spokette - I am quite familiar with analysis of stocks, bonds, markets etc.
When you talk about "quantitative analysis", you are mixing up two things: Fundamental analysis and technical analysis.
Past performance is used to predict future movements of stocks etc only in technical analysis. That is where you see lots of lines on price graphs. This is what traders use and has limited success in short term and little success in long term investments.
Fundamental analysis is where you look at a company's actual numbers and estimate what its coming quarter/year might be like, depending on its own strengths/weaknesses/etc. This is what serious investors listen to, and where you will also see the analyst value the company and give a target share price, for example.
"Despite these mathematical models, the market has crashed"
That is not surprising in itself. Booms are inevitably followed by busts. This is not the first and will not be the last.
"traders have no idea on whether prices will rise or fall"
You must be talking to some very clueless traders. Do they still have jobs?
"People are unpredictable and markets are at the mercy of how confident people feel about what they are buying into"
Naturally. That is why 'consumer confidence' is one of the most closely followed economic indicators.
People are not that unpredictable, by the way. They feel confident when things are going well, and that confidence vanishes when bad news start coming out. Like, say, several banks crashing and burning.
"The one thing this financial tsunami has shown is that trading is not an exact science"
Nobody said trading was an exact science. Trading is not even a science. It is done mostly on gut feeling.
Or did you mean investing?
"financial dark matter"
That refers to the credit derivatives, iirc, not to the entire financial assets of the world.