Sunday, March 19, 2017

Kolmogorov Complexity

Any random string has inherent complexity and taking the algorithmic complexity approach it is described by kolmogorov complexity. The random string is said to have complexity of K(w) which is given as the length of the shortest program that generates w.
If a program generates a string w has length less than w then kolmogorov complexity of the string is the length of that program. 
We usually have patterns of data taken from our surroundings. Complex processes of physics, chemistry and optics are at play in generation of the patterns that we see around us. Suppose we set out to catalog every pattern of strings generated by computers on the internet. With such a big data its mining would take much time under ordinary circumstances.
Just an image of 100 pixels cross 100 pixels with 8 bits per pixel depth would produce 2 power 80,000 different image combinations.

Research unto death

Knowledge gaps imply researchers from underprivileged backgrounds have to struggle much more. "As the infusion of mass media information into a social system increases, higher socioeconomic status segments tend to acquire this information faster than lower socioeconomic-status population segments so that the gap in knowledge between the two tends to increase rather than decrease"...(Source: google)

The thing is productivity of research and its ultimate end use are a function of the economy. After all the low hanging fruits have been plucked, it would seem there would come a slow death of research. The law of diminishing returns would dictate that this science, medicine and engineering thing would stop bearing fruits. Wells would turn dry. Once that happens and in a stagnant economy the dominant discourse would move from unlimited opportunities and synergy to "Sharing a pie" or a "zero sum game". Once that happens the dominant economic discourse would turn more leftist.

To strike at the roots of economic imbalance we have to have equal opportunities for all. 

Several people would just be required to study and be knowledgeable enough to predict the future. Professors just have one thing to do. Research and then some more research. (I thought a few random thoughts streaking through my mind when posted in this user generated content post would enrich the internet)