Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Fractions of a Degree in Latitude

So far, all of the tests that Grasshoff has reviewed to try to determine whether or not Ptolemy used a Hipparchan star catalog have proven inconclusive. In the last post, we showed that the solar theory was quite obviously in use in constructing the star catalog. This provides a reasonable explanation for the mean error being $\approx 1º$ as well as why the distribution of errors could have matched Hipparchus’ even without Ptolemy having used his data1. But just because it provides a reasonable explanation of how Ptolemy could have gotten similar incorrect results doesn’t mean that he did. Thus, Grasshoff needs another way to try to distinguish between these two historical interpretations.

Grasshoff now turns to the frequency of the fractions of degrees which he describes as a “powerful criterion to decided between suggested historical interpretations.” Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Fractions of a Degree in Latitude”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Errors in the Solar Theory

So far in Grasshoff’s analysis, he’s come to the conclusion that the distribution of errors (as well as some of the specific ones) point to Ptolemy having used Hipparchus’ data. The only possibility to rescue Ptolemy as an observer is if there is some sort of underlying bias in both of their observations that led to a similar set of errors.

The primary suspect for this would be errors in the solar theory because Ptolemy’s model was essentially the same as that of Hipparchus’1. So, at long last, Grasshoff is ready to explore the errors in the solar theory. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Errors in the Solar Theory”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Structures in the Catalog

In the last post, we followed along as Grasshoff explored the distribution of errors within Ptolemy catalog as compared to those of the reconstructed Hipparchan one. He demonstrated that the errors are highly correlated indicating that Ptolemy likely did use Hipparchan data, unless there was a systematic error common to both.

To build on that concept, Grasshoff begins exploring structures in the catalog by mapping the position of the stars in Ptolemy’s catalog as compared to the true positions as calculated by modern astronomy for the year $137$ CE1. Mapping things in this manner allows for several patterns to become apparent.

Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Structures in the Catalog”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Gundel

Having reviewed Vogt’s work, Grasshoff now turns to dissecting Gundel’s. As a reminder, Gundel discovered a $15^{th}$ century set of hermetic writings that contained a list of stars that was dated to the time of Hipparchus, potentially making it the first direct evidence of a Hipparchan star catalog.

But what Gundel’s analysis lacked is any exploration of how this related to  whether or not Ptolemy stole Hipparchus’ data. In this post, we’ll explore Grasshoff’s analysis of that topic. However, before doing so, Grasshoff works to ensure that we have the best possible understanding of the hermetic catalog before comparing the hermetic catalog to Ptolemy’s. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Grasshoff (1990) – Reviewing Gundel”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Newton (1977)

In the past few posts, we’ve demonstrated a rapidly forming consensus that Ptolemy’s star catalog was largely an original work. However, there were some holdouts. In $1977$ R. R. Newton published the book The Crime of Claudius Ptolemy1. In this work, Newton generally agrees with Lalande and Delambre – That Ptolemy’s “observations” are not true observations, but merely the result of theoretical calculations, extending this argument well beyond the star catalog, which Newton frequently describes as “fabricated”.

As a forewarning, this book raised a great deal of popular media attention as the alleged scheming of scientists is always a popular topic, but scientists reviewing the book have generally panned it as using flawed methodology, as we’ll see. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Newton (1977)”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Gundel, Pannekoek, and Peter & Schmidt (1936-1968)

In the last post, we explored the 1925 paper by Vogt that attempted to reverse engineer entries from the presumed Hipparchan star catalog. Assuming that the coordinates derived were actually representative of such, Vogt demonstrated that Ptolemy was unlikely to have based his catalog on that of Hipparchus.

Continuing in the theme of defending Ptolemy, we’ll explore three more texts which come to Ptolemy’s defense: a book by Gundel (1936), a paper by Pannekoek (1955) and a paper by Petersen & Schmidt (1968). Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Gundel, Pannekoek, and Peter & Schmidt (1936-1968)”

Scholarly History of Commentary on Ptolemy’s Star Catalog: Vogt – 1925

In our last post we had established that it was impossible for Ptolemy to have stolen all of his data from Hipparchus as indirect evidence of the number of stars that would have been included in Hipparchus’ catalog indicate that Ptolemy’s catalog had around $200$ stars that Hipparchus’ presumptive catalog did not. Furthermore, we cited Dreyer and Fotheringham who both showed that errors in the determination of the position of equinoxes and solstices would have resulted in the $1º$ error at the heart of the accusation against Ptolemy, eliminating the need for Ptolemy to have used Hipparchus’ catalog.

Thus, while it’s not necessary that Ptolemy took all of his data from Hipparchus, the possibility remains that he took some. But to determine that, we’d need more information about Hipparchus’ presumed catalog which is what we’ll explore in this post looking at an important 1925 paper by Vogt. Continue reading “Scholarly History of Commentary on Ptolemy’s Star Catalog: Vogt – 1925”