If you cant do it right, do it random!

I was trying to understand how random projections can be used for dimensionality reduction instead of PCA. It was not obvious how random projections could even attempt to match projections computed through Eigen decomposition of the covariance matrix (which sounds computationally demanding!). After a discussion with my friend, I realised that random projections were essentially similar to finding the Eigen vector through the Power method. I was really amazed as I thought of Power method only as a numerical method.

Now for some philosophy :-)

I was trying to build some intuition / wondering where else this method could be applied. Probably, I am stretching my analogy, but I couldnt help notice a strong connection to life. We all want to find something that we are good at, a job/lifestyle that is well oriented ( Now, thats more like it :-) ) with our skills and interests. How do we find it ?
You start doing something random, see if that suits you, and based on how you feel, you update what you are doing. If you persevere (iterate) enough, your lifestyle will converge to what you truly want!

If you cant do it right, do it random! And hope that the dots will connect! :-)