognized as among its founders. His primary contribution was to define its scope, to clarify its terminology, and to establish its fundamental principles. Maintaining close sceptical watch over the information scene for more than twenty years, Fairthorne dissected the problems of this period of development by applying to them the keen cutting edge of his logic, mathematics, and Shannon information theory. He applied these instruments of analysis and criticism with firmness of purpose, clear insight, and meticulous precision and so evolved a theory of documentation.

It is pleasant to be able to welcome some theory in a social science field such as librarianship. It is especially pleasing when direct and forceful applications of the theory are fruitful. It is the intent of this paper to demonstrate to librarians how the theory of Robert Arthur Fairthorne can aid in systematizing the analysis and improvement of library operations. This demonstration has evolved during the teaching of information science courses in graduate library schools.

About two years ago I got an invitation to spend some time with the Center for Communication and Documentation Research, which is a part of the School of Library Science in the Western Reserve University at Cleveland, Ohio. I was very pleased about this, not only because I happened to know the people personally but also because it was a place which had been getting on with its job, yet quite prepared to change what it was doing, for a considerable time. So by going there I would find out what really were the real difficulties in this line of work, particularly in what I consider to be the fundamentals of information. This is better than thinking it up in an armchair. We are still at the alchemical stage of this business, and the first thing one can do is to find out what is really happening, rather than build an enormous mathematical edifice on nothing at all—rather like a large elephant balancing on a small ball‐bearing—which is not unknown in computing circles.

Some thirty years ago, when the laboratory where I worked needed light alloy castings, success depended on divination carried out by the foreman. This hinged upon the effects of spitting in the crucible, and the results beat any scientific method hollow. About five years later we were using more dependable and repeatable, if less picturesque, criteria. This came about because meantime various theoretically‐minded people had studied various apparently minor and irrelevant matters such as the behaviour of single crystals of aluminium. Some of the personal skill and experience hitherto needed for routine operations now could be delegated; at times even to instruments.

While Fairthorne may not have been the first person to recognize it, certainly, for this author, Fairthorne was the first to make explicit the fundamental problems of information retrieval systems, namely the clash between OBNA and ABNO (Only‐But‐Not‐All and All‐But‐Not‐Only). Although it was not until 1958 that the terms occur in Fairthorne's writings, the concept had been discussed in many meetings of the AGARD Documentation Panel and elsewhere. Originally it was considered that to meet these two requirements, it might be necessary to have two separate systems, and the test of the UNITERM system in 1954 was based on the hypothesis that a ‘Marshalling’ system (e.g. U.D.C.) was fundamentally different from a ‘Retrieval’ system (e.g. UNITERM). While the idea persisted in this form for some time, it gradually evolved into the inverse relationship of recall and precision, which is to say that while it is possible to obtain, of the relevant documents, All‐But‐Not‐Only, or alternatively to obtain Only‐But‐Not‐All, it is not possible to obtain All and Only.

Some parameters and techniques in use for describing the results of tests on IR systems are analysed. Several considerations outside the scope of the usual 2 x 2 table are relevant to the choice of parameters. In particular, a variable which produces a ‘performance curve’ of a system corresponds to an extension of the 2 x 2 table. Also, the statistical relationships between parameters are all‐important. It is considered that precision is not such a useful measure of performance (in conjunction with recall) as fallout. A more powerful alternative to Cleverdon's ‘inevitable inverse relationship between recall and precision’ is proposed and justified, namely that the recall‐fallout graph is convex.

The papers by Robert A. Fairthorne are always both stimulating and challenging to me. Their insights and their obscurities are fascinating. While my own intellectual works have usually been quite separate from his, we have frequently shared a concern with many of the same topics in the principles of information work. These have included such topics as the mathematical basis of classification, applications of mathematical lattice theory, insights from Shannon's signalling theory (habitually misnamed ‘information theory’), and the delegation of retrieval.

Since 1960, and especially during the past three years, many papers have appeared about particular manifestations and applications of a certain class of empirical laws to a field that may be labelled conveniently ‘Bibliometrics’. This term, resuscitated by Alan Pritchard (see page 348), denotes, in my paraphrase, quantitative treatment of the properties of recorded discourse and behaviour appertaining to it.