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In-Depth Information
It is interesting that the cranial capacity and brain sizes of both Neanderthals
and Cro-Magnons appear to be slightly larger than modern homo sapiens, although
modern frontal lobes are larger. Brain size does not translate directly into intelli-
gence, but it does indicate that some form of abstract reasoning might have oc-
curred very early. Cave paintings date back more than 40,000 years, so at least
some form of abstraction did exist.
In addition to counting objects and possessions, it was also important to be able
to keep at least approximate track of the passage of time. Probably the length of a
year was known at least subjectively more than 10,000 years ago. With the arrival
of agriculture, also about 10,000 years ago, knowing when to plant certain crops
and when to harvest them would have aided in food production.
One of the first known settlements was Catal Huyuk in Turkey, dating from
around 7,000 BCE . This village, constructed of mud bricks, probably held several
hundred people. Archaeological findings indicate agriculture of wheat, barley, and
peas. Meat came from cattle and wild animals.
Findings of arrowheads, mace heads, pottery, copper, and lead indicate that
probably some forms of trading took place at Catul Huyuk. Trading is not easily
accomplished without some method of keeping track of objects. There were also
many images painted on walls and this may indicate artistic interests.
The probable early sequence of humans acquiring numerical knowledge may
have started with several key topics:
• Prehistoric numeric and mathematical knowledge:
Counting objects to record ownership
Understanding the two basic operations of addition and subtraction
Measuring angles, such as due east or west, to keep from getting lost
Counting the passage of time during a year to aid agriculture
Counting the passage of daily time to coordinate group actions
• Numeric and mathematical knowledge from early civilizations:
Counting physical length, width, and height in order to build structures
Measuring weights and volumes for trade purposes
Measuring long distances such as those between cities
Measuring the heights of mountains and the position of the sun above
the horizon
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