Counting and measuring
counting
measuring
"sensing the difference"
counting
associated with "numbers"
standard, uniform unit based
on counting
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2024
3500 BCE
50000 BCE
counting
measuring
counting
!!!cognitive revolution!!!
most of the animals can compare:
- "quantities"
- distances
- magnitudes
- movements
meaning: can make difference between
"one" and "many"
near and far
small and big
counting = systematic recording in "numbers"
animals and human infants can't do, but they have basic "number sense"
beginnings
anthropology
- tribes: "one", "pair", many
- "binary principle" (five=2+2+1)
- perceptional/memory limitation
human etology
- children: counting by hand
Lebombo bone
40000 BCE
Ishango bone
20000 BCE
Why do archaeologists and historians suggest that these bones were used for counting?
Lebombo bone
40000 BCE
Ishango bone
20000 BCE
29 notches
lunar phase?
menstrual period?
numeric system?
what to count?
hunting?
counting = not only an abstraction
counting = RECORDING (freeing working memory)
RECORDING = formalization (formal language)
formalization = notation system
proto-cuneiform pictograms
tabulated sheets
geometric calculations
tokens
Townplan of Nippur (ca1400 BCE)
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2024
3500 BCE
50000 BCE
counting
measuring
measuring
units
length
area
volume
weight
time
reference/benchmark
words
THE HUMAN BODY
cubit = elbow
inch
hand
foot
arm
head
GRAIN/LIQUID
barley
corn
carat = keration=carob seed
VERBS
talanton
mina = mene = mine = to number/weight
shekel = to weight
kati = to weight
Writing on the Wall: "Mene, Mene, Tekel, Upharsin"
"Numbered, Numbered, Weighted and Divided in Half"
Book of Daniel: Belshazzar's feast
God numbered and weighted your kingdom, found wanting (light) and destroy it (divide it to the Medes and the Persians)
standard talent
1/2 Sumerian mina
Roman bronze modius
with imperial measurements
"standards"
Nippur cubit rod
Ptolemaios' "World Map"
There are at least as many standards and numeric systems as there are empires and city-states, and the standards change rapidly as one empire conquers another.
Egyptian royal cubit not equal to Sumerian cubit or Biblical "common" cubit, etc
Greek talentum not equal to Ugarit talentum, not equal to Roman imperial talentum, etc
Difficult conversions between standards and numeric systems
Obstacle of centralization, taxation and commerce
and this story continues until the 18th century! (somewhere 'til today!)
The French Revolution and the Birth of the Metric System
preludes
- 16th, 17th century - proposals for the decimal system
- 18th century = 800 different units and measurements
Condorcet: "without a universal and standard system no man can be equal in rights and free"
Charles-Maurice de Talleyrand-Périgord
1790: Talleyrand proposed the idea of a universal, unchanged, standard metric system which creates "order from chaos"
National Assembly/Academy of Sciences, led by Condorcet: "one nation, one weight and one measure" (1794: Condorcet suicide)
1799: seven basic units based on (mostly) decimal system
- lenght: metre
- mass: kilogram
- time: second (sexagesimal = 60)
- electricity: ampere
- temperature: kelvin
- luminous intensity: candela
- amount of substance: mole
Systeme International d'unités (SI)
requirements
- must be realisable (mutual accaptance aggreement)
- must be coherent
- must be convertible
- must be derivable (speed = length/time, m/s)
Counting and measuring
By Attila Bátorfy
Counting and measuring
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