Writing is much more socially complex than making art and making music. Art and music draw on natural forms and make sense at a low level of neurological processing. A single person could invent a form of visual art or music that might be engaging to many others without a specific investment in teaching them. Inventing writing, in contrast, requires teaching a group of persons a common code for meaning-making.
At least in Mesopotamia, the emergence of writing seems to be associated with accounting for goods. Large-scale farming and industry, stratified societies, systematized economic tributes, and relatively high-density, geographically fixed population centers all developed together. The general model is producers who are able to produce enough extra goods to pay tribute to the ruler and his associated administrative and military apparatus that forms the nucleus of a population center. Systematized economic tribute requires accounting. The first writing in Mesopotamia arose from this accounting.
A key innovation was the use of small, clay tokens. A specific type of token represented a particular amount of a particular good. For example, a spherical token might represent a small basket of barley, and three such tokens, three small baskets of barley. Such tokens could be used to record goods collected or delivered. The tokens thus provided a physical tool for thinking about quantities of objects. Many such tokens have been recovered from Mesopotamian sites dating from 10000 to 5000 years before the present.
Tokens led to impressed and incised signs. First, tokens associated with a particular person were kept in clay envelopes on which the person’s seal was impressed. To indicate the tokens that were sealed in the envelope, the tokens placed within the envelope were also pressed against the outer surface of envelope. Those marks thus indicated with a one-to-one, geometric correspondence the tokens within the envelope. Over time, the envelopes became writing slabs. The marks retained their meaning without the corresponding tokens being contained within the envelope/slab. In addition, instead of impressing the marks using tokens, the marks were incised with a stylus. Once the mental skill of reading written signs was well-developed and institutionalized, the physical tokens were no longer needed.
By about 5000 years ago, accounting signs had evolved into a general-purpose written language. Signs related by physical quantities of goods (a large basket of barley vs. a small basket of barley) evolved into abstract numbers (the sign for the large basket came to mean, e.g., “ten times as much”). Pictographs were associated with the sounds of items pictured, and combinations of such pictographs were probably first used to indicate the sound of personal names. Such pictographs provide more flexible and efficient attribution than personal seals. Demand for funereal objects that could “speak” prayers for the dead through written phrases seems to have stimulated further development of syntax and sign repertoire.
The time scale of the development of writing suggests social network effects. The use of tokens for accounting endured for about 5000 years. Once such accounting had led to incised signs, a general written language developed within a span of about 500 years. Incised signs could be created, copied, and circulated relatively cheaply. Texts thus provided a new communication network. That network in turn supported rapid social-symbolic innovation.
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 Humans have been making art and music much longer than they have been writing. Artifacts testifying to prehistoric art include ochre engraved with abstract markings (more than 70,000 years before the present [BP]), the Chauvet cave paintings (probably about 30,000 BP), a lion-headed figurine (32,000 BP), and various female figurines (about 25,000 BP). Prehistoric musical instruments include a bone pipe from Geissenklösterle in Germany (36,000 BP). In contrast, the earliest writing occurred only about 5,500 years ago, with various evidence from China, Egypt, Uruk (Mesopotamia), and Harappa (Indus valley).
 My account of the development of writing is based on the work of Denise Schmandt-Besserat, as set out in her highly readable book, How Writing Came About (Austin: University of Texas Press, 1996). The development of writing in China may have been driven more by political and familial-religious demands.