As a colleague once observed, the odds of my connecting with Harrison were rather low. At the time, I was a graduate student in a different discipline (psychology) in a university (Melbourne) close to the polar opposite of Harrison’s base at Harvard. And the shortest network path between us was at least four, probably five. But I had met Australian National University sociologist, Al Klovdahl, at my first conference in 1974 as a new graduate student and Al had given me a copy of the 1971 article by François Lorrain and Harrison White. It became the inspiration for my PhD thesis. In 1976, I wrote to Harrison for the first time and told him of the work I was doing. His response was warm and welcoming, with some strong advice. “I am glad you wrote now, for you are hacking at the same jungle my associates and I have spent several years in ... and we should be glad to enlist your help.” I have continued to hack.
Harrison sent the now famous 1976 American Journal of Sociology papers, preprints, working papers, APL code, and lists of associates to whom he had also written and asked to send recent reprints. And his advice was: “I would URGE you to develop further approaches ONLY in conjunction with work on some good data ... you need some feedback as to practical utility, there are so many formal possibilities.” That advice, including the capitalized emphasis, came to be repeated several times over the years—it was clearly needed.
I visited Harvard in early 1977 and then again for the North American summer that year. Correspondence by letter with Harrison, Ron Breiger, and others followed for the next decade or so. It was the period before email and the mail took several weeks in each direction, so letters were often lengthier and considered quite relative to many of the emails that followed. Needless to say, my letters were longer—sometimes running to eight pages or so—but Harrison was encouraging, generous, and full of suggestions (“I’d like to open up an argument ...”, “we never use and you don’t ...”, “don’t you think ...?”, “have you thought ...?”, “I do hope I say enough to get you fired up ...”).
It is hard to convey just how much I learned from Harrison, Ron, and many others in Harrison’s circle during this period, but I especially valued the discussions about the insightful nature of this or that concept or the value of this or that approach. The gap between sociology and psychology was wide and I had a lot of reading to catch up on. Harrison was especially critical of social psychology’s cognitive turn; as he put it, when you change lanes on the freeway, it matters if someone is there. He made the importance of dynamics and interaction palpable.
One of the few books we had read in common on first encounter was Nadel’s “Theory of Social Structure”—and that was because, on whim, I had bought a remaindered copy in my university’s bookshop. We agreed instantly on the appealing and lucid character of Nadel’s challenge and the perplexing nature of his formalisms. Boorman and White’s (1976) paper made tangible Nadel’s goal of understanding the “interlocking of social relationships” (Nadel, 1957, p.16). My initial work was focused on further exploration of the semigroups of blockmodels constructed by Boorman and White as a characterization of this interlocking. I was seeking to understand how mathematical concepts could advance our understanding of role structures, for example, the potential of algebraic decomposition of the semigroup to reveal more elemental and varied forms of interlock; of partial semigroups based on paths of limited length to reveal the interlocked structure of shorter (and arguably more important) network paths; and later, with Ron Breiger, of local role algebras to reveal variations in the form of interlock across a network (Breiger & Pattison, 1986; Pattison, 1993). Ron also introduced me to thinking relationally about the relation between distinct sets and hence to exploring the potential of lattices for algebraic analysis of bipartite networks (Pattison & Breiger, 2002). I picked this interest up again while Harrison was Director at the Paul Lazarsfeld Centre for the Social Sciences at Columbia University, working with Anne Mische (Mische & Pattison, 2000) as well as David Gibson.
Despite the very natural appeal of the link between algebraic operations on relations and human understanding and representation of relations, Harrison’s account of social life as a “shambles” (White, 1992, p.22) was a potent reminder of the limitation of deterministic algebraic approaches, and led to a clear challenge to develop methods that were responsive both to structural tendencies at multiple levels as well as to unstructured influences. As Harrison expressed it in his critique of Nadel’s response to his own challenge, “... no large ordering that is deterministic in either cultural assertion or social arrangement could sustain and reproduce itself across so many and such large network populations as in the current world. Some sort of stochastic environment must be assumed and requires modelling” (White, 2008, p. 371). Many different approaches to handling both structural regularity and randomness in relational data and social life have been developed in the past 30 years and a substantial body of modeling work contributed by many members of our social network community has now been amassed.
Importantly, as I began personally to adopt a statistical perspective with guidance from those with more expert statistical knowledge, I came to find Harrison’s view of the social world an even more significant influence. His insights into the fluidity of social nodes, social ties, and social settings and of the interdependencies among and between them strongly encouraged the exploration of approaches that avoid assuming away the dynamic and interdependent character of nodes, ties, and the settings or domains in which they are embedded and instead make them the focus of interest (Pattison & Robins, 2002).
The importance of the interdependence among ties had already been recognized by Nadel. He referred to these interdependencies as “the further linkage of the links themselves” with “the important consequence that, what happens so-to-speak between one pair of ‘knots’ must affect what happens between other adjacent ones” (Nadel, 1957, p.16). White likewise emphasized the interdependence of ties: “A social tie exists in, and only in, a relation between actors which catenates, that is entails (some) compound relation through other such ties of those actors ... Thus [a tie] is subject to, and known to be subject to, the hegemonic pressures of others engaged in the social construction of that network”. As he stressed, “This is the axiomatic essential” (White, 1998, p.4).
Of course, White (1992, 1998, 2008) presents a much richer and more comprehensive vision than this. Actors or nodes are cast as “dynamic structures, identities, co-generated along with the multiple networks in which they embed” and relational processes in networks are seen as inducing and generating “distinct further levels of actors, such as tribes and neighbourhoods, and also markets and firms” (White, 1998, p3). White stressed the importance of a unified approach to the social and cultural aspects across this dynamic, multilevel conceptualization—and this, of course, presents a far grander challenge than Nadel’s.
It is, nonetheless, a challenge that has inspired much of my interest in statistical models for networks. Some years ago, I used to begin presentations of the work I was then doing with Garry Robins, Peng Wang, Tom Snijders, and others with a visual sketch across three levels: nodes, ties among nodes, and grouping structures imposed on nodes, with each level changing over time, and with interdependences within and across the three levels. Johan Koskinen would gently tease by referring to this as “the grand unified theory”. The teasing was appropriate because it was not a theory (nor intended as such) and, indeed, all (or even most) of the interdependencies could not be accommodated at the same time by the evolving suite of methods. Nonetheless, the conceptual framework was important in serving as a reminder that, on any occasion, we are almost certainly missing some of the value of the genuinely unified approach that Harrison championed and there is much to gain by continuing to strive toward a more faithful instantiation—in lockstep with the analysis of good data—as many colleagues continue to do.
I should add that, in addition to the theoretical importance Harrison attached to the dynamics of nodes, ties, and domains and their interdependencies, the other breakthrough insight informing the evolution of many of these statistical approaches was the development by Frank & Strauss (1986) of a principled approach to thinking about interdependencies among ties (based on earlier work by Besag (1974) on spatial interdependencies), particularly an approach to conceptualizing interdependencies as “local” in a network sense. I never discussed this in detail with Harrison, but assuming that interdependencies are predominantly local seems an effective way to reflect the importance of “catenation” to tie formation. The many members of the social network community who have been involved in the development of models for the dynamic, multilevel, and interactive nature of social processes may well cite other motivations, but for my part, Harrison’s influence was always present and still is (Pattison et al., 2024).
Of course, Harrison’s account of the social world is much richer still, based as it is on the insights from good data across multiple case studies. His attention to both detailed case studies and careful modeling emphasize the value not just of tools that uncover and quantify regularities in the social world but also of those that bring its variations into sharper focus. I feel sure, for example, that he would be encouraging careful scrutiny of the homogeneity assumption of any particular statistical model while also urging joint attention to data reflecting both the relational and cultural aspects of a domain of interest.
Harrison’s work will surely serve as motivation for the further development of theory and methods for many years to come.
Personally, Harrison’s work has been a source of energy and inspiration. He has also been for me, and I’m sure for many others, a valued advisor, supporter, and sponsor. I have valued it all, but I treasure especially his very practical directness and tangible forms of support. He created opportunities and he obliged with many letters of reference over the years. And he continued to provide very direct advice (and to capitalize the important bits). I am deeply indebted.
As a final cogent example, I share his advice when I asked him to be a referee for an administrative position I was contemplating at my university some years ago.
“Dear Pip. Of course I am always delighted to support your efforts, no problem. BUT WHY IN THE WORLD DO YOU WANT TO LEAVE THESE EXCITING RESEARCH ACTIVITIES?? ... We need you doing science not administering it. My two cents. Let me know whether and when.”