You can find the answer to this question in two ways. First, you can look at Figure 12.1, which indicates that there are four independent or possibly independent origins of writing and indicates which ones of them are only “possible.” Second, you can look on p. 218 and then on p. 222 (in the paperback edition). Each of these pages lists one of the indisputably independent inventions of writing. The two paces are Sumer and Mesopotamia.
Sumer was the first place where writing originated. Diamond says that Sumer invented writing by 3000 BC. This was the writing that has come to be known as cuneiform. It was written using pointed tools to make marks in clay tablets. The tablets were then baked to make the writing permanent.
The second place where writing originated independently was in Mesoamerica. This occurred by 600 BC. It is believed that this writing was independent because there is no credible evidence of contact with the Old World. In addition, these scripts are very different from anything created in the Old World.
The answer, then, is that Sumer and Mesoamerica were the only two places where we know for sure that writing was invented independently.