local optimal success{ordinals of life 2.0 }

Shivshanker Singh Patel
Bangalore, 560012, India

May 16, 2013

Figure1: Local and global optimum

This post is an extension of my previous post Ordinals of life, where I discussed about Mr. Sanjay who always wanted to enjoy a normal life and was always considered as extraordinary by rest of the normal population. In this post again, I try to capture as usual a mathematical purview of human life, Some of my friends try to put this in to fixed genre(i.e Metaphysics). This post is motivated by Weierstrass’ Theorem for functions and human interactions. My knowledge in the field of sociology and psychology is limited. So I tried to surrogate the social exchange theory and related issues to information theory, contributed by Claude E. Shannon.
We know that a human gets birth and dies one day so this set of life(time), which closed and bounded. And if success(happiness/utility) is function time i.e. f(t) then we can map each success points on to Real line.
Definition:
Success is a real valued continuous function f(s) : s-->ℜ. Where f(s)∈ S, s∈F.
Theorem 1 (Weierstrass’ Theorem for functions) Let f(s) be a continuous real-valued function on the compact non-empty set F ⊂ℜ . Then F contains a point that minimizes(maximizes) f(s) on the set F.

          Above theorem clearly states that if the set is closed and bounded then the function will be having a maximum or minimum value in that domain. As i have already defined above the life of individual is closed and bounded set of time. It means that a human life will reach to its maximum value(in terms of success/happiness) in that compact set. This success(happiness) is defined in the previous post(see figure:2). It can be only considered a success when there will be ordinal comparison or benchmark.

Figure2: Ordinals and success as continuous function

Now I would like to bring the notion of information exchange. This information can be exchange by different means, if I consider that the natural language was not discovered, our sensory capability could capture some information from the surrounding. It means neighbour hood. For the time being, I try to introduce two types of neighbourhoods. First one is temporal and the other is spatial. In the case of single human with time(temporal neighbourhood)  he/she sees his/her own success/happiness and it’s graph and traverse according to his/her ordinal preference and jumping on other curves(see Figure2). In this case I have dropped its spatial movement and its implicit nature of comparison. I would like to mention again the person named Sanjay who was always enjoying his life where he considered his success with his own compact set of time, and his comparison was always with him.

If I apply Theorem1 to understand the two dimensions, where I include both the temporal and spatial type of neighbourhood and then the whole situation would be like Figure1 where there are successes, continuous function with respect to time and space. So if I take every individual human and his life is a subset of the bigger set which includes the every human and with either a fixed time frame or we can consider the superimposing of different  time window where success can be brought in the same comparison platform.
 Hypothesis
Every single person is success full and happy if i consider subset d ∈ {space X time} and this subset is assumed as a compact set, so means whatever that has been consider a local optimal success becomes a global optimal success with respect to that person in that compact set. This subset is defined within the constraint of information exchange. The more volatile and large information network will exist the bigger the compact set will be. And than his own global optimal success will become a local optimal success in this bigger compact set.

Need psychological Manumission

lets start the whole discussion with the definition of  Manumission: formal emancipation from slavery(click). It is very important to understand the dimension of slavery that exist in our society. With a limited capacity of understanding that i have about Indian society and as an individual about myself, i will try to focus on the issues related to internal and external slavery. What we can see around us is the social system, which includes a stratification with respect to either caste/clan or economical disparities.

And whenever there is inequality and non-equitableness we(conscious citizen) think about fairness and justice. i would like to capture the whole scuttle slavery that has been introduced in our society since post Aryan or post Mouryan era. It has a nature of deriving utility of aristocracy, since the people who were living in the territory bounded with Indus, Himalaya and Brahmaputra were not aware about philosophical evolution in the west. This slavery was different from the exclusive slavery that existed in Confederate United States(Southern United States).   Some thing that was going to come from the countries(Europe), who have been living in dark ages(almost) and poverty since  1400A.D.  Thomas Mun(1571–1641) brought the idea of balance of trade and mercantile system. Which gave thrust to Europe to expand their manufacturing, international trade, and building colony across the globe. But the involved negative externalities in this ambition was scarcity of man power and their military capability helped them to conquer the less military equipped countries and penetrated the psychology of hierarchy on the basis of skin color. The voyagers' guts help them in this task. They took black color human from Africa and put in to their plantation and etc. to fight the scarcity of manpower for their ambitions.

I will not spend much of details which can explain how the whole Aryan system that was based on division of types of work. And how that system was escalated to extreme caste system and unaccountability. When British came to this part of the world they brought their defined slavery. And then our own so called Indian(was called by western) started differentiating themselves to find aristocracy. In the beginning the whole aristocracy was associated with kings and then it started percolated to lower levels and every second person wanted some landholding and workers on that land to project themselves as aristocrat. 

Now what is the present situation, the reluctance for change to break old school of thoughts is our internal slavery. However USA had worst slavery but they also broke their internal slavery and the example is of an Afro-American president. We need to understand how we are slave to our own thoughts of looking around for some kind of special treatment. That start from not standing in the queue for tickets to disrespecting women. why i m bringing these examples because we think that we aristocrat and how can we stand in a queue, because queue is for slaves. Also as a matter of fact an aristocrat should and can sleep with so many women by his will that leads them exhibiting machismo and try to seduce women and further to disrespect by doing heinous act of rape and assault.

These all are resultant of our internal(psychological) slavery that has been grown a lot. And need for a psychological manumission.