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Two papers stand out for me in the early history of diffusion. The first is Einstein's (1905) paper on Brownian motion. In that, Einstein derives what is often called the "diffusion approximation," the solution to which is that the density of particles at point x at time t (assuming a starting point of x=0 and t=0) is normal with mean zero and variance equal to the 2Dt (where D is the diffusion constant). Among other things, it means that a particle's displacement increases proportional to sqrt(t) rather than linearly with time. The diffusion approximation is used quite a bit in population biology to estimate stochastic growth rates, times-to-extinction, etc. The paper I know best on this is Lande and Orzack (1988) but Ludwig (1996) is another important one.

The second paper is Fisher's (1937) paper on the spread of an advantageous allele. It's a reaction-diffusion equation which can yield a traveling-wave solution. In the case of an advantageous allele, the speed of the wave front is given by its fitness, r.

Ken Aoki (1987) used the Fisher model for cultural spread and Ammerman and Cavali-Sforza (1971) used it to model the spread of agriculture in Neolithic Europe. These ideas are largely independent of the diffusion-of-innovations literature (as exemplified by Rogers) with which we are probably most familiar, but there are clearly addressing related problems.

Cheers,
Jamie

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On Dec 4, 2017, at 12:56 PM, martina morris <[log in to unmask]<mailto:[log in to unmask]>> wrote:

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Thanks for sharing this info Thomas -- it's very interesting.

'Pre-paradigmatic' seems like an apt term insofar as the dominant paradigm today wrt diffusion processes assumes s-shaped, scalable, exponential curves embedded in models of proportionate growth.

Those of us who work on network structured diffusion have a more general paradigm.  Much of this work has emerged in the context of network modeling of epidemics, so doesn't make it into the Network journals.

question. A good example is Lynn White's 1966 book Medieval Technology and Social Change, which traces the development of medieval warfare to innovations in horse saddlery, specifically, the introduction of the foot stirrup around the 6th CE. However, her description of the process(es) associated with the 'spreading' and adoption of saddle stirrups is considerably lumpier than any smooth, s-shaped curve would suggest.

And indeed, a network structured by clustering (for whatever reason) would produce just this pattern.


On Mon, Dec 4, 2017 at 2:05 PM, Thomas William Valente <[log in to unmask]<mailto:[log in to unmask]>> wrote:
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     We classified those studies as pre-paradigmatic, quite a few studies on the diffusion of
     arrowheads and other archeologic evidence. The paradigm, however, coalesced with the Ryan &
     Gross publication which strongly influenced the Rural Sociology tradition.


     From: George Barnett [mailto:[log in to unmask]]
     Sent: Monday, December 04, 2017 10:03 AM
     To: Thomas William Valente
     Cc: [log in to unmask]<mailto:[log in to unmask]>
     Subject: Re: [SOCNET] History and origins of diffusion processes


     Tom & Thomas,

        It actually goes back a whole lot further to the work of Galton (cultural trait
     diffusion), and then  Pemberton (the diffusion of postage stamps) and Stuart Chapin. I
     haven't looked at the early research in 40+ years, but there was lots of research which
     preceded Ryan and Gross.


     George

      George A. Barnett, Ph.D.

     Distinguished Professor Emeritus

     Department of Communication

     393 Kerr Hall

     University of California – Davis

     Davis, CA 95616-8695

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     On Mon, Dec 4, 2017 at 9:00 AM, Thomas William Valente <[log in to unmask]<mailto:[log in to unmask]>> wrote:

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     Thomas

     Although this isn’t quite what you are looking for, in the 1990-1991 time frame I interview
     (along with Everett Rogers) a number of early pioneers of diffusion of innovations research.
     We published our findings in this paper:


     Valente, T. W., & Rogers, E. M. (1995). The origins and development of the diffusion of
     innovations paradigm as an example of scientific growth. Science Communication: An
     Interdisciplinary Social Science Journal. 16, 238-269.


     The abstract reads:

     This article traces the emergence of the basic paradigm for early diffusion research created
     by two rural sociologists at Iowa State University, Bryce Ryan and Neal C. Gross. The
     diffusion paradigm spread to an invisible college of midwestern rural sociological
     researchers in the 1950s and 1960s, and then to a larger, interdisciplinary field of
     diffusion scholars. By the late 1960s, rural sociologists lost interest in diffusion studies,
     not because it was ineffective scientifically, but because of lack of support for such study
     as a consequence of farm overproduction and because most of the interesting research
     questions were thought to be answered.


     -Tom


     Thomas W. Valente, PhD

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     If one looks up the word 'diffusion' in the Dictionary of the History of Science, you get the
     standard explanation that 'diffusion' originated in the 19th c with Graham and Maxwell and
     has a Latin etymology in the word, diffundere, which means "to spread out." There has to be
     more to the story than this, right?

     Earlier references might include the  "diffusion of refracted light" in Robert Greene (1727)
     and "diffusion of light" in Newton's Optical Lectures (1728).


     My question for these listservs is, does anyone have any additional insight into the history
     and origins of the abstract idea of 'diffusion?'


     Thank you,

     Thomas Ball




     Thomas W. Valente, PhD

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     University of Southern California

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