## How de Solla Price influenced my work

I was fortunate enough to meet Derek de Solla Price at a lecture he gave in Brussels in 1981. At that time, I was at a crossroads in my career: after my Ph.D. in mathematics in 1978, I became chief librarian of the Limburgs Universitair Centrum (now Universiteit Hasselt), a position I still occupy. In 1983, together with the then chief librarian of the University of Antwerp, Prof. H. Vervliet, I prepared the foundation of the degree in library and information science. In that year, I became part-time professor in this field and still teach courses on Quantitative Methods in Library and Information Science and Information Retrieval. After finishing a book on mathematics in 1984 *(1)*, I switched to informetrics research. When I met de Solla Price, I was not yet an informetrician and had no idea of the influence he was going to have on my future career.

### The science of science

It was not so much de Solla Price’s mathematical work that influenced me, as his universal philosophy on the science of science. His book *Little Science, Big Science* *(2)* describes growth distributions and size- and rank-frequency distributions of very different phenomena in information science, the physical world, linguistics, econometrics and so on. This book showed me that many of those phenomena have common laws and can be described in one framework, which I called Information Production Processes (IPPs) *(3, 4)*. IPPs can be constructed far beyond information science, as de Solla Price explained *(2)*. I defined an IPP as a system where one has ‘sources’ that have or produce ‘items’.

A classic bibliography is an example of an IPP. Authors have papers, yielding another example. But papers can also be sources, producing or receiving items as references or citations. Books are sources of their borrowings: words are sources (known as ‘types’ in linguistics) and their occurrences in the text are the items (’tokens’ in linguistics). Beyond informetrics, as de Solla Price describes, we have communities (cities and villages) as sources and their inhabitants as items (demography), and in econometrics one can consider employees as sources and their production or salary as items *(2)*.

This universality is not the only remarkable thing. De Solla Price notices that all these phenomena (or IPPs) also satisfy the same sociometric (informetric) laws:

- exponential or S-shaped growth functions;
- size-frequency functions (expressing the number of sources with a certain number of items) of power-law type, such as Lotka’s law (
*5*), and; - rank-frequency functions (expressing the number of items in the source on rank r – sources are arranged in decreasing order of the number of items they have) also of power-law type but with another exponent than in the size-frequency case, such as Zipf (linguistics) and Mandelbrot and Pareto (econometrics).

Essentially, these are all the same laws and are equivalent to Lotka’s law.

### Success breeds success

It is remarkable that while rank-frequency functions are studied in informetrics, linguistics and econometrics, informetrics only studies size-frequency functions via Lotka’s law. De Solla Price introduced Lotka’s law into informetrics and – although equivalent with the rank-frequency laws – the size-frequency function (Lotka’s law) is easier to work with since it does not use source-rankings.

The university of de Solla Price's view of the science of science has influenced my entire informetrics career.

De Solla Price even introduces the econometric principle ‘success breeds success’ (SBS) into informetrics based on the earlier work of Nobel Prize-winner Herbert Simon *(6, 7)*. SBS is the principle that (in my terminology): the probability is higher that a new item is produced by a source that already has many items, than the probability that a new item is produced by a source with only a few items. This leads de Solla Price to a partial explanation of Lotka’s law *(7)*.

More recently, de Solla Price’s work *(8)* has lent itself to research I am currently undertaking on the relation between productivity (number of papers) and collaboration (co-authorship). He indicates (in my terminology) that for a certain author (the IPP) for whom sources are his or her papers and items are the co-authors of each paper, you may find that researchers produce more papers if they collaborate more, a finding that seems to be confirmed in my recent work (in progress).

The universality of de Solla Price’s view of the science of science has influenced my entire informetrics career. Since 1985, I have worked so much with IPPs and Lotka’s law that I published a mathematically-orientated book *(9)* in which Lotka’s law is used as an axiom that many mathematical results in all subfields of informetrics follow.

Professor Leo Egghe

*Universiteit Hasselt, Belgium, and Universiteit Antwerpen, Belgium*

#### References:

*(1)*Egghe, L. (1984) “Stopping time techniques for analysts and probabilists”,

*London Mathematical Society Lecture Notes Series 100*. Cambridge, UK: Cambridge University Press.

*(2)*de Solla Price, D.J. (1963)

*Little Science, Big Science*. New York, USA: Columbia University Press.

*(3)*Egghe, L. (1989)

*The Duality of Informetric Systems with Applications to the Empirical Laws*. Ph.D. Thesis, City University, London, UK.

*(4)*Egghe, L. (1990) “The duality of informetric systems with applications to the empirical laws”,

*Journal of Information Science*, Vol. 16, No. 1, pp. 17–27.

*(5)*Lotka, A.J. (1926) “The frequency distribution of scientific productivity”,

*Journal of the Washington Academy of Sciences*, Vol. 16, No. 12, pp. 317–324.

*(6)*de Solla Price, D.J. (1976) “A general theory of bibliometric and other cumulative advantage processes”,

*Journal of the American Society for Information Science*, Vol. 27, pp. 292–306.

*(7)*Simon, H.A. (1957) “On a class of skew distribution functions”, In:

*Models of man: Social and Rational*, Ch. 9. New York, USA: John Wiley and Sons.

*(8)*de Solla Price, D.J. and Beaver, D.B. (1966) “Collaboration in an invisible college”,

*American Psychologist*, Vol. 21, pp. 1011–1018.

*(9)*Egghe, L. (2005)

*Power Laws in the Information Production Process: Lotkaian Informetrics*. Oxford, UK: Elsevier.