Roger:

I think that if you use a two week interval rather than a 2 million year interval (to acquire observed probability data points/events)...the answer could change from 'Not Random' to 'Random' and vice versa. Same for changing the area under study. This argument alone calls for at least one of the "null hypotheses" to be the the random distribution ('cause who says that one has to evaulate with just one null hypothesis? ).

In statistics, adding just a few more data points can make all the difference (e.g. changing the estimate of what type of distribution one is dealing with from a normal distribution to a tailed one).

In a related thought, there are things which appear to be random but do in fact sometimes have hidden order (see Chaos theory). So a random process may be used as the null hypothesis to test a theory for prediction even though there may be embedded order lurking in the details. Whether the hidden order exists or not should not effect using the random process as a null hypothesis (for testing) IMO.

* * * *

Regarding this statement - Article #6:
"Rather than debating whether or not reliable and accurate earthquake prediction is possible, we should instead be debating the extent to which
earthquake occurrence is stochastic. Since it appears likely that earthquake occurrence is at least partly stochastic (or effectively stochastic), efforts at achieving deterministic prediction seem unwarranted."

+ One presumes that a certain amount of data and knowledge was accumulated before making the statement above. If one is dealing with a choatic process which has no hidden order (and this conclusion is drawn from data viewing up to the moment of the statement it seems) then the statement seems reasonable. However, if other looks at the data exists (including from other data type maybe) suggesting that the underlying choatic process has some hidden order to it, then the direction of fire, so to speak, should be aimed towards finding that hidden order and not discouraging the pursuit of first undestandng the hidden order and then using it for prediction purposes. IOWs, just because the speaker turned up Nada at the time of his statement does not preclude:
a) Further data analysis by others searching for Hidden order in seemingly chaotic events &
b) Using that acquired knowledge to possibly predict future events.
{ & Just Maybe
c)Developing a better theory which points to

d) Collecting data not being collected now }

So in summary, when one's paradigm belief system confines one search to a limited set of data and the data appears mostly chaotic then the conclusion insofar as successful prediction is concerned is "fait complete" (sp -?) and the outcome is written in stone in the negative (i.e. it can't be done).

However, given that one is not confined to subject areas of data study derived from formal academics, institutional biases, and funding considerations...then other formerly "off-limits" areas of data investigation are opened up. This possibly leads to the discovery of perhpas unexpected correlations which may lead to successful prediction. To expedite one "gettting on there horse and getting it done" one might pose the question: What data exists that we have looked at (and in what way) and what data exists that we have Not looked at ?

Just my $.02 worth