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Just one more…

Just one more…. Alex James Biomathematics Research Centre University of Canterbury. NZAMT 2013. Innumeracy. A long history… Gargantua (Rabelais, 1534). NZAMT 2013. Gargantua. As an infant he needed 17,913 cows to supply him milk. Combed cannonballs from his hair with a 900 foot rake

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Just one more…

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  1. Just one more… Alex James Biomathematics Research Centre University of Canterbury NZAMT 2013

  2. Innumeracy A long history… Gargantua (Rabelais, 1534) NZAMT 2013

  3. Gargantua • As an infant he needed 17,913 cows to supply him milk. • Combed cannonballs from his hair with a 900 foot rake • Cut lettuces as large as walnut trees for his salad • Devoured half a dozen pilgrims. • As a young student travelled on a mare as large as 6 elephants • Hung the bells of Notre Dame on the mares neck as jingles NZAMT 2013

  4. Combed cannonballs from his hair with a 900 foot rake • Cut lettuces as large as walnut trees for his salad • Devoured half a dozen pilgrims. 300m 2m (not to scale!) ~30m NZAMT 2013

  5. 3-4m 4,000 – 7,000kg • As a young student travelled on a mare as large as 6 elephants • Hung the bells of Notre Dame on the mares neck as jingles 1m 800kg 2.6m 13,000kg NZAMT 2013

  6. 3-4m 4,000 – 7,000kg As large (weight?) as 6 elephants 5,000 x 6 = 30,000 kg 1m 800kg 2.6m 13,000kg NZAMT 2013

  7. 3-4m 4,000 – 7,000kg As large (size?) as 6 elephants 3m x 6 = 18m 5,000 x 63 = 1,080,000 kg 1m 800kg 2.6m 13,000kg NZAMT 2013

  8. Innumeracy Even further back… Noah (Genesis, 4004BC?) ~2349BC (Ussher’s chronology, 1650) NZAMT 2013

  9. And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered. 8,000m 200m per day NZAMT 2013

  10. Fifteen cubits upward did the waters prevail; and the mountains were covered. 15 cubits = 6m Much smaller mountains back then? or Noah lived in Holland? NZAMT 2013

  11. Fifteen cubits upward did the waters prevail. How much water is this? Radius earth (polar) = 6,356,752.3m Vol earth = Vol extra water = = 3 x 1015 m3 = 6 million Sydney harbours (500 GL) = one thousandth of all the water on earth NZAMT 2013

  12. Other random questions • How fast does your hair grow? • How far is it to Britain (shortest route possible)? • How much (human) blood is there in the world? • How long has rock music been around for? NZAMT 2013

  13. Other random questions • How fast does your hair grow? • 1 cm / month • How far is it to Britain (shortest route possible)? • 12,740 km • How much (human) blood is there in the world? • 35 billion litres • How long has rock music been around for? • 50 years NZAMT 2013

  14. Other random questions • How fast does your hair grow? • 1 cm / month • 0.01 furlongs / fortnight • 1 angstroms / second • How far is it to Britain (shortest route possible)? • 12,740 km • 4 concorde hours • 200 snail years • How much (human) blood is there in the world? • 35 billion litres • 0.07 Sydney Harbours • 14,000 Olympic swimming pools • How long has rock music been around for? • 50 years • 2 billion seconds NZAMT 2013

  15. Are we descended from Noah? Consider a population of N0 (female!) individuals Every individual has R0 (female) babies. In the next generation there will be N1 individuals In the second generation there will be N2 individuals In the Gth generation there will be NG individuals NZAMT 2013

  16. Are we descended from Noah? NZAMT 2013

  17. Are we descended from Noah?Count females only G = generations since NoahNG = number of females in the world nowR0 = number of (girl) babies per female girl babies per female NZAMT 2013

  18. Innumeracy - today NZAMT 2013

  19. Could Europe go extinct? Count females only Consider only two generations G = 2 N0 = number of females in Europe now Exclude non-European immigrants (approx 4%) Assume “extinction” means NG = 50 (IUCN definition of critically endangered). girl babies per female Or 1 girl baby per 3,000 females. NZAMT 2013

  20. Could cod go extinct? NZAMT 2013

  21. How do you reach this conclusion? Qn: How long do cod live? Ans: up to 25 years. Assumption: So an average adult cod must be about 13 years old. Qn: How many cod over 13 years old are there? Ans: Not very many. Therefore: NZAMT 2013

  22. How do you reach this conclusion? Actually there are many species of cod. North Sea only live to about 13 years old. Qn: How long do cod live? Ans: up to 25 years. Assumption: So an average adult cod must be about 13 years old. Qn: How many cod over 13 years old are there? Ans: Not very many. Therefore: NZAMT 2013

  23. How do you reach this conclusion? Actually there are many species of cod. North Sea only live to about 13 years old. Qn: How long do cod live? Ans: up to 25 years. Assumption: So an average adult cod must be about 13 years old. Qn: How many cod over 13 years old are there? Ans: Not very many. Therefore: Actually cod aren’t like humans. They don’t all live till they are old. So there are a lot more young cod than old anyway NZAMT 2013

  24. How do you reach this conclusion? Actually there are many species of cod. North Sea only live to about 13 years old. Qn: How long do cod live? Ans: up to 25 years. Assumption: So an average adult cod must be about 13 years old. Qn: How many cod over 13 years old are there? Ans: Not very many. Therefore: Actually cod aren’t like humans. They don’t all live till they are old. So there are a lot more young cod than old anyway Actually cod are sexually mature at between 1 and 2 years of age. NZAMT 2013

  25. How do you reach this conclusion? Actually there are many species of cod. North Sea only live to about 13 years old. Qn: How long do cod live? Ans: up to 25 years. Assumption: So an average adult cod must be about 13 years old. Qn: How many cod over 13 years old are there? Ans: Not very many. Therefore: Actually cod aren’t like humans. They don’t all live till they are old. So there are a lot more young cod than old anyway Actually cod are sexually mature at between 1 and 2 years of age. Well that’s not really surprising is it! NZAMT 2013

  26. NZAMT 2013

  27. So what’s the solution? Not everyone could or should be a mathematician but… NZAMT 2013

  28. So what’s the solution? Not everyone could or should be a mathematician but… they could do just one more… NZAMT 2013

  29. What are we doing to help this? A-level maths (1985-2000) NZAMT 2013

  30. What are we doing to help this? UC MATH100 (2013) NZAMT 2013

  31. The beauty of Mathematics NZAMT 2013

  32. Something a bit more interesting? Pascal’s triangle (revisited) NZAMT 2013

  33. Pascal’s triangle? NZAMT 2013

  34. Game of Life? NZAMT 2013

  35. Game of Life? NZAMT 2013

  36. Game of Life? NZAMT 2013

  37. Game of Life? NZAMT 2013

  38. Game of Life? How many rules do we need? 8 ( = 23) How many rules sets are there? 256 ( = 28) Are they all different? No – some are symmetries of others. NZAMT 2013

  39. Game of Life? NZAMT 2013

  40. Game of Life – 2D • Count the occupied squares around you • You need at least 2 to stay alive • Any more than 3 and you'll die from overcrowding • It takes 3 to make a baby

  41. Game of Life– 2D NZAMT 2013

  42. Game of Life– 2D NZAMT 2013

  43. Closing thoughts • Do we plan our curriculum to include the fun stuff? • How many of our students leave being able to use the world’s most widely available mathematical and statistical software package? (How many of us can use it?) • Can we lose just a little bit of content to persuade our students to do just one more… NZAMT 2013

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