Babylonian mathematics

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Babylonian mathematics

• Eleanor Robson
• University of Cambridge

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Outline

• Introducing ourselves
• Going to school in ancient Babylonia
• Learning about Babylonian numbers
• Learning about Babylonian shapes
• Question time

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Who were the Babylonians?

• Where did they live?
• When did they live?
• What were their lives like?

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We live here
The Babylonians lived here, 5000-2000 years ago
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Babylonia, 19001650 BC

• Cities and writing for 1500 years already
• Brick-built cities on rivers and canals
• Wealth through farming barley and sheep
• Central temples, to worship many gods
• King Hammurabi (17921750 BC)
• Most children didnt go to school

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Babylonian men and women
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Cuneiform writing

• Wedges on clay
• Whole words
• Syllables
• Word types
• 600 different signs
• Sumerian language
• No known relatives
• Akkadian language
• Related to Hebrew, Arabic, and other modern
  Middle Eastern languages

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Cuneiform objects
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Professional scribes

• Employed by
• Temples
• Palaces
• Courts of law
• Wealthy families
• Status
• Slaves
• Senior officials
• Nobility

• In order to write
• Receipts and lists
• Monthly and annual accounts
• Loans, leases, rentals, and sales
• Marriage contracts, dowries, and wills
• Royal inscriptions
• Records of legal disputes
• Letters

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Im an archaeologist of maths

• Archaeology is the study of rubbish
• To discover how people lived and died
• To discover how people made and used objects to
  work with and think with
• Doing maths leaves a trail of rubbish behind
• I study the mathematical rubbish of the ancient
  Babylonians

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Imagine an earthquake destroys your school in the
middle of the night

• An archaeologist comes to your school 500 years
  from now
• What mathematical things might she find in your
  school?
• What would they tell her about the maths you do?

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Some mathematical things in modern schools

• Text books and exercise books
• Scrap paper and doodles
• Mathematical instruments from rulers to
  calculators
• Mathematical displays from models to posters
• Computer files and hardware

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But isnt maths the same everywhere?

• Two different ways of thinking about maths
• Maths is discovered, like fossils
• Its history is just about who discovered what,
  and when
• Maths is created by people, like language
• Its history is about who thought and used what,
  and why

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The archaeology of Babylonian maths

• Looking at things in context tells us far more
  than studying single objects
• What sort of people wrote those tablets and why?

• Tablets dont rot like paper or papyrus do
• They got lost, thrown away, or re-used
• Archaeologists dig them up just like pots, bones
  or buildings

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The ancient city of Nippur
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Maths at school House F

• A small house in Nippur, 10m x 5m
• Excavated in 1951
• From the 1740s BC
• 1400 fragments of tablets with school exercises
• Tablets now in Chicago, Philadelphia, and Baghdad
• Tablet recycling bin
• Kitchen with oven
• Room for a few students

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The House F curriculum

• Wedges and signs
• Peoples names
• Words for things (wood, reed, stone, metal, )
• How cuneiform works
• Weights, measures, and multiplications
• Sumerian sentences
• Sumerian proverbs
• Sumerian literature

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Babylonian numbers

• Different cuneiform signs pressed into clay
• Vertical wedges 19
• Arrow wedges 1050
• Different/same in base 60
• What do we still count in base 60?
• Same order matters
• Place value systems

Different no zero and no boundary between
whole numbers fractions
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1 52 30
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Playing with Babylonian numbers

• Try to write
• 32
• 23
• 18
• 81
• 107
• 4 1/2

• Think of a number for your friend to write.
  Did they do it right?

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Multiplication tables

• 1 30
• 2 1
• 3 1 30
• 4 2
• 5 2 30
• 6 3
• 7 3 30
• 8 4
• 9 4 30
• 10 5
• 11 5 30
• 12 6
• 13 6 30

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continued

• 14 7
• 15 7 30
• 16 8
• 17 8 30
• 18 9
• 20-1 9 30
• 20 10
• 30 15
• 40 20
• 50 25

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Practicing calculations

• 5 155 1527 33 45
• 5.25x 5.25 27.5625
• or 325x 325 105,625

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Was Babylonian maths so different from ours?

• Draw or imagine a triangle

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(No Transcript)
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Two Babylonian triangles
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Cultural preferences

• Horizontal base
• Vertical axis of symmetry
• Equilateral
• Left-hand vertical edge
• Hanging right-angled triangle or horizontal axis
  of symmetry
• Elongated

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A Babylonian maths book
back
front
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What are these shapes?

• The side of the square is 60 rods. Inside it are
  
• 4 triangles,
• 16 barges,
• 5 cow's noses.
• What are their areas?

"Triangle" is actually santakkum "cuneiform
wedge" and doesn't have to have straight edges
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Barge and cows nose
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A father praises his sons teacher

• My little fellow has opened wide his hand, and
  you made wisdom enter there. You showed him all
  the fine points of the scribal art you even made
  him see the solutions of mathematical and
  arithmetical problems.