The Babylonian civilisation was an important component of the Mesopotamian civilisation.
On the ravages of the Sumerian civilisation grew up Babylonian civilisation.
The Amorites were the founder of this civilisation. The appearance of Hammurabi, the great king of the Amorites, made this civilisation progressive.
Image Source: kenraggio.com/Nebu-Statue-05-Babylon.jpg
Hammurabi was the first law giver in the history of the world. The writings, literature, religion, art, architecture and science of the Babylonians were unique in their own way.
Art of Writing and Education:
Like the Sumerians, the people of Babylon used Cuneiform writing. They used more than 350 signs in their writing. They used to write on soft clay tablets by pen made of bone and bamboo. Then they baked tablets on sun shine and kept one after another. During the reign of Hammurabi, the famous Emperor of Babylon, education spread in the look and corner of that land.
He established many schools for the students. The Babylonian boys put emphasis on writing, reading and Mathematics and girls were fond of song and dance. From the ruins of a Babylonia an inspiring sentence was written on the wall of school. That sentence was—”He who shall excel in tablet-writing shall shine like the sun”. This shows the love of the Babylonians for education.
The literature of Babylon was very rich. The Babylonians wrote around 2000 books. They composed books on religion, science, mathematics and astrology. In the domain of Babylonian literature, ‘Gilgamesh’ carved a special position. This epic describes about king Gilgamesh, the legendary hero of Babylon. Once, god sent flood to teach sinner Babylonians a lesson. A sage knew about this and left Babylon with others. King Gilgamesh with the help of God Enlil defeated the flood. His heroic deeds have been described in ‘Gilgamesh’.
Code of Hammurabi:
Hammurabi was the First Law Giver of the world. He was the leader of the Amorites and a brave fighter. There were different sets of laws in ancient Babylon concerning religion, agriculture, administration and business. Hammurabi codified all these laws in a simple form which became famous as the ‘Code of Hammurabi’.
These laws were engraved on a diorite stone of 8 feet high and that stone was erected in the temple of the great Babylonian god Marduk. On the top of the stone the picture of Hammurabi receiving laws from the Sun god Samas was engraved.
There were four parts in the code of Hammurabi, viz.—civil code, penal code, code of procedure and commercial code.
Hammurabi’s code was a flat fledged law book. It contained laws relating to marriage, divorce, property, contract, trade and commerce, mortgage of land, religion etc. It contained criminal laws concerning murder, theft, treachery, dishonesty, negligence in duty etc.
The basic aim of this code was—”An eye for an eye and a tooth for a tooth”. A murderer was awarded death penalty. If the roof or a wall of a house fell down, the mason who had built it was punished. If a thief was caught while steeling away an animal from a temple, he had to return triple price of that animal. If a trader charged more than the fixed price of an article, he was given a death sentence.
The code of Hammurabi empowered women right over property. For the first time, this code protected the widows, slaves and orphans. The Code of Hammurabi is treated as the ‘First law book of the world.”
Like the Sumerians, the Babylonians were polytheists. Their chief god was ‘Marduk’ who was regarded as the creator of the world. ‘Istar’ was regarded as Mother Goddess. They also worshipped ‘Samas’ as sun god and ‘Tamuj’ as the god of agriculture. The Babylonians believed that the gods and goddess take birth, come under sorrows, sufferings and happiness and die.
They also marry like human beings, resort to war and sue for peace. The priests could predict future by casting a glance on the liver of a sacrificed animal. The priests stayed at the top storey of a Ziggurat. They worshipped god or goddess and predicted future.
The Babylonians also excelled in the field of science. The priests watched the sun, moon planet and star very carefully and forecast the future. Like the Sumerians, the Babylonians also adopted lunar calendar. They divided one year into 12 months and each month was divided into 30 days.
They also used sun dial and water clock to know time. They also knew the use of numbers from 1 to 9. The priests also predicted future. They had acquired knowledge in geography, life science and astrology. All these things prove the love of the Babylonians for science.
Art and Architecture:
The Babylonian kings were famous builders. They built big palaces. They kept the gigantic images of bulls having the heads of man near the entrance gate of the palace. The great Ziggurat built by Hammurabi in honour of ‘Marduk’ and big granary to preserve grains for future calamities testify the architectural skills of the Babylonians.
The figure of human beings birds and animals show their skill in the field of art. Varieties of seals have been discovered by excavation which further shows the artistic skills of the Babylonians.
The Babylonians were very famous in the field of administration. Besides the code of Hammurabi, laws were also written on clay tablets. The royal orders written on 55 clay tablets have been discovered from different places of Babylon. Hammurabi had sent message to administrators through these tablets to adopt compassion, liberal attitude and honesty in the field of administration. Undoubtedly, the Babylonian administration was directed for the welfare of the people.
Agriculture, Trade and Commerce:
The Babylonians were skilled agriculturists and traders. They liked to produce variety of crops. That is why they dug canals and irrigated the corn fields. During the reign of Hammurabi a big canal was dug from the city Kish to Persian gulf Herodotus, the father of history had lavishly Praised the wheat and barly among other crops of Babylon.
The Babylonians exported dates, food grains, oil, leather works, clay pots etc. to the outside world. They imported gold, silver, copper, stone, wood and salt. Among the ancient countries, Babylon was regarded as a flouring country.
Infact, the contributions of the Babylonians to the human civilisation were immense. The Code of Hammurabi helped in building a healthy society. Besides this, their contributions in the field of art, architecture, science, trade and commerce were worth noting.
Next: About this document
Our first knowledge of mankind's use of mathematics comes from the Egyptians and Babylonians. Both civilizations developed mathematics that was similar in some ways but also very different in others.
Some basic facts about ancient Babylon.
- The dates of the Mesopotamian civilizations date from 2000-600 BC. Occasionally, the region, at least between the two rivers (Tigris and Euphrates) is described as Chaldea.
- The Sumerians of the Mesopotamian valley built home and temple decorated with artistic pottery and mosaics in geometric patterns.
- Powerful rulers united the local Principates into an empire which completed vast public works, such as irrigation canals. One of the most powerful was Sargon (ca. 2276-2221 BC).
- The cuneiform (wedge) pattern of writing that the Sumerians had developed during the fourth millennium may have been the earliest form of written communication. It probably antedates the Egyptian hieroglyphic.
- The Mesopotamian civilizations are often called Babylonian, though this is not correct. Actually, Babylon was not the first great city, though the whole civilization is called Babylonian. Babylon, during its existence, was not always the center of Mesopotamian culture.
- Babylon fell to Cyrus of Persia in 538 BC, but the city was spared. The great empire was finished.
- The use of cuneiform script formed a strong bond. Laws, tax accounts, stories, school lessons, personal letters were impressed on soft clay tablets and then were baked in the hot sun or in ovens.
- From one region, the site of ancient Nippur, there have been recovered some 50,000 tablets.
- Many university libraries have large collections.
- Deciphering cuneiform succeeded the Egyptian hieroglyphic. Indeed, just as for hieroglyphics, the key to deciphering was a trilingual inscription. Found at Behistun by a British office, Henry Rawlinson (1810-1890), stationed as an advisor to the Shah, this inscription depicts the greatness and glory of Darius the Great. In 516 B.C. Darius commissioned his lasting monument to be engraved on a foot surface on a rock cliff, the ``Mountain of the Gods" at Behistun. Like the Rosetta stone, it was inscribed in three languages -- Old Persian, Elamite, and Akkadian (Babylonian). However, all three were unknown. Only because Old Persian has only 43 signs and had been the subject of serious investigation since the beginning of the 19th century was the deciphering accomplished. Nonetheless, progress was very slow. Rawlinson was correctly able to assign correct values to 246 characters and discovered that the same sign could stand for different consonantal sounds, depending on the vowel that followed. (polyphony) It has only been in this century that substantial publications have appeared.
In mathematics, the Babylonians were somewhat more advanced than the Egyptians.
- Their mathematical notation was positional but sexigesimal.
- They used no zero.
- More general fractions, though not all fractions, were admitted.
- They could extract square roots.
- They could solve linear systems.
- They worked with Pythagorean triples.
- They solved cubic equations with the help of tables.
- They studied circular measurement.
- Their geometry was sometimes incorrect.
For enumeration the Babylonians used two symbols.
All numbers were forms from these symbols.
Note the notation was positional and sexigesimal:
There is no clear reason why the Babylonians selected the sexigesimal system. It was possibly selected in the interest of metrology, this according to Theon of Alexandria, a commentator of the fourth century A.D.: i.e. the values 2,3,5,10,12,15,20, and 30 all divide 60.
Remnants still exist today with time and angular measurement. In fact the Babylonians used a 24 hour clock, with 60 minute hours, and 60 second minutes.
Because of the large base, multiplication was carried out with the aide of a table.
A positional fault??? Which is it?
- There is no ``gap" designator.
- There is a true floating point -- its location is undetermined except from context.
The ``gap" problem was overcome by the time of Alexander the Great, rather late in the game for the Chaldeans.
We use the notation:
The values are all integers.
This number was found on the Old Babylonian Tablet (Yale Collection #7289) and is a very high precision estimate of .
The exact value of , to 8 decimal places is = 1.41421356.
Fractions. Generally the only fractions permitted were such as
because the sexigesimal expression was known.
Irregular fractions such as , etc are generally not used.
A table of all products equal to sixty has been found.
The table is also used for reciprocals. For example,
Two tablets found at Senkerah on the Euphrates in 1854 date from 2000 B.C. They give squares of the numbers up to 59 and cubes up to 32. The Babylonians used the formula
to assist in multiplication.
Division relied on multiplication, i.e.
There apparently was no long division.
The Babylonians knew some approximations of irregular fractions.
However, they do not appear to have noticed infinite periodic expansions.
They seemed to have an elementary knowledge of logarithms.
Square Roots Recall the approximation of . How did they get it? There are two possibilities:
- Applying the approximation
- Applying the method of the mean.
The product of 30 by 1;24,51,10 is precisely 42;25,35.
Method of the mean.
- Take as an initial approximation.
- Idea: If then
- So take
- Repeat the process.
Now carry out this process in sexigesimal, begining with . Remember to us Babylonian arithmetic. Using full decimal arithmetic will not give the value 1;25,51,10. Use Babylonian arithmetic.
Note: was commonly used as a brief, rough and ready, approximation.
The Plimpton 322 tablet dates from about 1700 BC.
If appears to have the left section broken away. What was found has numbers tabulated as follows.
What it means.
How did they determine these. Assuming they knew the Pythagorean relation , divide by b to get
Choose u+v and find u-v in the table of reciprocals.
Example. Take u+v=2;15. Then u-v=0;26,60 Solve for u and v to get
Multiply by an appropriate integer to clear the fraction. We get a=65, c=97. So b=72. This is line 5 of the table.
It is tempting to think that there must have been known general principles, nothing short of a theory, but all that has been discovered are tablets of specific numbers and worked problems.
O. Neugebauer and A. Sachs. Mathematical Cuneiform Texts. Amer. Oriental Series 29. American Oriental Society, New Haven, 1945
E. M. Bruins. On Plimpton 322, Pythagorean numbers in Babylonian mathematics. Afdeling Naturkunde, Proc. 52 (149), 629-632.
Problem. Solve x(x+p)=q.
Solution. Set y=x+p Then we have the system
All three forms
are solved similarly. The third is solve by equating it to the nonlinear system, . Moreover, all three date back 4,000 years!
The Babylonians must have had extraordinary manipulative skills and as well a maturity and flexibility of algebraic skills.
Solving linear systems.
Solution. Select such that
So, . Now make the model
So, d=300 and thus
Can you generalize this algorithm to arbitrary systems??!!
Generally, the Babylonians used for practical computation. But, in 1936 at Susa (captured by Alexander the Great in 331B.C.), a number of tablets with significant geometric results were unearthed.
One tablet compares the areas and the squares of the sides of the regular polygons of three to seven sides. For example
This gives an effective (Not bad.)
There are two forms for the volume of a frustum
The second is correct, the first is not.
There are many geometric problems in the cunieform texts. For example, the Babylonians were aware that
- The altitude of an isosceles triangle bisects the base.
- An angle inscribed in a semicircle is a right angle. (Thales)
- Problems contain only specific cases. There seem to be no general formulations.
- There is an absence of clear cut distinctions between exact and approximate results.
- Questions about solvability or unsolvability are absent.
- The concept of ``proof" is unclear and uncertain.
- Overall, there is no sense of abstraction.
- Their mathematics, like the Egyptians, is utilitarian -- but apparently far more advanced.
Next: About this document Don Allen
Tue Jan 28 09:43:40 CST 1997