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"

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)