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

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

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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

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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. ~30m 300m 2m (not to scale!) NZAMT 2013

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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 2.6m 13,000kg 1m 800kg 3-4m 4,000 – 7,000kg NZAMT 2013

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

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

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Innumeracy Even further back… Noah (Genesis, 4004BC?) ~2349BC (Usshers chronology, 1650) NZAMT 2013

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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

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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

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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

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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

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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

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Are we descended from Noah? NZAMT 2013

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Are we descended from Noah? NZAMT 2013

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Innumeracy - today NZAMT 2013

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Could Europe go extinct? NZAMT 2013

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Could cod go extinct? NZAMT 2013

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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

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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: Actually there are many species of cod. North Sea only live to about 13 years old. NZAMT 2013

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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: Actually there are many species of cod. North Sea only live to about 13 years old. Actually cod arent like humans. They dont all live till they are old. So there are a lot more young cod than old anyway NZAMT 2013

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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: Actually there are many species of cod. North Sea only live to about 13 years old. Actually cod are sexually mature at between 1 and 2 years of age. Actually cod arent like humans. They dont all live till they are old. So there are a lot more young cod than old anyway NZAMT 2013

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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: Actually there are many species of cod. North Sea only live to about 13 years old. Actually cod are sexually mature at between 1 and 2 years of age. Actually cod arent like humans. They dont all live till they are old. So there are a lot more young cod than old anyway Well thats not really surprising is it! NZAMT 2013

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So whats the solution? Not everyone could or should be a mathematician but… NZAMT 2013

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So whats the solution? Not everyone could or should be a mathematician but… they could do just one more… NZAMT 2013

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

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

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The beauty of Mathematics

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Something a bit more interesting? NZAMT 2013 Pascals triangle (revisited)

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Pascals triangle? NZAMT 2013

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Game of Life? NZAMT 2013 Current cells Next cells Current cells

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Game of Life? NZAMT 2013 Current cells Next cells Current cells

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Game of Life? NZAMT 2013 Current cells Next cells Current cells

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Game of Life? NZAMT 2013 Current cells Next cells Current cells

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Game of Life? NZAMT 2013 Current cells Next cells How many rules do we need? 8 ( = 2 3 ) How many rules sets are there? 256 ( = 2 8 ) Are they all different? No – some are symmetries of others.

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Game of Life? NZAMT 2013

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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 Game of Life – 2D

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NZAMT 2013

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Game of Life – 2D NZAMT 2013

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Closing thoughts Do we plan our curriculum to include the fun stuff? How many of our students leave being able to use the worlds 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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End Simplify A. 13B. 147 C. 17D. 336 30 – 2(5)+7.

End Simplify A. 13B. 147 C. 17D. 336 30 – 2(5)+7.

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