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Well, that question actually has a simple answer. Correlation can be any of the following: Causation (one event caused the other), Coincidence (no relationship between the two events), or Correlated (some shared factor influences both events).

(emphasis added)

Excellent, we have agreement:
coincidence == correlation != causation

with the bonus tautology:
correlation == correlation

We can stop debating this now.

Well, we've certainly established that you can't read. So I agree that we can stop debating this now.
 
Well, we've certainly established that you can't read. So I agree that we can stop debating this now.
I don't think I'm the one with the reading problem here, but I may have been too charitable in interpreting what I read. Maybe the problem is that despite your imprecise language and use of bidirectional inequality for unidirectional implications, I gave you the benefit of the doubt...

Or maybe the problem is that you simply aren't returning the favor.

Ignore your pseudo-mathematical inequality for a second and look at the language-- help me see what you think is different between these two statements:
Unless I misunderstand what you're after, I think that events occurring at roughly the same time are (roughly) correlated, but not necessarily causal.

Correlated events may be either coincidental (aka spurious) or causal. Causal events are correlated, but correlated events need not be causal. Coincidental events may be correlated for small sample sets but that correlation may weaken as the the sample size increases to the level of statistical significance unless the correlation is due to a hidden variable (which, depending on what you mean by coincidence, may not fit your definition-- the events "coincide" but not by random chance).
Correlation can be any of the following: Causation (one event caused the other), Coincidence (no relationship between the two events), or Correlated (some shared factor influences both events).
I'm going to continue assuming for the moment that we agree on what causality means-- god help us if we don't.

Based on the parenthetical phrase, I'm going to assume that your second use of "Correlated" means that there is a hidden or confounding variable at work.

You seem to think our difference is in your phrase "no relationship", which does conflict with my statement that they're related by correlation. Rather than beat on that minor distinction I assumed that by "no relationship" you simply meant no causal relationship-- and maybe that's where the problem lies.

If they're correlated, they're related-- correlation in itself is a relationship.
They are related to each other because they coincide in space and time-- that's all correlation means.
Correlation has a rigorous mathematical definition, but it can be boiled down to this for the purpose of the discussion we're having since this massive body of evidence you describe doesn't contain any data to run a mathematical analysis on.

Ironically, the only data that exists from this test of "unlimited size and scope" are some of the correlation peaks-- a few of the data points that show the strongest correlation are recorded in the NASA database, but they had to break a threshold of detection before being recorded and the pilot had to decide voluntarily to go through the trouble of making the report.

So we do have the evidence of correlation that you refute, but we don't have any contextual data with which to view it.
 
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