Empirical evidence for the Church-Turing thesis in other disciplines I am aware of the fact that, since the concept of "effectively calculable function" is not rigorous or formally definable, the Church-Turing thesis may not be proven by symbolic or formal reasoning alone.

My impression, though, is that under the domain of physics, philosophy, cognitive science or other disciplines, we may find empirical evidence that gives us a strong reason for accepting it, for instance in the field of numerical cognition. Even if those disciplines are not directly related to computer science, the importance of this thesis in CS make this, in my opinion, an important issue to consider for us; that's why I'm asking this question here. (If you feel like there are better SE suited for this questions, let me know please.)

So, what is the current state of the research for evidence to support the Church-Turing thesis? Are there any recent developments? 

A good answer would also provide a list of all the major efforts to this day to empirically validate or refute the CT-Thesis, and the main problems posed by this issue. Investigations on the notion of "effectively calculable" in cognitive science, or what does it mean to "compute" in physics are also welcome.
Proof is an inherently mathematical concept. "Effectively calculable function" has no definition in mathematics and you can't prove something that doesn't have a definition.