I said that statistical science is not a physical science but physical probability machines prove me wrong:
http://www.youtube.com/watch?v=9xUBhhM4vbM&list=PLDF301534C65CED18&noredirect=1
There is a statistical flight physics
problem I worked on back in the 80s. It
involved estimating the scattered impact of the pieces breaking up in the atmosphere from the STS main external tank in the S. Atlantic.
The algorithm used deterministic Kepler equations to compute an impact point but these equations were formulated for vacuum and not for the atmospheric buffeting and shear conditions that were present.
Further, there was no certain way to determine how many pieces and what size pieces the tank would break into.
The solution was statistical. The algorithm ran a Monte Carlo iteration of about 10,000 or more cycles, each time varying in a random sense the atmospheric buffeting and wind shear as well as varying the number and size distribution of the pieces, and computing a scatter impact for each cycle.
At the end of the Monte Carlo run, all impact points were used to calculate a 95% confidence ellipse. And we made sure the ellipse was far away from coastal cities and heavy traffic shipping lanes. From feedback data we knew some of the pieces were as big as Greyhound buses.
The statistical science worked like a charm. Satellite images confirmed our statistical ellipse was safe and reliable in predicting the impact area.
It’s kind of like a political poll - 95% probable 24 out of 25 times!
You haven’t computed where the pieces would fall. You’ve only calculated a general probability. There is no guarantee where the parts WILL fall.
10,000 cycles versus 6.23*1^23 for 1 mole. I’ll believe chemistry, not limited mathematical guesses.