Re: "The problem is that statistics can be screwed"
"Even perfect statistics are useless when you try to predict a single event, without having a clear enough comprehension of the mechanism underlying the event - a theory (and its validation)."
You needed to stop at the first comma. I can predict perfectly the probably your lottery numbers will come up. I can't tell you whether they will. Likewise the spin of an electron in a magnetic field.
"That's something that comes from the "science" of economics, which is still unable to deliver real theories (and their proofs), and so builds on statistical data, and delivers wild and often wrong predictions, but most pretend it works because they make money on it."
I've been reading Simon Wren Lewis's Mainly Macro blog and delving into the theory, and I think you're unfair on economics. I think they have a good understanding of some of the core basics. And while short-term predictions are always tricky, they can get the long term trends right. Unfortunately, the truth has that well known left wing bias, and gets drowned out by politicians and media.
I think the future will look back on our economics in the way we look back on the astrophysics of Galileo: shut away by vested interests.