Technical analysis is based on one assumption:  that there exists time-correlations in market prices.

If someone manages to formally prove the existence of these correlations, that would settle it for me.

I've seen very complex attempts at extracting these correlations, through artificial intelligence algorithms such as high-dimensional support vector methods. These algorithms can find extremely complex correlations in the data that would be very hard for us humans to grasp, or completely unintuitive. If these methods fail at detecting correlations, I have a hard time with the credibility of "toy functions" used in classical TA.

My 2 bitcents. I could be completely wrong and thats fine.

(note: finding correlations amounts to predicting the price better than random. Of course, random can be right sometimes, but it's predictive power is useless.)