From the time of its composing in the 2nd century CE, Claudius Ptolemys Almagest stood at the forefront of mathematical astronomy for nearly 1,500 years. This work included a brochure of 1,025 stars, listing their collaborates (in ecliptic longitude and latitude) and brightnesses. While astronomers within a few centuries realized that the models for the sun, moon, and planets all had problems (which we today acknowledge as being a result of them being inaccurate, geocentric models depending on epicycles and circles instead of a heliocentric model with elliptical orbits), the catalog of stars was normally believed to be correct.
That was, until the end of the 16th century, when the popular observation astronomer Tycho Brahe understood that there was a fundamental defect with the catalog: the ecliptic longitudes were low by approximately 1 degree.
Whats more, Brahe proposed an explanation for why. He suggested that Ptolemy had taken the data from the astronomer Hipparchus some 250 years earlier, and after that incorrectly updated the coordinates.
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The concern of whether this was a cosmic coincidence or the earliest case of clinical plagiarism is a concern that historians of astronomy have argued for over 400 years.
The Accusation
To comprehend why Brahe made this allegation, we must first comprehend the preferred coordinate system of astronomers at the time: the ecliptic coordinate system.
In basic, this system functions precisely like coordinates on earth, with a longitude and latitude. The difference is these are applied to the celestial sphere with the suns course (the ecliptic) changing the equator, and the position of the sun on the vernal equinox changing Greenwich.
Nevertheless, a phenomenon referred to as the precession of the equinoxes indicates that the position of the vernal equinox wanders gradually west, dragging the whole coordinate system with it. It does this at a rate of 1 degree every 72 years, or roughly 0.014 degrees annually.
In the Almagest, Ptolemy gives the time between Hipparchus and the year for which his star catalog was created as 265 years. Because quantity of time, the coordinate system would have drifted by about 3 2/3 degrees.
Ptolemy had an inaccurate value for the rate of precession. To astronomers of the time, this seemed to condemn Ptolemy as the observer for the catalog within the Almagest.
If these texts summed up a lost Hipparchan brochure, it would show that Ptolemy should have observed at least some of the stars in his brochure. That star could then be used as a referral point from which to determine other stars. Just for a handful of stars did Vogt discover that the coordinates for both the Almagest (after accounting for the 1 degree error) and the recuperated Hipparchan catalog were off by similar amounts in the very same instructions. Whats more, they compared the circulation of errors and discovered that Hipparchus catalog was likely more accurate based on the restricted selection of stars available.
The startlingly similar mistakes for stars in both Ptolemys catalog as in the Aratus Commentary seem to indicate that some data was most likely taken.
How multispectral imaging exposes text. Credit: Museum of the Bible CC BY-SA 4.0
The scientists analyzed the coordinates for the stars of all four constellations and compared them with those of Ptolemy. The team found that they did not match. Whats more, they compared the circulation of errors and found that Hipparchus catalog was likely more accurate based on the minimal choice of stars available.
Conclusions
When examining the 400+ year debate over the origin of Ptolemys star brochure, the historian Noel Swerdlow said, “I am just too pleased that I have never composed anything on the subject myself that I may wish to protect.”
Here, Swerdlow summarizes the ferocity of the argument on this subject, keeping in mind that there are persuading arguments in both instructions. The startlingly comparable errors for stars in both Ptolemys catalog as in the Aratus Commentary seem to suggest that some information was more than likely taken. The self-reliance of other stars in the Aratus Latinus collections suggests that much was not.
Thus, the general consensus amongst historians appears to be crystalizing around the notion that there is likely a part of the Almagests star brochure that is based upon Hipparchus data. In action, historians have been asking: How much?
Price quotes have varied hugely. Swerdlow concludes that the quantity of overlap ought to be no more than 10%. Duke confidently states it to be over 80%, and more most likely over 90%.
However while this dispute has raged for over 4 centuries, Swerdlow thinks about the question of whether it has been worth it:
” The labour and ingenuity that have been invested in this question should far surpass the labour spent by Ptolemy in putting together the catalogue in the very first place, nevertheless he might have done it, and perhaps it is time for a moratorium on the subject on the ground that life is too short to squander on concerns that can not be answered.”
A representation of the stars from Ptolemys star catalog, with the actual placement of the ecliptic coordinate system for 127 BCE (Hipparchus), 137 CE (Ptolemy) and where Ptolemy declared it was.
The Hipparchan Catalog
Before we get any even more, it is a reasonable question to ask whether there is any evidence that Hipparchus had a star brochure which Ptolemy might have utilized. And certainly there is.
Pliny the Elder, circa 1st C. CE, records that Hipparchus did indeed develop a star catalog because he had experienced the birth of a new star, which was believed to be difficult. In response, Hipparchus apparently set out to produce a brochure of stars against which future astronomers could compare to determine how the heavens altered.
If Hipparchus did have a brochure, why did historians have no other record of it? The response is the Almagest itself. Ptolemys work was so comprehensive that astronomers were no longer inclined to commission the tiresome copying of other works. The Almagest was all they needed. A lot of previous huge works have been lost to time.
Undoubtedly, the only surviving work of Hipparchus is a commentary he composed criticizing two other natural philosophers, Aratus and Eudoxus.
Counting Stars
Towards completion of the 19th C., numerous historians were revitalized by the discovery and subsequent reinterpretation of ancient and middle ages astrological manuscripts.
In 1892, Ernst Maas was put in charge of modifying a codex from the 18th C. and found it contained a list of constellations. Based upon using language, the text was attributed to Hipparchus, even more supporting the concept that he may have had a star brochure.
Shortly afterwards, 2 more texts were discovered. The first was by Alessandro Olivieri in 1898 and the second by Franz Boll in 1901. These were also credited to Hipparchus and, in addition to the names of the constellations, they also consisted of a count of stars in each constellation.
However, the variety of stars given was irregular with the number that Ptolemy provides in the Almagest. If these texts summarized a lost Hipparchan catalog, it would show that Ptolemy should have observed a minimum of some of the stars in his brochure. This did not free Ptolemy from the accusation that he took some, if not most, of the information.
Dreyers 1/4 Degree Stars
Among the curiosity in Ptolemys catalog surrounds the precision to which the coordinates are given. For the bulk of stars, these appear to be given up increments of 1/6 of a degree. Nevertheless, for a subset of stars, we discover that they are offered to an accuracy of 1/4 of a degree.
In 1917, the astronomer John Dreyer released a paper suggesting and highlighting this reality that this might be a sign of 2 instruments or two observers.
Statistical tests were done on this hypothesis by Gerd Grasshoff in his 1990 book The History of Ptolemys Star Catalogue. There, he compared the mistake in the positions of each star as compared to their true positions as calculated by modern astronomical means. He separated the stars with 1/4 and 1/6 degree precision and examined the circulations of mistakes of each.
A significantly various distribution would support Dreyers hypothesis, however Grasshoff found that they were essentially identical making the test inconclusive.
Here Comes the Sun
One of the biggest difficulties to Brahes assertion came from the famous French mathematician Pierre-Simon Laplace. Examining Ptolemys work, he saw that there was a minute mistake in the worth Ptolemy used for the length of a year. It was somewhat too long– by about 6.5 minutes (a 0.0012% error).
This becomes essential since Ptolemys solar model is, in truth, Hipparchus solar model. While Ptolemy inspected Hipparchus worths, he found them to be accurate and therefore made no modifications. Hence, the date for which the solar design was adjusted was actually throughout the date of Hipparchus.
If the mistake in the length of the year is compounded over the 265 years between the 2 astronomers, it leads to the suns typical position dragging where it needs to have been by approximately 1 degree in the time of Ptolemy.
This matters since to determine the position of a star, historic astronomers would initially have to determine the position of an object with known collaborates and measure from there.
For historical astronomers, this implied computing the position of the sun (which would then be “understood”) and after that observing the difference between the position of the sun just as it set, and the position of a bright star that was noticeable in the fading daytime. That star might then be used as a reference point from which to determine other stars. Eventually, any mistake in the solar position would be imprinted on the collaborates of the stars.
More evidence for this description is offered in by Grasshoff. The Greeks understood that the suns obvious motion accelerated and decreased throughout the year. Today, we recognize this as being due to our elliptical orbit but Ptolemy modeled it by positioning the sphere on which the sun traveled slightly off of the earth. When the sun was closer, it would appear to move much faster and vice-versa when it was even more. This duration motion would also be caught in the solar model and would affect the typical mistake Laplace described by similarly increasing and decreasing the error throughout the year.
Grasshoff examined the mistake in the stellar positions as a function of ecliptic longitude and found that they had a sinusoidal pattern that matched the one from the solar design. Hence, the mistake in the solar design was an entirely possible description for the inconsistency.
It did not totally discharge Ptolemy since the really same pattern would have been present if Hipparchus had been the initial observer, but without the 1 degree mistake because the solar model was adjusted for his time.
Appropriate Motions
An interesting technique to determine the period the star catalog was created involved the positions of the stars relative to one another. Ancient astronomers thought the positions of the stars were fixed, they do move very slowly– a phenomenon understood as appropriate motion.
In the late 1980s the astronomers Efremov and Pavlovskaya tried to utilize this to date the star catalog. Their method was to think about the fastest moving stars in the brochure and figure out what year the position of these quick moving stars were best described relative to the other stars in the same constellation.
Initially, they had problem as the year differed extremely depending upon which other stars they included to compare against. However, in 2000, Efremov and Dambis published a 2nd paper declaring success and dating the star brochure to the period of Hipparchus
This conclusion was quickly turned down by Dennis Duke from the University of Florida who kept in mind that the quantity of correct movement over the 265 years in between Hipparchus and Ptolemy was below the 1/6 degree accuracy for nearly every star. Just 3 stars moved more than 1/6 of a degree in that time duration.
While Dambris and Efremov claimed to have actually adequately accounted for the fundamental unpredictability from the instrumentation, Duke refuted this stating that, when appropriately represented, this approach would not have the ability to compare the era of Hipparchus and Ptolemy at all.
Recuperating Hipparchus.
With all of the tests that astronomers created not able to respond to the concern, what would actually be required was a copy of Hipparchus lost brochure. Sadly, the only text historians had available was the Aratus Commentary. This text was Hipparchus response to a poem by Aratus entitled The Phaenomena, in which Aratus tried to explain the stars that were increasing, setting, or culminating (i.e., at their acme) at the very same time that other stars or points on the ecliptic were likewise increasing, setting, or culminating.
Hipparchus slammed Aratus descriptions and, very first corrected them for the latitude of Aratus, and then supplied pairings for his own longitude of Athens in an appendix. Starting in the early 1900s, historians thought about that, if these pairings had actually been calculated based upon the lost Hipparchan brochure, it might be possible to reverse-calculate the collaborates from the brochure.
In 1925 Heinrich Vogt declared to have actually effectively recuperated the coordinates of 122 stars without “auxiliary hypotheses.” Vogt initially compared the positions for these stars to the ones provided by Ptolemy If the collaborates were the same, with the exception of a 2 2/3 balanced out, then it would support the hypothesis that Ptolemy utilized Hipparchus data.
Vogt found that, by and large, the coordinates did not match. He went further, by comparing the mistake against the modern-day calculated position for both Hipparchus and Ptolemy and analyzed the distribution of errors. Again, he found that they were especially various. Only for a handful of stars did Vogt find that the coordinates for both the Almagest (after representing the 1 degree mistake) and the recovered Hipparchan brochure were off by comparable amounts in the very same instructions. Theta Eridani, for instance, was off by more than 3 degrees from its real position in both brochures, once again indicating that Ptolemy used a minimum of some of Hipparchus data.
Vogts findings were not totally free from criticism. When Grasshoff evaluated Vogts analysis, he questioned much of the underlying assumptions Vogt utilized. In particular, historians have actually acknowledged that different parts of the Aratus Commentary were composed at different times during Hipparchus life.
While Vogt states he accounted for this, he is uncertain on which computations were for which age. The 2 portions of the text were offered for different latitudes. Vogts techniques just ever point out Aratus latitude raising doubt over whether he accounted for this at all.
Perhaps worst, some stars are provided as part of several pairings permitting their positions to be determined in numerous ways. But frequently they did not if the presumptions and methodology are sound they should match.
The combined outcome of these potential mistakes is that the coordinates in Vogts rebuilded Hipparchan brochure might have been scrambled, making them not match when certainly they must have. And unfortunately, due to the unsolved questions about when numerous portions were composed, it seemed not likely this approach might ever be successful.
The Phaenomena of Ptolemy.
If efforts to reconstruct Hipparchus brochure from the Aratus Commentary were not likely to work, what would occur if we went the other method around, recreating the rising/setting/culminating descriptions of the Aratus Commentary utilizing the data from the Almagest? This would eliminate the questionable assumptions in transforming the phenomena explained in the Aratus Commentary to standardized collaborates.
Grasshoff carried out precisely these calculations and compared the phenomena described in the Aratus Commentary to what must be anticipated utilizing contemporary huge theory to figure out the error in the description for each star. He then did the exact same for the ones calculated from the Almagest. The error for each could then be outlined against one another. If both had the very same, big mistake, it would be a strong indicator of common origin.
When he did so, Grasshoff found that there were, indeed, a number of stars that revealed a strong correlation in their errors (including Theta Eridani and three other stars that Vogt had actually also flagged as suspicious).
Nevertheless, there were some that had notably different mistakes. This view supports the hypothesis that Ptolemys catalog was only partially based on Hipparchus.
Aratus Latinus
In the 8th C., this same Aratus Commentary had grown popular amongst scholars studying astronomy and it was equated into Latin. These texts became known jointly as Aratus Latinus. To supplement the work, they were typically put together with extra huge product.
Among the works that became consisted of in some, were passages including descriptions of the boundaries of three constellations (Ursa Major, Ursa Minor, and Draco) by offering the ranges of the bounding stars from the north celestial pole and their ecliptic longitude.
While these portions were originally attributed to Aratus, in the late 19th C., historians understood their descriptions and language much better matched those of Hipparchus. It was further recognized that the collaborates for Polaris precisely matched the value Hipparchus used according to Ptolemy in another of his works, Geographia.
Therefore, historians now accept Hipparchus as the author of these portions, and these passages provided another method to recover the positions of some stars from the Hipparchan catalog.
Codex Climaci Rescriptus
In 2012, biblical scholar Peter Williams, provided his trainees a number of pages from a text found at a Greek Orthodox monastery in Egypt. These pages contained Christian texts, however were understood to have been scraped clean before the Christian text was included, removing a previous text (a phenomenon understood as palimpsest).
The students imaged the pages under numerous colors of light and utilized computer system algorithms to try to recover the hidden text start in 2017. They quickly understood that the texts were huge, consisting of star-origin mythos from Eratosthenes, but likewise segments of the Aratus Latinus and associated works. Amongst those associated works was the Hipparchan work, however this time consisted of a brand-new constellation: Corona Borealis.
A more extensive conversation of each of the arguments here and more is readily available in Jons blog.
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