>From Wikipedia, the free encyclopedia Mathematics in prehistory
Long before the earliest written records, there are drawings that indicate a knowledge of mathematics and of measurement of time based on the stars. For example, paleontologists <http://en.wikipedia.org/wiki/Paleontology> have discovered ochre <http://en.wikipedia.org/wiki/Ochre> rocks in a cave in South Africa <http://en.wikipedia.org/wiki/South_Africa> adorned with scratched geometric <http://en.wikipedia.org/wiki/Geometry> patterns dating back to c. 70,000 BC [1] <http://www.accessexcellence.org/WN/SU/caveart.html> . Also prehistoric <http://en.wikipedia.org/wiki/Prehistory> artifacts <http://en.wikipedia.org/wiki/Artifact_%28archaeology%29> discovered in Africa <http://en.wikipedia.org/wiki/Africa> and France <http://en.wikipedia.org/wiki/France> , dated between 35,000 BC <http://en.wikipedia.org/wiki/35000_BC> and 20,000 BC <http://en.wikipedia.org/wiki/Upper_Paleolithic> , indicate early attempts to quantify <http://en.wikipedia.org/wiki/Quantification> time <http://en.wikipedia.org/wiki/Time> . Evidence exists that early counting involved women who kept records of their monthly biological cycles; twenty-eight, twenty-nine, or thirty scratches on bone or stone, followed by a distinctive scratching on the bone or stone, for example. Moreover, hunters had the concepts of one, two, and many, as well as the idea of none or zero, when considering herds of animals. (references: [2] <http://www.tacomacc.edu/home/jkellerm/Papers/Menses/Menses.htm> , [3] <http://www.math.buffalo.edu/mad/Ancient-Africa/lebombo.html> , [4] <http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html> ). The Ishango Bone <http://en.wikipedia.org/wiki/Ishango_Bone> , found in the area of the headwaters of the Nile River <http://en.wikipedia.org/wiki/Nile_River> (northeastern Congo <http://en.wikipedia.org/wiki/Democratic_Republic_of_the_Congo> ), is the earliest known demonstration of sequences <http://en.wikipedia.org/wiki/Sequence> of prime numbers <http://en.wikipedia.org/wiki/Prime_number> , and some series of multiples, dating as early as 20,000 BC <http://en.wikipedia.org/wiki/Upper_Paleolithic> . Predynastic Egyptians <http://en.wikipedia.org/wiki/Predynastic_Egypt> of the 5th millennium BC <http://en.wikipedia.org/wiki/5th_millennium_BC> pictorially represented geometric <http://en.wikipedia.org/wiki/Geometry> spatial <http://en.wikipedia.org/wiki/Spatial> designs. Megalithic <http://en.wikipedia.org/wiki/Megalith> monuments from as early as the 5th millennium BC <http://en.wikipedia.org/wiki/5th_millennium_BC> in Egypt <http://en.wikipedia.org/wiki/Egypt> , and then subsequently England <http://en.wikipedia.org/wiki/England> and Scotland <http://en.wikipedia.org/wiki/Scotland> from the 3rd millennium BC <http://en.wikipedia.org/wiki/3rd_millennium_BC> , incorporate geometric ideas such as circles <http://en.wikipedia.org/wiki/Circle> , ellipses <http://en.wikipedia.org/wiki/Ellipse> , and Pythagorean triples <http://en.wikipedia.org/wiki/Pythagorean_triples> in their design, as well as a possible understanding of the measurement of time based on the movement of the stars. From circa 3100 BC <http://en.wikipedia.org/wiki/3100_BC> , Egyptians introduced the earliest known decimal system <http://en.wikipedia.org/wiki/Decimal> , allowing indefinite counting by way of introducing new symbols, [5] <http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.htm l#berlin> . The earliest known mathematics in ancient India <http://en.wikipedia.org/wiki/Ancient_India> dates back to circa 3000 BC <http://en.wikipedia.org/wiki/3000_BC> in the Indus Valley Civilization <http://en.wikipedia.org/wiki/Indus_Valley_Civilization> (Harappan civilization <http://en.wikipedia.org/wiki/Harappan_civilization> ) of North India <http://en.wikipedia.org/wiki/North_India> and Pakistan <http://en.wikipedia.org/wiki/Pakistan> , which developed a system of uniform weights and measures <http://en.wikipedia.org/wiki/Ancient_Indus_Valley_units_of_measurement> that used decimal <http://en.wikipedia.org/wiki/Decimal> fractions <http://en.wikipedia.org/wiki/Fraction> , a surprisingly advanced brick <http://en.wikipedia.org/wiki/Brick> technology which utilised ratios <http://en.wikipedia.org/wiki/Ratio> , streets laid out in perfect right angles <http://en.wikipedia.org/wiki/Right_angle> , and a number of geometrical shapes and designs, including cuboids <http://en.wikipedia.org/wiki/Cuboid> , barrels <http://en.wikipedia.org/wiki/Barrel> , cones <http://en.wikipedia.org/wiki/Cone_%28solid%29> , cylinders <http://en.wikipedia.org/wiki/Cylinder> , and drawings of concentric and intersecting circles <http://en.wikipedia.org/wiki/Circle> and triangles <http://en.wikipedia.org/wiki/Triangle> . Mathematical instruments discovered include an accurate decimal ruler with small and precise subdivisions, a shell instrument that served as a compass <http://en.wikipedia.org/wiki/Compass> to measure angles on plane surfaces or in horizon in multiples of 40-360 degrees, a shell instrument used to measure 8-12 whole sections of the horizon and sky, and an instrument for measuring the positions of stars for navigational purposes. The Indus script <http://en.wikipedia.org/wiki/Indus_script> has not yet been deciphered; hence very little is known about the written forms of Harappan mathematics <http://en.wikipedia.org/wiki/Indian_mathematics#Harappan_Mathematics_.28330 0_BC_-_1700_BC.29> . Archeological evidence has led some historians to believe that this civilization used a base 8 <http://en.wikipedia.org/wiki/Base_8> numeral system <http://en.wikipedia.org/wiki/Numeral_system> and possessed knowledge of the ratio of the length of the circumference <http://en.wikipedia.org/wiki/Circumference> of the circle to its diameter <http://en.wikipedia.org/wiki/Diameter> , thus a value of π <http://en.wikipedia.org/wiki/%CE%A0> . Circa 2600 BC <http://en.wikipedia.org/wiki/2600_BC> , Egypt's massive construction techniques represent not only precision surveying <http://en.wikipedia.org/wiki/Surveying> but also suggest knowledge of the golden ratio <http://en.wikipedia.org/wiki/Golden_ratio> . _______________________________________________ Marxism-Thaxis mailing list [email protected] To change your options or unsubscribe go to: http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
