Strange Loop

Over the last few months, this entire concept of structures, number theory etc. has continued to vex me in a very vague, un-definable, un-scientific way. Hence, seeing that grasping fundamental sciences is beyond ordinary mortals such as I, it seemed more prudent to hear what various greats had to say and discover any isomorphism with other fundamental sciences, such as music. The thought process was revived today morning, after scanning an article that covered the recent Noble Prize awards. Here's what some of the leading thinkers have to say.

Nobel Prize winner Robert J Aumann: “While constructing a theory, we are not trying to get at the truth or even to approximate to it. Rather, we are trying to organize our thoughts and observations in a useful manner.”

Douglas R Hofstadter: “What is important is not finding the answer, but looking for it. You probably have made some attempts to produce MU” … [NB: MU is not important for the discussion here] … “ In so doing, you have built up your own private collection of strings. Such strings, producible by rules, are called theorems.”

A translation of an undecipherable statement by Godel: “All consistent axiomatic formulations of number theory include un-decidable propositions”

Robert M Pirsig: “Quality is the phenomenon that occurs when subject and object meet” (I’m quoting this from an eight – year old memory, so forgive me if the statement has been disfigured beyond belief)

What is clear here is that thought structures and formal systems attempt to synthesize observations or inferences in a rule-based fashion. Having done so, the test of the system is the power to be predictive, repetitive and stable. Once accepted by the public at large, any observation that destabilizes or proves that the system is not repetitive leads to large-scale paranoia e.g. bumblebees cannot fly as per the principles of aero-dynamics, Black Sea is actually a lake, platypus is a mammal that lays eggs etc.

However, the true test of a formal rule-based system is its ability to absorb changes and morph accordingly based on the relative permanence of the changes. Take, for instance, music. Bands that stuck to the original format of lead, rhythm, bass guitars, optional synthesizers, 4 x 4 riffs and basic drum rolls are out. Musicians who are social ambassadors are thriving e.g. Bono, Bob Geldoff etc. Or musicians that have decided to seek inspirations in lesser – known cultures e.g. Page and Plant going to Morocco. Or music systems such as Thai music that doesn’t follow the traditional “octave” system, continue to survive.

There are three things that a formal system can do when de-stabilizing change occurs – observe and do-nothing, reach out and measure or become change. This is described extremely well in various philosophical treatises. (Take the Hindu philosophy, for instance.) The point is that change is random, and hence there needs to be an element in any theorem design of being prepared to embark on a "Random Walk".

This leads to a very obvious and well – worn conclusion, which was articulated by Mr Aumann:
If you are rational, you will break rules.

On that note, wishing your family and you a Happy Dassera, Durga Puja, Navratri and Vijaya Dashami (or Bijoya Dashami)