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Number Sense

Number Sense. Why do we need numbers? Munduruku Foraging Society Numbers . Number Sense. Why do we need numbers? Munduruku Foraging Society Numbers What is culture? What is nature?. Munduruku Dot Placement Experiment. =. Munduruku Dot Placement Experiment.

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Number Sense

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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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