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We all know that Correlation does not imply causation, but I am wondering whether there can be causation without correlation. If there are such cases, could you explain them?

I am asking this question in order to validate my statement that "Correlation is required but not sufficient condition of causation.", but I'd like a broader context, not just yes or no.

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    $\begingroup$ Please research our site. Although you could not have guessed it, searching for Anscombe's Quartet will be a good start. Since according to the conventional technical meaning of "correlation" the answer is obvious, I suspect your understanding of "correlation" might be different from the technical one that would be assumed by many readers. Could you please edit this post to elaborate on what precisely you mean by "correlation"? $\endgroup$ – whuber♦ May 22 '15 at 14:00
  • $\begingroup$ I can't see why would it seem that my understanding of correlation is different from the technical one. I am talking about the statistical relationship between variable values. As described on Wikipedia. $\endgroup$ – Tomáš Zato - Reinstate Monica May 22 '15 at 14:04
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    $\begingroup$ Correlation is not the "statistical relationship...". As most commonly used, it is a specific combination of first and second order bivariate moments of a dataset or distribution. (There are other closely-related ways to quantify similarly definite relationships.) "Statistical relationship" itself is too vague to have any meaning at all. Could you be more specific about exactly what relationship you intend the word "correlation" to describe? $\endgroup$ – whuber♦ May 22 '15 at 14:08
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    $\begingroup$ It's perfectly possible to have a well-defined deterministic relationship between variables for which the correlation is zero. For example, the trajectory of a projectile is a parabola or quadratic but follows from simple Newtonian mechanics. If you want to redefine correlation as meaning (e.g.) predictable relationship, that needs to be explicit (but would in my view be perverse). I guess that is part of what @whuber has in mind. $\endgroup$ – Nick Cox May 22 '15 at 14:08
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    $\begingroup$ Ok, thanks for explaining. I have read the answers to the other questions and I see that I happened to ask a duplicate question. I googled it first, though! $\endgroup$ – Tomáš Zato - Reinstate Monica May 22 '15 at 14:10