There’s a very modern element to Ptolemy’s Catalogue: The use of checksums.
Modern data processing has to address the dilemma of error. Any time a file or other body of data is copied, there’s the possibility of error in the process of transcription. Digital computers make use of checksums to identify, even correct such errors in transcription.
Imagine a datafile represented by a digital string of 1s and 0s, which are clustered in groups of 8. Of each cluster, the first 7 represent useful information, and the last is a checkbit, generated by applying an algorithm to the seven data-bits. For example: if the first seven digits contain an even number of zeroes, the checksum bit is 0; if an odd number of zeroes, the checksum is 1. If there is an error in copying this block of 8 bits, the checkbit will not align with the seven databits. This mismatch doesn’t tell you what the error is; it simply says that the information of this block is suspect. (A method like this assumes that errors are randomly distributed, and sufficiently rare that the chance of more than one error in a single block is very, very small.)
In more sophisticated formats, datablocks are larger, and checksums are more complex, allowing both detection and correction of most errors.
There are many chances for error in the preparation of a text manuscript. Publishers today employ proofreaders to detect and correct errors before committing to a press run. Ancient scribes typically served as their own proofreaders, relying upon an understanding of the text at hand. (In some traditions, religious texts are transcribed by a team of two or more, with one writing and another proofreading.) In the case of the Mathematical Treatises, we presume that most copies were prepared by students of Ptolemy’s geometric arts.
A text such as Ptolemy’s Star Catalogue poses a challenge to a scribe. In copying a paragraph of prose, the rules of grammar and logic, and the overall meaning or narrative of the text provide clues to guide the scribe toward a faithful reproduction. When copying poetry, meter and rhyme limit the possibilites for error. But in copying a database like the Star Catalogue, which lists names and descriptions and longitudes and latitudes and magnitudes, it’s easy to imagine a weary scribe duplicating or switching or skipping a star.
An error of duplication is readily visible, easily corrected.
An error of switched data might pass unnoticed by most, yet is easily corrected by those who do notice. We suppose that most of those studying Ptolemy were noticers.
But an error of omitted text is hard to see.
Somebody, somewhere recognized the difficulty of accurately reproducing a text like a star-chart, and invented a tool to help mininize errors of transcription – an early sort of checksum.
Here’s how Ptolemy employs it:
For each constellation, constiuent stars are listed, naming or describing each in the context of the figure, and listing stellar longitude and latitude and magnitude for each. Following each constellation, a brief accounting of the stars: n1 stars of magnitude 1, n2 stars of magnitude 2, n3 of mag 3, and so on, for a total of nt stars.
This information isn’t of much use to the end-user of the star catalog, but it’s a great help to a scribe preparing a copy of this text. Copying this summary checklist helps to prod the scribe into auditing the accuracy of the starlist on an ongoing basis – and it provides a tool for conducting this review, constellation by constellation.
A checksum.
There are several other tables of numerical information scattered throughout Almagest, such as trigonometry tables, and tables of ‘anomalies’ (correction factors for calculated values). None of these have associated checksum tools. Why the difference?
Our best guess is that while most of Almagest was of interest only to a select few mathematical adepts, the Star Catalogue circulated widely among astrologers, scholars, and wealthy dilettantes. Most copies of the whole of Ptolemy’s opus, we’d wager, were prepared by their owners and users, likely in the course of an apprenticeship. Such a scribe is personally invested in the accuracy of transcription.
But copies of the Star Catalogue circulated separately, prepared by professional scribes for sale to astrologers, scholars, and wealthy dilettantes. The utility of checksums in such a database is obvious.