In Search of Lost Time
An Astronomical View of Ancient Egyptian Star Clocks
Though most of the astronomical knowledge from the ancient world that we rely on comes from Babylonian and Greek sources, Egyptians had their own repeating sets of astronomical data. How (and how much!) this data corresponded to the night sky is still debated. I am interested in approaching this question empirically and in a visually stimulating way. Therefore, I will talk about three separate steps of approaching this question:
- What does the data look like, and where do we get it? This is the Egyptology bit.
- How do we get information about the sky over Ancient Egypt, and what do we do with it? This is the astronomy bit.
- Finally, how do we try to visualize those data in accessible ways that could be useful for pedagogy and research? This is the DH/visualization bit.
Ancient Egyptian astronomical data
First, let us begin by introducing the data I am interested in and putting it in its proper context. The type of data I will be considering is called a Diagonal Star Table (once known as Diagonal Star Calendars or Diagonal Star Clocks). These tables are primarily found on rectangular Middle Kingdom coffin lids (with a single New Kingdom exception in the Osireion), making their funerary context undeniable.
Today, we know of 28 coffins containing diagonal star tables and have publications describing 23 of them (Symons et al., 2013). Most of the coffins are from Asyut, with a few from Gebelein, Thebes, and Aswan. Based on their decanal content the lists have been divided into K-tables and T-tables, which I will explain in a moment. The location data to the right is based on information found in Symons et al. (2013) and doesn't point to individual tombs but rather the general area.
The data presented on each of the 23 coffin lids are not identical and can be divided into two types (T tables and K tables) based on the starting decan. No one table contains all of the aggregate information we have from diagonal star tables and there are variations even within a single type. Nevertheless, Neugebauer and Parker (1960) reconstructed an "ideal star table" schematic for illustrating their form and use. The one on the right is the version from Symons et al. (2013; see here ).
Each star table has a horizontal strip (HS) and vertical strip (VS) with hieroglyphic text. The rows are not labeled, but the number 12 suggests hours of the night. The columns suggest 36 decades of the year from right to left, with the five epagomenal days separately represented on the far left. "Ordinary" decans are numbered 1-36, while "triangle" decans are labelled A-K. While Depuydt (2010) sees these as an idealized description of the night sky, Symons (2015a) points to the inclusion of the triangle decans as "the clearest evidence we have that these tables did have an observational basis."
As an example of a non-ideal and existing diagonal star coffin, let us take this drawing of part of a Middle Kingdom coffin lid. The coffin in question is Cairo J 47355, labeled "Coffin 6" in Plate 9 of Neugebauer and Parker Vol. I (1960). It is dated to Dynasty XI under the reign of Mentuhotep II (approximately 2061-2011 B.C.) and was located in Thebes (near Deir el-Bahri). On the right, we can see a part of the horizontal strip and the full vertical strip in this image, as well as ordinary decans in rows 1-17.
More information, as well as images and publications of the coffin, can be found here .
The coffin belonged to a woman named '3shyt, who had the title "King's wife, King's sole ornament, Priestess of Hathor." In addition to the horizontal row of text praising '3shyt and giving her name and title, the vertical column references
- Sopdet (Spdt), which we know as Sirius
- Sah (S3h), which refers to parts of the constellation Orion
- Meshkhetiyu (Mshtyw), "the foreleg of the ox", corresponding to our Big Dipper
- Nut (Nwt), the Egyptian goddess of the sky
Inscribed in the table we see 5-pointed stars, signifying decans, along with names of the individual decans. This diagonal star table is a T type, starting with the decan TmAt Hrt . The decans move across the table diagonally as suggested by the overall name of the structure. For instance, we see a decan named Hry-ib wiA ("the middle of the ship") starting out in hour 11 of the first week, then moving to hour 10 in the second week, and so on until it reaches hour 1 in the eleventh week.
While diagonal star tables give us an ordered list of decan names, we need to consider the decans' actions. These are somewhat described in the Book of Nut or The Fundamentals of the Course of the Stars (von Lieven, 2010). Note that the earliest attested copies of the text date to the reign of Seti I in the New Kingdom, significantly later than the diagonal star tables discussed above, though the text itself could have originated earlier. The text itself includes two decan lists, one of which possibly dates the sky to its ideal occurrence in 3300 BCE (or 1870 BCE), when the going out of Sopdet (prt-spdt, understood to be when Sirius rises with the Sun) begins the first day of the new year.
This is also the text which best describes motions of the stars and places Sopdet as a template for decans Per The Fundamentals, the decans follow a pattern where they are:
- “first”, then spend 90 days “in the west"
- spend 70 days “enclosed by the dw3t”, then are “born”
- spend 80 days “in the east”
- spend 120 days “working"
Here, "working" is associated with marking the 12 hours in the sky for 10 days each, presumably transiting the celestial meridian (Neugebauer and Parker, 1960), though Depuydt (2010) and Symons (2002a, 2015a) have pointed out the astronomical problems with such a scheme.
Where does this leave us? We know at least a few of the named decans correspond to asterisms we know (like Sirius and Orion), and we know they have four defined actions that take 90 + 70 + 80 + 120 days to complete. Ideally, we could use the motion of Sirius and Orion to identify what the actions mean, then perhaps even use those actions and the diagonal star tables to guess at other asterisms and constellations. In practice, work like this has been done before in planetarium software like Stellarium (see e.g. Conman 2003), but the actions of rising and transiting could not be reconciled with the decans in a clean way. In this work, I explore some alternative ways of visualizing decanal motions in the hopes of getting a step closer towards the observational foundations of decanal star lists.
Stellar coordinates, courtesy of Python
To begin visualizing decanal motions, we must first know how stars' positions were changing thousands of years ago. Thankfully, astronomers love Python, and have developed a common core package called AstroPy . AstroPy already contains functions that can track the coordinates of any named astronomical object in a given timeframe and at a given location on Earth. I used this functionality to write a code called decanOpy which calculates star positions and returns them in a conveniently formatted .txt file for plotting and mapping.
An illustration of azimuth and altitude. Source: timeanddate.com
What kind of coordinates?
Given the name of an object and a location on Earth, decanOpy returns celestial coordinates called altitude and azimuth. Altitude expresses the elevation of the star in the sky, while azimuth expresses how many degrees clockwise away from North it is. I find this coordinate system particularly appropriate to use because it is anchored to the location of the observer on Earth—just like it would be for someone observing in Egypt.
How does decanOpy work?
The decanOpy GitHub contains three basic pieces: the actual code (decanO.py), a Jupyter notebook to quickly visualize some of the outputs (decanPlotting.ipynb), and a folder of outputs to plot (/DecanLists). Right now, there are a few .txt files in the /DecanLists folder to play around with while plotting.
As input, decanOpy takes: a decan name, a year BCE, and a starting month.
As output, decanOpy produces a .txt file with the name of the object and location specified at the top, and then a list of coordinates arranged in the following columns:
Julian Date|Human Readable Date|<Decan name> Azimuth|<Decan name> Altitude|Sun Azimuth|Sun Altitude
Example of decanO.py code and accompanying Jupyter notebook.
Which decans do we start with?
Above, we mentioned three asterisms generally understood to correspond to Sirius, Orion, and the Big Dipper. I chose some of the brighter stars in each of these modern constellations (Sirius, Rigel, Betelgeuse, Alkaid, Mizar, and Alioth) and ran them through decanOpy for the year 1300 BCE in Luxor, Egypt.
Some of the stars in modern constellations we'll be tracking.
Visualizing the Data
Once we have the coordinate data of our test stars, let us go back to the actions they are said to perform and explore ways of visualizing them.
The Dw3t
Recall that decans are said to spend 70 days "in the dw3t," or the Ancient Egyptian hereafter, before being "born." Though the actual location of the dw3t is ambiguous (Zago 2018), Neugebauer and Parker (1960) identify this with the time the star is under the horizon and invisible, before helically rising (rising with the Sun in the morning), which can be identified with being "born".
One way to visualize how many days per year the given star is invisible is to plot its maximum altitude in the sky between sunset and sunrise. If it's less than zero, the star's invisible!
Sirius and Orion
Let's take a look at Sirius and Orion's bright stars, Rigel and Betelgeuse. Their maximum altitude every night is shown in green and blue. The vertical dashed lines delineate months, while the big gray swatch at the bottom represents altitudes of less than zero. The reddish mountains represent possible obstructions that could exist on the horizon, up to 10 degrees of altitude. Sirius and Rigel spend about 70 days below the horizon, while Betelgeuse spends closer to 50. This illustrates one of the issues with identifying decans with modern constellations: even within a single asterism, the stars can behave very differently on a given night.
The Big Dipper
On the other hand, the stars of the Big Dipper never fall under the horizon for the entire night. This makes sense since the Big Dipper is listed as a constellation but not as a decan, meaning that we wouldn't expect it to behave the same way as Sirius and Orion. Indeed, the Big Dipper is a circumpolar constellation at the latitude of Luxor.
West and East
Before being "in the dw3t," the decans spend "90 days in the west"; after, they spend "80 days in the east." If we accept that "in the dw3t" means under the horizon, this follows almost automatically because stars rise in the east and set in the west.
Sirius
After heliacally rising, Sirius climbs higher and higher right at sunrise, until it peaks after about 60 days. Similarly, it peak at sunrise about 60 days before falling under the horizon. This is close, but doesn't quite fit with the 80-90 days of the text. Note, however, that this doesn't directly tell us the azimuth of Sirius; we turn to that next.
We can also see that Sirius heliacally rises in the SE, drifting westwards across the sky until it's due South in about 60 days. Similarly, it is due South at sunset about 60 days before it is to set below the horizon, drifting westwards. This again seems shorter than the 80/90 days as prescribed by The Fundamentals of the Course of Stars; however, it should be noted that I'm only accounting for true cardinal directions here, not the actual azimuth of the rising Sun.
If we take the above image and add the azimuth of the Sun at sunset and sunrise, perhaps the picture changes. Using the location of the Sun on the horizon to mark a more ephemeral "east" and "eest," Sirius now takes around 120 days to reach the same azimuth as the Sun before and after being under the horizon. This period is now significantly longer than the 80/90 days from The Fundamentals, suggesting that what marks the end of being in the east/west is neither crossing the north/south meridian nor catching up to the Sun. Rather, perhaps it is the onset of the "working" period which ends the action of being "in the east," and the end of the "working" period which marks the beginning of being "in the west."
Working
Unfortunately, "working" is the hardest action to nail down, and I haven't been able to produce a worthwhile plot of it thus far. While Neugebauer and Parker link this with transiting the local meridian, Symons (2015b) has pointed out that stars that are "born" (aka, heliacally rise) in sequence do not necessarily culminate in sequence. The action of "working" could correspond to a different astronomical phenomenon, but so far I haven't been able to think of a viable alternative.
Future Directions
Additional visualization options I'm exploring include using ArcGIS to make stellar maps (great example here !), though stationary maps cannot quite capture the decans' actions which are inherently tied to motion. On the other hand software like Stellarium captures motion beautifully, but doesn't quite give me easy access to the stars' coordinates and other numerical data to easily parse with code. One option that combines these nicely that has recently been pointed out to me is D3-Celestial by Olaf Frohn , which uses geographic data structures ( GeoJSON ) and the D3 visualization library to make beautiful and manipulatable visualizations of the night sky:
"Simple map" example of D3-Celestial Star Map.
What I appreciate about D3-Celestial is the ease of transitioning between a 3D/spherical representation of the sky and a 2D/map-like view. However, its GitHub repository currently only includes modern star coordinates, going back only as far as 2011. With a little modification, decanOpy could easily be made to output appropriately formatted data files for representing the sky as it looked millennia ago which could be used with D3-Celestial for visualization. As an example, one could imagine using D3-Celestial to bring Neubauer and Parker's illustrations of the "decanal belt" to three dimensions:
Example of a possible visualization using D3-Celestial and decanOpy: re-creating Fig. 24 from Neugebauer and Parker Vol. I (1960).
(A Slighly Poetic) Conclusion
In conclusion, the night sky and the stars' movements have captivated the human imagination since time immemorial and will continue to do so far into the future. Similarly, Egyptian decans have captivated the minds of modern scholars for over sixty years and I believe they will continue to do so despite (or perhaps because of) the lack of one clear story of which stars the decans were, what actions they performed, and what observations they were based on. The key to cracking this code may lie in different perspectives on decans, or simply in new data we might one day soon unearth, or we may never quite reach that stage. Nevertheless, for so long as we continue to perform the innately human action of stargazing (even if the stars are digital!), we remain in a sort of communion with those that have come before and those who will come after us.
Thank you for your Attention!
contact on my website !
Do you have thoughts or ideas on how this sort of representation and plotting could be useful to your project? Questions about decanOpy? Other fun uses for it or visualizations with D3-Celestial?
Let me know!
Acknowledgments
My funding for this project has been generously provided by the Franke Program in Science and the Humanities where I am a Fellow. Furthermore, I'd like to thank Dr. Priya Natarajan and Dr. John Darnell for their support on the astronomy and Egyptology portions of this project. Finally, I'd like to thank the staff of the Yale DHLab for all their help, including my wonderful supervisor Dr. Catherine DeRose for encouraging me to present an earlier version of this talk at CTDH 2021, as well as Monica Ong for the wonderful graphic at the top of this presentation.
References
Conman, J., 2003. It's about time: ancient Egyptian cosmology. Studien zur Altägyptischen Kultur, pp. 33-71.
Depuydt, L., 2010. Ancient Egyptian star tables: A reinterpretation of their fundamental structure. In A. Imhausen & T. Pommerening, eds. Writings of early scholars in the ancient Near East, Egypt, Rome, and Greece: translating ancient scientific texts. Beiträge zur Altertumskunde. Berlin; New York: de Gruyter, pp. 241–276.
Neugebauer, O. and Parker, R.A., 1960. Egyptian astronomical texts (Vol. 1). Brown University Press.
Symons, S. L., 2002a. “The ‘transit star clock’ in the Book of Nut”. In J. M. Steele & A. Imhausen, eds. Under One Sky: Astronomy and Mathematics in the Ancient Near East. Alter Orient und Altes Testament 297. Münster: Ugarit-Ver- lag, 429–446.
Symons, S.L., Cockcroft, R., Bettencourt, J. and Koykka, C., 2013. Ancient Egyptian Astronomy. [Online database] Available at: < http://aea.physics.mcmaster.ca/ >
Symons, S.L., 2015a. Contexts and elements of decanal star lists in ancient Egypt. In A. Imhausen & D. Bawanypeck, eds. Traditions of written knowledge in ancient Egypt and Mesopotamia. Alter Orient und Altes Testament. Münster: Ugarit, pp. 91-122.
- von Lieven, 2010. “Translating the Fundamentals of the Course of the Stars”. In: A. Imhausen & T. Pommerening, eds. Writings of Early Scholars in the Ancient Near East, Egypt, Rome, and Greece: Translating Ancient Scientific Texts. Beiträge zur Altertumskunde. Berlin; New York: De Gruyter, 140–150.
Zago, S., 2018. Classifying the Duat. Zeitschrift für Ägyptische Sprache und Altertumskunde, 145(2), pp.205-218.
