Just one more…

Alex JamesBiomathematics Research Centre

University of Canterbury

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Innumeracy

A long history…

Gargantua(Rabelais, 1534)

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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

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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

300m2m

(not to scale!)

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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

2.6m13,000kg

1m800kg

3-4m4,000 – 7,000kg

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As large (weight?) as 6 elephants

5,000 x 6 = 30,000 kg

2.6m13,000kg

1m800kg

3-4m4,000 – 7,000kg

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As large (size?) as 6 elephants

3m x 6 = 18m5,000 x 63 = 1,080,000 kg

2.6m13,000kg

1m800kg

3-4m4,000 – 7,000kg

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Innumeracy

Even further back…

Noah (Genesis, 4004BC?)

~2349BC (Ussher’s chronology, 1650)

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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

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• Fifteen cubits upward did the waters prevail; and the mountains were covered.

15 cubits = 6m

Much smaller mountains back then?

orNoah lived in Holland?

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Fifteen cubits upward did the waters prevail.

How much water is this?

Radius earth (polar) = 6,356,752.3mVol earth = Vol extra water = = 3 x 1015 m3

= 6 million Sydney harbours (500 GL)= one thousandth of all the water on earth

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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?

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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

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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

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Are we descended from Noah?

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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

Are we descended from Noah?

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Are we descended from Noah?Count females only

G = generations since Noah

NG = number of females in the world now

R0 = number of (girl) babies per female

girl babies per female

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Innumeracy - today

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Could Europe go extinct?

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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.

Could cod go extinct?

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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:

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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.

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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 aren’t like humans. They don’t all live till they are old. So there are a lot more young cod than old anyway

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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 aren’t like humans. They don’t all live till they are old. So there are a lot more young cod than old anyway

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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 aren’t like humans. They don’t all live till they are old. So there are a lot more young cod than old anyway

Well that’s not really surprising is it!

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So what’s the solution?

Not everyone could or should be a mathematician

but…

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So what’s the solution?

Not everyone could or should be a mathematician

but…

they could do just one more…

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What are we doing to help this?

A-level maths(1985-2000)

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What are we doing to help this?

UC MATH100(2013)

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The beauty of Mathematics

Something a bit more interesting?

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Pascal’s triangle (revisited)

Pascal’s triangle?

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Game of Life?

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Current cells

Next cells

Current cells

Game of Life?

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Current cells

Next cells

Current cells

Game of Life?

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Current cells

Next cells

Current cells

Game of Life?

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Current cells

Next cells

Current cells

Game of Life?

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Current cells

Next cells

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.

Game of Life?

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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

Game of Life – 2D

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Game of Life – 2D

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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 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…

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