GRACE: Alright, look — I don’t have the answers yet, I’m just now starting to even frame the questions. What we think we know — is that there’s some kind of electrochemical communication between the roots of the trees. Like the synapses between neurons. Each tree has ten to the fourth connections to the trees around it, and there are ten to the twelfth trees on Pandora –

SELFRIDGE: That’s a lot I’m guessing.

GRACE: That’s more connections than the human brain. You get it? It’s a network — a global network. And the Na’vi can access it — they can upload and download data — memories — at sites like the one you destroyed.

So we multiply 10⁴ and 10¹² (perhaps dividing by 2 so as not to count connections twice), and get 10¹⁶ (within 1 order of magnitude).  A 1988 article in Annual Review of Neuroscience suggests a human brain has  100 billion (10¹¹) neurons and 100 trillion (10¹⁴) synapses, so the Avatar claim seems reasonable.

Can we quantify human memory like this?  Yeah, probably.

1. Make a grid of 0’s.  Really you just need a border of 0’s, but filling an area is faster.  It should be twice as wide as tall.
2. Select cell B2, and give it the formula =MOD(A1+c1,10).
   
3. Copy B2 and paste it into all the cells in the grid except for the top row and the left and right columns.
4. Now they are all adding the values of the two cells diagonally above them.  Just put a “1″ in the middle of the top row and see what happens.
   
5. To color the different digits, click Format, Conditional Formatting, and make some stuff up.
   
6. I changed the font color to white and clicked File > Web Page Preview:
   

You could do some fun experiments with this, leading kids toward the idea of cellular automata!

A pack of zombie dogs (ZDs) is reproducing quickly and killing humans. Scientists and calculus students have determined that the the total number of human deaths due to ZDs t days after the start of 2010 is given by

1. At the end of January 1st (t = 1), how many deaths have occurred?

2. At the end of January, how many deaths will have occurred?

3. Determine the number of deaths/day after t days: h′(t).
Hint: you may want to go “outside-in” with the chain rule.

4. Graph both h(t) and h’(t) on the same axes:

5. On what day will 90% of the human population (6.8 billion) be annihilated by ZDs?

6. When does the death rate reach half a billion per day?

7. When does the death rate hit its peak?

Can you match them all? Height of a projectile, iTunes sales, World Population of gorillas, Transfer speed versus message size on several networks, Heights of a group of men, Population of fruit flies in a container, Decay of radioactive atoms, Heights of babies over time.

If you want to play it, here it is.