GRGR(3) - The Map(s)

[calbert at pop.tiac.net]

> Mexico has a map onto which he records the bomb hits AFTER the fact, right?
> His insight is the ability to relate these strikes to a Poisson
> Distribution.  The bombs FOLLOW the P.D., but he can't PREDICT where the
> most likely next hits will be, RIGHT?

Neither will Poisson, nor would he ever have claimed to. Poisson 
allows Mexico to determine that a particular box in the grid will be 
hit n number of times, but it cannot tell him when.  His map simply 
confirms that this process is subject to Poisson analysis. An ability 
to recognize such a connection is not the province of a savant or 
genius, just someone of a probabilistic bent.

> Some thoughts on Mexico's Map:
> 
> 1.  It seems to me that this application of the P.D. formula has very little
> practical value other than to project death-rates if population densities
> were overlaid onto the map, or maybe property losses for insurance company
> use.

The text suggests that this is used to maximize the efficiency of the 
rescue apparatus, but I'm not sure the method is made clear. Poisson 
is a great thing, but it must be used within its limitations. Quality 
controll is a principal application (again, it will not predict 
where, just how many flaws you can expect in a sample of n.)

> 2.  Like Jess, I too, am having trouble with the concept of a predictable
> pattern which doesn't give one clues as to which squares would be safest or
> most dangerous.  Wouldn't there be places on the map which don't conform to
> this pattern?

I'm going out on a limb here (GODDAMM YOU MATTHEW WIENER - AWOL 
BITCH) but my guess is that the rocket strikes concentrate about a 
conical section pattern with London somewhere near the "center". Any 
strike outside the cone would represent a "totally" random event. And 
yes, I can see how the idea would be frustrating, given the practical 
use to which it can be put, but then again, GR would be about 200 
pages long if we weren't obliged to consider the madness of such 
activity.


> 3.  Also, I expect that over an extended time all squares would eventually
> be hit, and thus no pattern would then exist, so this pattern has to have a
> frame of time component distinguishing between recent and old hits, right?

The appropriate application of Poisson DOES require some 
consideration of the statistical notion of "sample". It can be time 
or number of occurences, for example, a production process.

love,
cfa