While walking on the roads of the campus, if someone casually asked me ‘where are you going?’ I would reply ‘Nowhere..I am just moving parallel to the road’ 😀 😀 I always believed that most of our path is decided by the road, we just move along the road!; It’s only at the turnings where we get to make our choice. Yet, we get complete freedom to choose our final destination!. I was always amused at it. Probably because, I used time/length as a measure of domination. When I say we always walk along the road, and make a choice only once in while, I mean, our walk is dominated by instances where the road decides the path. Invariably I am comparing the chosen part of the travel and the predetermined part of the travel in terms of the time spent or the distance travelled. This is clearly an incorrect measure to quantify and compare how much do we get to choose and how much is predetermined.
Recently I came across a formal study of similar properties in a language. A language has got some rules in the form grammar etc.. As in, once I start writing, I don’t have complete freedom to decide the next character. There are restrictions to it. There are choices left to us and, in between the restrictions, we make use of the choices to give the meaning at our will. This is beautifully captured in what is known as redundancy of a language. This is a number between 0 and 1. A completely random language has zero redundancy; any character can appear after any character. It is completely up to our choice. A language where the user gets no chance to choose is a completely redundant language; every character is uniquely decided by its previous character. Anything in between these two extremes is assigned a number between 0 and 1(there are more beautiful results; the redundancy of a language is related to existence of arbitrary infinite n-dimensional cross word puzzles!). I was so fascinated that, in fact I started using the word ‘redundancy’ almost whenever I feel like! 😀 😀
Rules might seem like they are restrictions on our freedom. However, even in a very general abstract system, rules are very much necessary. I started comparing the rules and the freedom in a system to those of a game. There is no game without rules; also, there is no game with the moves completely determined by the rules. It’s a proper combination of freedom and redundancy which makes the game interesting. There are rules to be followed while playing a game. However, the real playing happens in the free region; If I am spending all his energy to merely be religious in following the rules, and doing nothing with the freedom, I am not playing at all! To play is to find gaps in between the rules and sneak into them!
So to play a game is to sneak in to the gaps between rules to get our job done. We might expect it to be easier to do so with lesser rules. But it is just the opposite!. The reason is, rules just give us a platform to work on; we are actually working in the free region. So, larger the free region, difficult it is. This is quite the reason why simplifying assumptions are made to begin with a new theory. We just don’t know how to work with very few constraints!. The extra assumptions give us the guidelines to work. That seems to be the purpose of rules. This post is abstract..probably because, the thoughts are so 😀 😀