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The Evolution of Number Systems in Human Culture

Explore the origin of numbers, the Munduruku tribe's dot placement experiment, historical base systems, and the impact of Arab science on mathematics and astronomy. Learn about numerical sense and the mathematical advantages of different base systems.

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The Evolution of Number Systems in Human Culture

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  1. Number Sense • Why do we need numbers? • Munduruku • Foraging Society • Numbers

  2. Number Sense • Why do we need numbers? • Munduruku • Foraging Society • Numbers • What is culture? • What is nature?

  3. Munduruku Dot Placement Experiment • =

  4. Munduruku Dot Placement Experiment

  5. Little Kids, Dot Placement

  6. Little Kids, Dot Placement

  7. Dealing with Big Numbers • Exact Sense for Small Numbers

  8. Dealing with Big Numbers • Exact Sense for Small Numbers • Rough Sense of Big Numbers

  9. Dealing with Big Numbers • Exact Sense for Small Numbers • Rough Sense of Big Numbers

  10. Dealing with Big Numbers • Exact Sense for Small Numbers • Rough Sense of Big Numbers

  11. Dealing with Big Numbers • Exact Sense for Small Numbers • Rough Sense of Big Numbers • 10 vs. 13: 90 % Accurate • 20 vs. 26: 90 % Accurate

  12. Dealing with Big Numbers • Munduruku Number Sense

  13. English Shepherds

  14. English Shepherds

  15. Base 1

  16. Base 2 and 4

  17. Base 10

  18. Base 12 • Mathematical Advantages?

  19. Base 12 • Mathematical Advantages?

  20. Base 12 • Mathematical Advantages? • Vestiges of Base 12

  21. Base 12 • Mathematical Advantages? • Vestiges of Base 12 • Feet • Time • Dozen/Gross/Grocer • Counting

  22. Eleven And Twelve

  23. Other Historical Bases • Base 20 • Word for 80 in French? • Vestiges of Base 8

  24. Other Historical Bases • Base 20 • Word for 80 in French? • Vestiges of Base 8

  25. Other Historical Bases • Base 20 • Word for 80 in French? • Vestiges of Base 8 • Cuneiform

  26. Before Place Value 1861: MDCCCLXI

  27. Place Value • Our Base 20 Shepherd

  28. One Number System in the Vedas • 422,396 • 6 • 9 dasa • 3 Sata • 2 Sahasra • 2 Ayuta • 4 Niyuta

  29. One Number System in the Vedas • 422,396 • 6 • 9 dasa • 3 Sata • 2 Sahasra • 2 Ayuta • 4 Niyuta • What about 403,396? • How many Ayuta? • Shunya 0

  30. A FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with?

  31. Other Factors -Trading -Urbanization Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic Get copies of Greek works through conquests, raids, or negotiations w/Byz’s FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  32. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Get copies of Greek works through? FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  33. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Get copies of Greek works through conquests, raids, or negotiations w/Byz’s FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  34. A Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic Get copies of Greek works through conquests, raids, or negotiations w/Byz’s FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  35. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46) Get copies of Greek works through conquests, raids, or negotiations w/Byz’s

  36. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic Get copies of Greek works through conquests, raids, or negotiations w/Byz’s Math: • Fused Indian place value digits w/Grk math Algebra & trigonometry w/sine, cosine, & cotangent functions Arabs take Greek math & science & do their own original work Physics & optics: • Calculated earth’s size •Proved light goes fr. object to eye •Formulae for specific & absolute weights Medicine: •Advanced w/o microscope •Suturing w/animal gut •Mercury ointments for eye & skin diseases FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  37. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic Get copies of Greek works through conquests, raids, or negotiations w/Byz’s Math: • Fused Indian place value digits w/Grk math Algebra & trigonometry w/sine, cosine, & cotangent functions Arabs take Greek math & science & do their own original work Physics & optics: • Calculated earth’s size •Proved light goes fr. object to eye •Formulae for specific & absolute weights Medicine: •Advanced w/o microscope •Suturing w/animal gut •Mercury ointments for eye & skin diseases FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  38. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic Get copies of Greek works through conquests, raids, or negotiations w/Byz’s Math: • Fused Indian place value digits w/Grk math Algebra & trigonometry w/sine, cosine, & cotangent functions Arabs take Greek math & science & do their own original work Physics & optics: • Calculated earth’s size •Proved light goes fr. object to eye •Formulae for specific & absolute weights Medicine: •Advanced w/o microscope •Suturing w/animal gut •Mercury ointments for eye & skin diseases FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  39. A Extensive funding through religious foundations (waqfs) & caliph’s “House of Wisdom” Arabs willing & able to provide accurate versions of ancient texts thanks to: Excellent translators since new converts must read Quran in the orig. Arabic Get copies of Greek works through conquests, raids, or negotiations w/Byz’s Math: • Fused Indian place value digits w/Grk math Algebra & trigonometry w/sine, cosine, & cotangent functions Arabs take Greek math & science & do their own original work Physics & optics: • Calculated earth’s size •Proved light goes fr. object to eye •Formulae for specific & absolute weights Medicine: •Advanced w/o microscope •Suturing w/animal gut •Mercury ointments for eye & skin diseases FC.47 ARAB SCIENCE AND ITS LEGACY (c.750-1000 C.E.) Islamic belief there is no conflict between reason & faith Contact with Byz. & Persian civiliz’s (FC.46)

  40. Decline of Intellectual Life • Outside Invaders • Ulama • Sufis

  41. Spread to the West • Means of Spread • Hajj • Trade • Influence • Islamic Spain • Greek Learning • Crusades • Arabic Number by 1200s • ShopkeepersScientists

  42. Conclusion • Cultural • Number Lines • Bases • Cultural Breakthroughs • Place Value • Zero • Multiplication, Division, Logs, not to mention Calculus

  43. Conclusion • Cultural • Number Lines • Bases • Cultural Breakthroughs • Place Value • Zero • Multiplication, Division, Logs, not to mention Calculus • Natural • Cultural Breakthroughs describe something real: Logs, Calculus, Patterns in Dot Discernment • Math works in different bases • Music…

  44. Conclusion: Music

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