Correlation and Causality

When I was small, I had a strange feeling which surprisingly I also observed in my 3 years old nephew yesterday. Just wanted to share my foolishness, as I feel that I am not alone in this.
When I was a small kid, I used to believe that for running a car fast, you need to rotate the steering wheel fast! Sadly Yes :-(
And when I think deeply, it seems to be arising from the fundamental problem in statistics relating to correlation and causality. Let us try to understand what is meant by it.
So normally when I use to watch people driving a fast car (especially in movies…like some hero chasing the villain) the driver of the car used to rotate the steering wheel very quickly. And the reason was that as the chase used to happen usually on busy roads, the driver used to take many turns which accompanied by fast speed resulted in fast movement of steering wheel. In statistical terms, there was a significant correlation between movement of the steering wheel and the speed of the car.
And the error I (and now my three years old nephew) was doing is mistaking correlation for causality. To my rescue, some of the Physicists, many of the statisticians and almost all the economist, do the same. And a good test of Causality (Granger Causality) was found very recently and which was awarded Noble only in 2003. We generally tend to believe that if two things are moving in tandem then one is causing the other. And generally and mistakenly, the cause is attributed to the thing which is more conspicuous (like the moving of the steering wheel rather than pressing of the accelerator which hardly is observable to a young kid)
In some cases, neither A implies neither B nor B implies A. There is a third factor which implies both. For example, consider two spinners playing for the same team with similar style. If it is a turning pitch then both of them would spin the ball and if the pitch is flat then both of them would bowl badly. So definitely they are correlated. But does one imply the second or second imply the first? No because both are caused by a third factor which is roughness of the pitch.
And most of the times a Physicist, a Financial Modeler or an Economist main job is to observe different variable, finding whether they are correlated and if a causation exists between each other or there is a third factor which is causing the two. It is easier said than done. Needless to say, they almost always fail to do so and we pay them for doing postmortem rather than the surgery.

(Positive Correlation implies if one thing outperforms the other outperforms also while if one underperforms the other underperforms. Also to note that rather than it being a rule, it is simply an empirical observation which may not always hold
Mathematically if X and Y are random variables, Correlation(X,Y) = E[(X-E(X))(Y-E(Y))]