I and many others have referred to a concept called causation.

And yet, in any scientific experiment I have performed, discussed or could imagine,
I don't believe I could ever empirically observe a causation, only corollation or coincidence.

Correlation having the same meaning as coincidence. Coincidence being that one event coincides with another.

Even in reviewing the models of force interactions of sub atomic particles, I can only ever imagine the measurement of coincidence and not a presumed causative link.

To presume causation is to reduce a theory back down to a hypothesis, if you do not have empirical observation of a causative link, just correlation.

Even if you breakdown the measurement into lower scale or previous events, you will only find more correlation and not causation.

Correlation is observable, where as causation is imagined.

You could of course revise your semantics of "causation" to mean "Always coincides under specified conditions." but you could only test the validity of the application of the word "causation" by having access to empirical data for all occurrences.

The phrase "correlation does not imply causation." whilst not being an invalid statement, Is of no useful value, other than implying "Beware of the use of correlation as a tool until you have a trustworthy amount of it.", as to its trustworthiness, that can only be ascertained after repeated experiments. (or estimations thereof.)

Google use correlation without theory in their analysis of data to improve advertising revenue.

I should imagine Google use Bayesian networks or artificial neural networks in their analysis of data, Those networks would allow correlation information to inform action. Many spam filters rely on Bayesian analysis to accurately identify spam by building a probability network of words and their occurrence in messages. Beware, bayesian networks are open to bayesian poisoning. (look it up.)

It is very difficult if not on the verge of impossibility to extract Hypothesis or Theory from complex bayesian or neural networks (with the tools that I am aware of.). You just have to rely on it's measured usefulness.

Imagine this loose hypothetical situation, Every time you place your hand on an object that has very fast vibrations (hot), an undetected mischievous alien uses some sort of device to increase the vibrations of your hand (now your hand is hot), to elevate the correlation between the hot object and your hot hand to "the hot object CAUSES my hand to be hot." would be a mistake if you want to keep your theory as a theory. But we are still left with a causation, the alien, but how about NOTHING causes it, not even the alien, nothing can rule that out and that is to deny causation. (you will find it contradicts another of my hypothesis, but so what, I guess at least one is invalid. But as we can't guess which one is invalid without empirical observation, we have to assume positive probabilities for both.). My opinion is, that you could take a version of the alien hypothesis to the smallest scale and it would still apply.

You may want to try this experiment:

Download and install Thunderbird email client. (this has a built in bayesian filter.)

Get a free email account from goggle (or other) and setup Thunderbird to receive the email.

Sign up to as many newsletters (The more regular the better, daily ones are best.) on the most wide ranging of topics. (astrology, art, celebrity news, reuters, daily weather, etc.)

Choose a measurable concept such as Horses winning a race beginning with the letter S, or how many times attractive people look my in the eye.

Set a threshold on the measurable concept such as 3 or more horses.

At the end of each day, check if the number of horses beginning with the letter S reached 3 (your threshold.) and if they did, mark all the emails for that day as not spam, or if not then mark as spam. (this all relies on the basis that Thunderbird does not mark spam based upon sender, but on word probability.)

After training for a length of time (don't ask me.) you emails arriving automatically marked as spam or not will show weather there is a correlation between your data sources via email and the chosen measurable concept.

Remember to adjust timing for the teaching of the bayesian network, whether you looking for correlation before or after an event. (or something! :)

Viola, you have now setup your own data mining/ artificial intelligence experiment with no need of complex math or programming skills.

Good luck.