1,400 Years Before Europeans, Babylonians Used Calculus To Describe Celestial Movements

It has been generally believed that the first use of calculations employing geometry to describe the movement of celestial objects — what would now be done with calculus and referred to as celestial mechanics — occurred in 14th century Europe.

A discovery made by astrophysicist and science historian Mathieu Ossendrijver of Humboldt University in Berlin, detailed in a paper published Thursday in the journal Science, could now push that date back 1,400 years, giving the credit to ancient Babylonian astronomer priests.



Text B (BM 34757) Image Credit: Mathieu Ossendrijver via Washington Post

Discovery News - Ancient Babylonians Tracked Jupiter With Calculus

“It describes Jupiter’s velocity across the sky and how that changes with time.”

The tablets, which are housed at the British Museum, are believed to have been unearthed from an archaeological dig in what is now modern day Iraq sometime in the 1800s.

The almost completely intact tablets are thought to have been written in Babylon between 350 and 50 BCE.

The tablets are part of a larger collection of 450 astronomy tablets from Babylon and Uruk containing celestial data arranged in rows and columns, together with instructions.

Dr Ossendrijver examined five tablets numbered as trapezoid text A to trapezoid text E, four of which deal with geometrical trapezoid shapes, but nobody understood what they were about.

One tablet key to puzzle
However, one of the tablets — trapezoid text A — provided Dr Ossendrijver with the key to understanding the other four tablets.

“I discovered that they describe the motion of Jupiter as a velocity, the number of degrees it moves across the sky in a day,” Dr Ossendrijver said.

“If you plot the velocity of Jupiter against time, you get a creeping curve which looks like a rectangle with a slanted top — that’s the trapezoid.”

One possible explanation given by the author for the particular interest in the movement of Jupiter is that Jupiter, known to the Babylonians as the "White Star" was associated with Marduk, patron deity of Babylon. In some cases, Jupiter was therefore also identified as Nibiru (aka Nebiru, one of the 50 names of Marduk). From Wikipedia:

In the enumerations, Nibiru is mentioned at different astronomical locations in conjunction with the positions of stars and planets,[2] mostly as the "star of Marduk", however, the various stars or planets were not subject to any fixed interpretation. For example, the "star of Ea" was described at various "revelation spots" including Vela, Fomalhaut, and Venus. Similar interpretations were made for the other "stars of the gods", so multiple celestial coordinates must be considered.[2] Nibiru has been associated with the area of Libra: The Nibiru constellation rose in the month of Tišritum, around autumnal equinox, however Nibiru was also a name for the planet Jupiter[8] when observed in the month of Tišritum. In the MUL.APIN, Nibiru is identified as Jupiter:

When the stars of Enlil have been finished, one big star – although its light is dim – divides the sky in half and stands there: that is, the star of Marduk (MUL dAMAR.UD), Nibiru (né-bé-ru), Jupiter (MULSAG.ME.GAR); it keeps changing its position and crosses the sky.

Surprised I didn't see this posted about earlier as there are quite a few sources reporting. In addition to the two above, here are a few more:

Nature - Babylonian astronomers used geometry to track Jupiter
EurekaAlert - Ancient Babylonians used geometry to track Jupiter
NY Times - Signs of Modern Astronomy Seen in Ancient Babylon
Live Science - Babylonians Tracked Jupiter with Fancy Math, Tablet Reveals

a reply to: theantediluvian

Wow that's cool. So the next question is, did this information survive the Babylonians and get passed down through the ages or was it lost after the empire fell, only to be rediscovered 1400 years later? I have a feeling it is the latter as opposed to the former since we are pushing the date back so far, but you never know.

The Europeans also used geometry to describe celestial movements, at least back to 300BC

Aristarchus of Samos

originally posted by: Indigent
The Europeans also used geometry to describe celestial movements, at least back to 300BC

Aristarchus of Samos

The distinction I imagine would be that they were actually using rudimentary calculus to correctly predict the movement?

EDIT:

I've updated the title to reflect this.

a reply to: theantediluvian


Aristarchus math was good, his measurements were not but the math was solid

originally posted by: Krazysh0t
a reply to: theantediluvian

Wow that's cool. So the next question is, did this information survive the Babylonians and get passed down through the ages or was it lost after the empire fell, only to be rediscovered 1400 years later? I have a feeling it is the latter as opposed to the former since we are pushing the date back so far, but you never know.

There's no direct inspiration of the 14th century European scholars afaik but indirectly, particularly through the ancient Greeks, the Babylonians greatly influenced the development of mathematics in Western civilization. An example would be Hipparchus:

Hipparchus of Nicaea (/hɪˈpɑːrkəs/; Greek: Ἵππαρχος, Hipparkhos; c. 190 – c. 120 bc), was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry[1] but is most famous for his incidental discovery of precession of the equinoxes.[2]

Hipparchus was born in Nicaea, Bithynia (now Iznik, Turkey), and probably died on the island of Rhodes. He is known to have been a working astronomer at least from 162 to 127 bc.[3] Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and other people from Mesopotamia. He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue. It would be three centuries before Claudius Ptolemaeus' synthesis of astronomy would supersede the work of Hipparchus.

originally posted by: Krazysh0t
a reply to: theantediluvian

Wow that's cool. So the next question is, did this information survive the Babylonians and get passed down through the ages or was it lost after the empire fell, only to be rediscovered 1400 years later? I have a feeling it is the latter as opposed to the former since we are pushing the date back so far, but you never know.

I wouldn't be surprised if it did survive. Babylon fell to the Achaemenid Empire, which fell to the Greek Empire, which fell to the Roman Empire. Babylon heavily influenced European thinking.

a reply to: theantediluvian

Oh nice. So pockets of this information likely survived and were passed down until improved upon by other scientific greats. Makes sense.

a reply to: Debunkology

Yea, I'm getting that feeling now too. The knowledge may not have been as widespread, but it probably didn't die out. Hence the reason it is harder to locate usage of those techniques within that 1400 years.

a reply to: theantediluvian

This is not exactly news. Otto Neugebauer discovered that the Babylonians were using step functions in the middle of the last century. What the Babylonians did was not actually calculus, it was a first step towards it. The would have need to come up with a concept of infinitely small intervals and figured out a way to add these tiny infinities up.

To anticipate the inevitable: no, they did not learn calculus from aliens.

originally posted by: Krazysh0t
a reply to: theantediluvian

Oh nice. So pockets of this information likely survived and were passed down until improved upon by other scientific greats. Makes sense.

Actually, it probably survived in plain sight. The techniques were probably used by tradesmen to survey fields, determine how many skins they need to make a shield of a certain size, and so forth. In the middle ages, these would have constituted the "mysteries" of the guilds!

a reply to: DJW001

Hmm... I didn't think of that. Math not having been collected because it was held as secrets of various guilds and their crafts. Kind of like a pseudo conspiracy. It wasn't withheld to be detrimental to the advancement of mathematics, it was withheld to protect the user's professions. It just resulted in being obscured because of this.

originally posted by: Krazysh0t
a reply to: DJW001

Hmm... I didn't think of that. Math not having been collected because it was held as secrets of various guilds and their crafts. Kind of like a pseudo conspiracy. It wasn't withheld to be detrimental to the advancement of mathematics, it was withheld to protect the user's professions. It just resulted in being obscured because of this.

Exactly. The same is true of alchemy, as chemistry was then known. In the ancient world alchemists knew how to makes dyes, amalgams, poisons, and other handy things. This knowledge survived in coded books, the key to understanding them being transmitted orally from master to apprentice.

a reply to: DJW001

Yea. I definitely knew that alchemy was the precursor to chemistry. I guess knowing that I could have made the same connection here with calculus.

originally posted by: theantediluvian
It has been generally believed that the first use of calculations employing geometry to describe the movement of celestial objects — what would now be done with calculus and referred to as celestial mechanics — occurred in 14th century Europe.

A discovery made by astrophysicist and science historian Mathieu Ossendrijver of Humboldt University in Berlin, detailed in a paper published Thursday in the journal Science, could now push that date back 1,400 years, giving the credit to ancient Babylonian astronomer priests.

Text B (BM 34757) Image Credit: Mathieu Ossendrijver via Washington Post

Discovery News - Ancient Babylonians Tracked Jupiter With Calculus

“It describes Jupiter’s velocity across the sky and how that changes with time.”

The tablets, which are housed at the British Museum, are believed to have been unearthed from an archaeological dig in what is now modern day Iraq sometime in the 1800s.

The almost completely intact tablets are thought to have been written in Babylon between 350 and 50 BCE.

The tablets are part of a larger collection of 450 astronomy tablets from Babylon and Uruk containing celestial data arranged in rows and columns, together with instructions.

Dr Ossendrijver examined five tablets numbered as trapezoid text A to trapezoid text E, four of which deal with geometrical trapezoid shapes, but nobody understood what they were about.

One tablet key to puzzle
However, one of the tablets — trapezoid text A — provided Dr Ossendrijver with the key to understanding the other four tablets.

“I discovered that they describe the motion of Jupiter as a velocity, the number of degrees it moves across the sky in a day,” Dr Ossendrijver said.

“If you plot the velocity of Jupiter against time, you get a creeping curve which looks like a rectangle with a slanted top — that’s the trapezoid.”

One possible explanation given by the author for the particular interest in the movement of Jupiter is that Jupiter, known to the Babylonians as the "White Star" was associated with Marduk, patron deity of Babylon. In some cases, Jupiter was therefore also identified as Nibiru (aka Nebiru, one of the 50 names of Marduk). From Wikipedia:

In the enumerations, Nibiru is mentioned at different astronomical locations in conjunction with the positions of stars and planets,[2] mostly as the "star of Marduk", however, the various stars or planets were not subject to any fixed interpretation. For example, the "star of Ea" was described at various "revelation spots" including Vela, Fomalhaut, and Venus. Similar interpretations were made for the other "stars of the gods", so multiple celestial coordinates must be considered.[2] Nibiru has been associated with the area of Libra: The Nibiru constellation rose in the month of Tišritum, around autumnal equinox, however Nibiru was also a name for the planet Jupiter[8] when observed in the month of Tišritum. In the MUL.APIN, Nibiru is identified as Jupiter:

When the stars of Enlil have been finished, one big star – although its light is dim – divides the sky in half and stands there: that is, the star of Marduk (MUL dAMAR.UD), Nibiru (né-bé-ru), Jupiter (MULSAG.ME.GAR); it keeps changing its position and crosses the sky.

Surprised I didn't see this posted about earlier as there are quite a few sources reporting. In addition to the two above, here are a few more:

Nature - Babylonian astronomers used geometry to track Jupiter
EurekaAlert - Ancient Babylonians used geometry to track Jupiter
NY Times - Signs of Modern Astronomy Seen in Ancient Babylon
Live Science - Babylonians Tracked Jupiter with Fancy Math, Tablet Reveals

The trapezoid method of calculating the area under a line is similar to the calculus method of calculating the area under a curve, but it isn't calculus. It is, however, a very clever graphical solution.

This graphical method may partly be due to the Sumerian base 60 number system which makes conventional mathematics very difficult.

originally posted by: Krazysh0t
a reply to: theantediluvian

Wow that's cool. So the next question is, did this information survive the Babylonians and get passed down through the ages or was it lost after the empire fell, only to be rediscovered 1400 years later? I have a feeling it is the latter as opposed to the former since we are pushing the date back so far, but you never know.

Both the Sumerians and Babylons used clay tablets to take notes and for general business like order and receipts, as well as education. There's a good collection here. Everything from food and beer to astronomical observations and early maps of the world (www2.econ.iastate.edu...)

The "world" back then would have been centered around the Euphrates. So the Great Flood Legend is more a flooding of the area that the entire planet.

www2.econ.iastate.edu...

But they seemed to know that parts of the Earth did not see the Sun during different parts of the year.

a reply to: chr0naut

This graphical method may partly be due to the Sumerian base 60 number system which makes conventional mathematics very difficult.

Actually, it makes time keeping and astronomy very simple. If you assume that the year is 360 days long, and that the Sun moves one degree per day, you get a 12 month year of thirty 24 hour days, which is close to the length of a lunar month. The celestial sphere rotates 360 degrees in 24 hours, or 15 degrees/hour. (Of course you have to do a lot of fudging to correct for all that rounding off).

originally posted by: DJW001
a reply to: chr0naut

This graphical method may partly be due to the Sumerian base 60 number system which makes conventional mathematics very difficult.

Actually, it makes time keeping and astronomy very simple. If you assume that the year is 360 days long, and that the Sun moves one degree per day, you get a 12 month year of thirty 24 hour days, which is close to the length of a lunar month. The celestial sphere rotates 360 degrees in 24 hours, or 15 degrees/hour. (Of course you have to do a lot of fudging to correct for all that rounding off).

Right and that's not a coincidence. Here's a bit from a really interesting article from Scientific American:

Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day?

Hipparchus and other Greek astronomers employed astronomical techniques that were previously developed by the Babylonians, who resided in Mesopotamia. The Babylonians made astronomical calculations in the sexagesimal (base 60) system they inherited from the Sumerians, who developed it around 2000 B.C. Although it is unknown why 60 was chosen, it is notably convenient for expressing fractions, since 60 is the smallest number divisible by the first six counting numbers as well as by 10, 12, 15, 20 and 30.

Although it is no longer used for general computation, the sexagesimal system is still used to measure angles, geographic coordinates and time. In fact, both the circular face of a clock and the sphere of a globe owe their divisions to a 4,000-year-old numeric system of the Babylonians.

The Greek astronomer Eratosthenes (who lived circa 276 to 194 B.C.) used a sexagesimal system to divide a circle into 60 parts in order to devise an early geographic system of latitude, with the horizontal lines running through well-known places on the earth at the time. A century later, Hipparchus normalized the lines of latitude, making them parallel and obedient to the earth's geometry. He also devised a system of longitude lines that encompassed 360 degrees and that ran north to south, from pole to pole. In his treatise Almagest (circa A.D. 150), Claudius Ptolemy explained and expanded on Hipparchus' work by subdividing each of the 360 degrees of latitude and longitude into smaller segments. Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.

a reply to: Debunkology

Correct. The entire region around Babylon was on the migratory routes of humans exiting Africa. with the Sahara there, the only way out of Africa is through the Levant. And we have evidence of migrations and technology sharing from the ME to Europe that go far, far further back than Babylon.

Mathematics was considered Esoteric Knowledge typically held by a priest class. Secret societies and "The Mysteries" were a common way of accumulating knowledge like this, and passing it down via a fraternal order. I suspect that the Babylonian math survived via this method. Knowledge is power.