Data Science in the Babylonian Era
Lessons from Old and Late Babylonia on best practices in Data Science
While it is truly worthwhile to attend the lectures of the good Dr. Andrew Ng on AI, it is just as worthwhile to take a glimpse into a collection of Old and Late Babylonian clay tablets which can provide us with an equally insightful view of the best data science practices from two to four millennia ago.
For that purpose, the work of Mathieu Ossendrijver, a heliophysicist turned assyriologist, is remarkable. The research papers he has published since 2016 form the core source of this article (see references below) and reveal the full procedure and context of how Late Babylonians used numerical integration methods to compute the motion of Jupiter (which they called the “White Star”) along its velocity curve based on data they were carefully collecting.
By “Babylonians”, we mean a specific class of scribes and priests usually attached to major temples in Babylon and Uruk who were the ones typically educated in mathematics and astronomy. Here are some fundamental lessons of these Babylonians to us.
Babylonians selected an appropriate numerical system
Using a sexagesimal system for most of their surveys and calculations had a considerable advantage of simplifying fractions as 60 is divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. The only legacy inherited from that era is our use of sexagesimal units for the measurement of minutes, seconds and angular quantities.
Babylonians established a data collection strategy
Obviously, the position of Jupiter relative to the zodiac during one synodic cycle had to be recorded every night while it was visible in order to collect enough data points. Jupiter is generally only visible during a fraction of the night. The daily recording of these data involved a clearly established protocol that had to be followed during night shifts.
The existence of the tablet records proves that some preprocessing work had to be done to aggregate and compile these data into so called diaries used for later calculations. Babylonian astronomers were also recording the positions of other visible celestial bodies such as Saturn, Mars, Venus, the Moon and occasional comets.
Babylonians favored structured data
A subset of the analyzed tablets includes clearly tabular data, namely positions and times arranged in columns and rows filled from top to bottom and from left to right, exactly like in a modern spreadsheet. Some of these tablets could contain a large amount of data.
Babylonians knew their math
In addition to the basic arithmetic operations, extensive evidence exists that Babylonians were familiar with linear and quadratic dependencies as well as with computation involving arithmetic and geometric series. There have also been discovered multiple tablets which depict mathematical exercises commonly performed by the scribes.
Babylonians documented their algorithms
The Old Babylonian tablets describing the arithmetic procedures (or algorithms) all have a very specific structure that comprises a list of numerical quantities, a problem expressed as a question and a solution formulated as an ordered series of instructions to follow — all much like a pseudocode description of algorithms nowadays.
Popular among Babylonian scholars were the calculation of area of right and non-right trapezoids (which they literally called “forehead of an ox”) as well as the bisection of trapezoids into partitions of equal size, mostly used for designing dams and excavation of trapezoidal cross-section, or for the fair division of inherited fields between sons.
Here is a simple example of a trapezoid area calculation:
“Add (“Accumulate”) the upper width and the lower width, it is 24. 24, half of it is 12. Multiply (“go”) 12 by the length, 17, its area is 1 iku 2 sar.”
(tablet UET 5858, translation by Mathieu Ossendrijver)
A more complex example of the bisection of a quadrilateral:
“If a field, (one) length is inclined to (“eats”) (the other) length, the first length is 5.10, the second length 4.50, the upper width 17, the lower width 7, its area 2 bur: divide the field into two, 1 bur each. How much is my middle dividing line? How much should I put down as the long length and the short length so that it reaches 1 bur and, for the second 1 bur, how much should I put down as the long length and how much as the short length so that it reaches 1 bur? You add (“accumulate”) both total lengths and you break off their half, and 5.0 comes up for you. You solve the reciprocal of 5.0 which came up for you and, concerning the upper width, which exceeds the lower width by 10, you multiply (“raise”) it by 10, the excess, and it gives you 0;2. You turn around. You square (“make eat itself”) 17, the upper width, then 4.49 comes up for you. You remove 2.0 from 4.49, it is 2.49, the remainder. You take its square-side, and 13, the middle dividing line, comes up for you.”
(tablet YBC 4675, translation by Mathieu Ossendrijver)
Babylonians implemented numerical methods
The earliest findings of assyriologists in the field of mathematical astronomy are dominated by numerical techniques rather than geometrical ones, which are features of Hellenistic science. This can be seen as counterintuitive to the modern man who is usually introduced to mathematical reasoning by Euclidean geometry.
The revolutionary discovery of Mathieu Ossendrijver is that Late Babylonians not only used the trapezoidal rule to compute the area under the curve (or integral) of the velocity graph of Jupiter, but that it is the earliest evidence of the use of such an abstract space. Before that discovery, European Medieval scholars, namely the so-called “Oxford Calculators” and the French philosopher Nicole Oresme in the 14th century, were thought to be the first ones to have used such techniques.
Babylonians applied knowledge transfer
The aforementioned corpus clearly consists of two categories of tablets: purely arithmetic ones, that contain calculations along with the description of algorithmic procedures, and astronomical ones, that focus on reporting celestial events. It seems that only by the Late Babylonian time the synergy took place and some scholar(s) who possessed substantial knowledge of both tablet sets came up with the idea to apply the trapezoid calculations (bisection and trapezoidal rule) to the Jupiter movement data.
Babylonians made market predictions
The collected astronomical data and the computations done on them were actively used for the purpose of divination and the prediction of market rates as demonstrated by the most recent works of Mathieu Ossendrijver. In the diaries, the positions of planets in the zodiac were explicitly recorded along with the market rates of commodities and the level of the Euphrates.
Babylonian produced omens like the following:
“If in month VII a lunar eclipse occurs on the 14th day and it looks like a rainbow, there will be a deluge; barley will be sold in the market like sesame.”
(Enuma Anu Enlil tablet 59/60, translation by Mathieu Ossendrijver)
Or:
“If Jupiter stands therein and is bright: the market will prosper; if it is faint it will decrease.”
(BM 47494, translation by Mathieu Ossendrijver)
Conclusion
Obviously, the Babylonian culture produced enough educated and thoughtful people to come up with these advanced data science practices. These practices can be directly compared to the ones of today and should be familiar to any modern data scientist. Are you as cunning as a Babylonian data scientist?
References
- M. Ossendrijver (2016), Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph, Science, 351(6272), 482–484.
- M. Ossendrijver (2017), New Results on a Babylonian Scheme for Jupiter’s Motion along the Zodiac, Journal of Near Eastern Studies 76, no. 2: 231–247.
- M. Ossendrijver (2018), Bisecting the trapezoid: tracing the origins of a Babylonian computation of Jupiter’s motion, Arch. Hist. Exact Sci. 72, 145–189.
- M. Ossendrijver (2019), Babylonian Market Predictions, in Keeping Watch in Babylon: The Astronomical Diaries in Context, Brill.
This article was written for Sclable’s blog on Medium.
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