1. Weather Forecasting Problem (One Trillion Operations per Second?)
Predict the weather over United States and Canada
for the next two days:
Model the atmosphere from sea level to an altitude of 20 kilometers.,
and predict the weather at each hour for the next two days.
Standard Approach: Cover the region of interest with a grid and
then predict the weather at each vertex of the grid
Cubical grid with each cube measuring 0.1 kilometer on each side
Area of United States and Canada = 20 million square kilometers

2. Weather Forecasting Problem (One Trillion Operations per Second?)
Number of grid points = 2.0 * 10 ^7 * 20 * 10 ^3 = 4 * 10 ^11
No of calculations per grid point = 100
Predicting weather for each hour for 48 hours
Total number of calculations = 4 * 10 ^13 * 48 = 2 * 10^15
calculations

3. Weather Forecasting Problem (One Trillion Operations per Second?)
Number of instructions per second for an existing computer = 1 billion
(10^9)
Time needed = 2 * 10 ^15 /10^9 = 2 * 10^6 seconds = 23 days
Problem with Von Neumann Computer
Let us assume that we have a computer that can execute the following code
in one second:
For (I = 0; I < ONE_TRILLION; I++)
z[I] = x [I] + y[I]
Fetch x[I] and y[I] from memory
Store the result z[I] into memory
3 * 10 ^12 copies between memory and CPU per second

4. Weather Forecasting Problem (One Trillion Operations per Second?)
Speed of light = 3 * 10 ^8 m/sec
R is the average distance between memory and CPU
3 * 10^12 *R = 3 * 10^8
R = 10 ^-4
Use a square grid for memory and connect the CPU to the center of the
square S/2 = r = 10^-4
S= 2*10^-4
Capacity of memory = 3 * 10^12
“Row” of memory words will contain (3 * 10 ^12) = (3) * 10^6 words
Word length = (2 * 10 ^-4) /  (3) * 10 ^6 = 10 ^-10 meters
This is approximately size of an atom.
How do you represent 32/64 bits using the size of an atom?
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