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August 5, 2006
Marketing Models and The History of Israel: Random Thoughts
In preparation for my next two or three posts of how to identify a scribal school, I've been reading an ever growing collection of papers in the general area of education in ancient Israel. For now, I am focusing on the epigraphic evidence but I ran across a paper by Sean Warner that, while on a somewhat different subject, argues that the epigraphic evidence is not enough. And he suggests that, at least when thinking about the related areas of literacy and diffusion of reading, writing and the alphabet, we need to consider "sociological forces." The "sociological forces" that Warner describes in his proposed model are mostly market forces dressed up in terms of an ancient economic and social system.
While I think Warner makes his point, I am concerned that his argument takes place at such a high theoretical level that it is often hard to see the evidence. While the problems of definition of some things like "literacy" were well discussed, others like "sociological forces" were defined only by example. I would have liked to have seen more positive evidence for his conclusions. In fact some of his positive conclusions are based on the lack of evidence to support them! I also worry that he often confuses a technology, in this case the alphabet, with literacy, which is a social phenomenon independent of the technology used to support it. The fact that he strongly cautions against this error did not keep him from making it himself. The factors that might cause the diffusion of literacy within a population are very likely quite different from the factors that might cause the diffusion of the alphabet. And I don't buy for a minute his strong implication (89) that the ancient Israelites wrote mostly on potshards. Simply put, issues of preservation greatly skew the sample in favor of media that does not decompose while in the ground for two or three thousand years. An argument that explains the distribution of data in terms of the difficulty of use of papyrus, wood or leather just doesn't cut it.
One of the more interesting facts of my own experience is that papers that have problems often stimulate more thought than those that are more definitive and well supported. So, while I was reading Warner's paper I could not help thinking about a model for technology and product diffusion that is sometimes applied to consumer products in modern economies: the Bass model. Frank Bass of the University of Texas, Dallas, devised the following formula to explain technology and product diffusion. If you are mathaphobic and I haven't lost you as yet scroll down to the pictures.
where
m = the market potential; the total number of people who will eventually use the product.
p = the coefficient of external influence; the likelihood that somebody who is not yet using the product will start using it because of mass media coverage or other external factors, often called the "innovation coefficient."
q = the coefficient of internal influence; the likelihood that somebody who is not yet using the product will start using it because of "word-of-mouth" or other influence from those already using the product, often called the "imitation coefficient."
There is a neat tool on the web that will do the math for you.
Here's a plot of a Bass curve in which internal influences and external influences are considered equal. It assumes that the technology is introduced 2006
Now look what happens when I make the internal decision factors, primarily imitation, dominate the external factors.
Notice that the market becomes saturated much faster. The greater the degree of imitation, of keeping up with the Jones, the quicker a product or technology will be adopted.
Now what does this have to do with ancient Israel? Perhaps nothing, but if the ancient Levantine "markets" were dominated by imitation rather than innovation, and I expect they were, then this might help explain the relatively quick transition from one pottery form to another or the rate of adoption of the "Aramaic" form of the alphabet for writing Hebrew and several other seemly rapid transitions. Then again, it may not.
And just think, in the second paragraph of this post I accused Warner of being too theoretical, not doing a very good job of defining important terms and not offering enough supporting evidence. But what the heck, this is a blog.
Update: August 6, 2006
Fixed a couple of typos and removed what was intended to be a note to me about one of the images.
References:
Bass, Frank. M. (1986). "The adoption of a marketing model: Comments and observations". In V. Mahajan & Y. Wind (Eds.), Innovation Diffusion Models of New Product Acceptance. Cambridge, Mass.: Ballinger.
Warner, Sean, "The Alphabet: An Innovation and Its Diffusion," Vetus Testamentum, 30, January 1980, 81-90
Posted by Duane Smith at August 5, 2006 1:16 PM | Read more on Archaeology |
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Comments
But it makes a really interesting blog post, and perhaps when worked out more a stimulating paper. In terms of present life it seems to work, with the young usually being early adopters, and as you say there may well be evidence from ancient Israel, my questions are about how this works as a mathematical model, and since I am on my way to teach in town (through rush hour traffic) in "a minute" I don't have time to ponder them... maybe later... But do, please keep thinking, and posting, along these lines!
Posted by: Tim Bulkeley at August 6, 2006 12:59 PM
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