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.
Regulus and Spica
The first argument I’ll explore of Newton’s is related to Ptolemy’s use of Regulus to determine the rate of precession that we examined in this post. There, he came up with a movement of $2 \frac{2}{3}º$ in $265$ years which gives exactly a rate of precession of $1º$ per century. Newton declares that this is a statistical impossibility – to come up with a result that agrees perfectly with theory. Newton calculates this as $1:1,000,000$. He makes a similar argument for Spica, placing this at $1:2,000$.
Grasshoff doesn’t get into exactly how this is calculated but the estimation of probabilities is strongly criticized by others. Grasshoff cites Swerdlow, in an article for American Scholar, in which Swerdlow notes that Newton’s argument assumes that Ptolemy’s data be free of observational biases – such as the known inaccuracies of the solar model which we’ve already demonstrated it’s not. Without taking into account this factor, Newton’s calculations of probability of two independent observations are inherently meaningless. Grasshoff states that
Newton shows only that Ptolemy’s observations cannot be measurements free of systematic errors; something no one has ever seriously asserted.
Declinations
The next argument of Newton’s that Grasshoff discusses returns to the question of the stars that Ptolemy selected to determine the rate of precession. You’ll recall that when we discussed Vogt’s analysis, Vogt attempted to recalculate the rate of precession from all $18$ of the stars that Ptolemy had available as opposed to the $6$ he selected. Unfortunately, Vogt botched this, but Newton does so successfully. He then looks at the distribution of these values:
Newton criticizes this on the basis is that this is not the distribution that should be expected if Ptolemy legitimately made observations. If he did, it should look like a bell curve with its peak at the correct value – around $50$ arc seconds per year.
Again, Newton’s analysis fails here. The claim that it should look like a bell curve is only if the data is well sampled – A mere $18$ points is not enough to establish a normal distribution. As with before, it also fails to take into consideration the systemic issue with Ptolemy’s solar model.
Occultations
Next, Grasshoff explores Newton’s discussion of occultations of stars by the moon that we explored in this post. First, he takes aim at the claim that the observation quoted by Ptolemy of Timocharis describes that the “southern half of the moon was seen to cover exactly either the rearmost third or [the rearmost] half of the Pleiades.” Yet the calculation Ptolemy then proceeds to do indicates that it was the northern half of the moon that would have covered this section of the Pleiades – Something which should have been obvious to Ptolemy.
Grasshoff criticizes Newton for precisely that reason: Ptolemy should have been aware of this contradiction indicating it is more likely that the positioning of the moon may have been a scribal error at some point in which “northern” was replaced with “southern”. Whether this is the case or Ptolemy truly adjusted the observations is impossible to determine, but this is hardly the clear cut case of fraud Newton describes.
Newton similarly criticizes the occultation of the star Spica Ptolemy describes. There, Ptolemy quotes Timocharis having stated that Spica had risen $3 \frac{1}{2}$ hours after midnight – A timing Ptolemy rejects, instead substituting his own, calculated, value of Spica having risen $2 \frac{1}{2}$ hours after midnight.
Ultimately, I’m rather unclear on exactly what Newton’s criticism is here as he evidently calculated the timing using modern methods and determines Spica rose $2$ hours and $47$ minutes after midnight – a timing much closer to Ptolemy’s calculated value than the one initially quoted by Timocharis, thereby justifying Ptolemy’s use of the calculated time. I suppose Newton’s criticism is then that, because Ptolemy used this calculated position with the observation from Menelaus, this is evidence of fraud, but Grasshoff’s explanation here is quite poor.
Fractions of Degrees
Next, Newton explores the fractional degrees in Ptolemy’s catalog coming up with a novel interpretation. He proposes that there was a single instrument with divisions of $\frac{1}{2}º$. Ptolemy could then record either a whole number or one in increments of $\frac{1}{2}º$ if the observation were almost exactly on the line of division, $\frac{1}{4}º$ or $\frac{3}{4}º$ if they were half way between, and then increments of $\frac{1}{6}º$ if they were more to one side or the other of the estimated half way point between demarcations.
If, for instance, the accurate coordinate corresponds to fractions between $55’$ and $5’$, the observer would write down a $0’$; for coordinates between $42.5’$ and $47.5’$, the degree fraction would be $45’$; and if the value lies in the interval $35’$ to $42.5’$, $40’$ would then be noted down.
Newton then comes up with a set of “theoretical” predictions on how many stars from the catalog should fall into each bucket. These are then compared with the number of actual observations that fall into each, both for ecliptic latitude and longitude.
Here, we can see that the distribution in the latitude has a decent agreement with the theoretical predictions. It’s off most in the category of $45’$. However, there is a potential explanation here. In particular, the $45’$ was not expressed in texts as $\frac{3}{4}$. Rather it was written as $\frac{1}{2} + \frac{1}{4}$. Thus, if a scribe truncated this, it is possible that some of these were accidentally shifted to the $\frac{1}{2}$ or $\frac{1}{4}$ buckets. And indeed, there is a notable overage against the theoretical value for the $30’$ bucket.
However, this does require some special pleading, and there is little evidence in the texts that do survive of such transcription errors. Furthermore, Newton even admits there’s a flaw in this reasoning. In particular, we should see the same thing happening in the case of $50’$ increments which would have been expressed as $\frac{1}{2} + \frac{1}{3}$ but this aligns moderately well.
So how does this combine with Newton’s assertation that Ptolemy used values from Hipparchus’ catalog? Essentially, the above claim on the instrument would have to be regarded as Hipparchus’ instrument. Newton claims that Ptolemy took the values from Hipparchus and then did further rounding as described.
Arguments with Boll & Vogt
As we’ve seen in previous posts, other historians made compelling cases that Ptolemy catalog could not have been copied, at least entirely, from Hipparchus and Newton would need to address them. Although he acknowledges them, the response is underwhelming. In particular, he tries to criticize Boll’s work by claiming Boll identified the figures found in the medieval text as Hipparchan because of the name only. However, he presumes that this could have been an addition of a medieval scribe and not truly be Hipparchan in origin. But this ignores the fact that this was not the sole method by which Boll determined them to be Hipparchan. Specifically, he also looked at the terminology used which also date the records to Hipparchus.
Newton also attempts to criticize Boll’s estimation on how many stars the Hipparchan catalog could have included. Boll estimated that there should be $761 – 881$ stars in the Hipparchan catalog. Newton makes his own estimation and claims that there would have been about $751$ stars. The argument becomes hard to follow here as Grasshoff then states this corresponds “roughly to the number in the catalogue in the Almagest,” which is entirely incorrect as there are $1,025$ stars in Ptolemy’s catalog. Perhaps Newton was only referring to the constellations that are in both the Aratus commentary and the Almagest?
Newton also takes aim at Vogt’s reconstruction of the Hipparchan catalog. Grasshoff doesn’t spare Newton here and states, “Newton’s arguments against Vogt’s article shows his small understanding of it.” Specifically, Newton simply denies that the Aratus commentary could have been based on a catalog. This should be immediately regarded as suspect since, as Grasshoff notes, Newton’s position flatly contradicts his position on Boll which he assumes that the Aratus commentary is based on a catalog to attempt to infer the number of stars in said catalog.
Newton’s only apparent argument for rejecting the Aratus commentary as derived from is that the declination is quite easy to determine by measuring the altitude of the object as it transits the meridian and then adjusting for latitude while calculating it from a catalog is more laborious – a weak argument if it can be called one. Worse, Vogt’s procedure for reconstruction scarcely depends on the declinations making Newton’s argument largely superfluous anyway.
Another criticism against Newton is that, using the Aratus commentary, Vogt showed that at least five stars were likely copied into the Almagest as they had similar and significant errors to the Aratus reconstruction. Thus, they must both have drawn from the same source which inherently links the Aratus commentary to the Hipparchan catalog.
Conclusion
Ultimately, while Newton had a great deal to write on this subject, it is only worth mentioning in order to have a complete discussion of the history of this topic even though nothing of value was added and Newton’s conclusions are generally disregarded.