I am more unpredictable than you are ! (Entropy measure with an difference)

"I am moody, I'm unpredictable". Well this article is for all those who are often characterized as moody and unpredictable. Well its a into information theory for measuring the moodiness/entropy. Answering "Who is more moody than other ?". If not interested please don't proceed beyond this. Why would you like such a measure ? Quantitative measures are good aren't they ? 0.9 of an feminist is a better than a 0.5 feminist isn't it ?

If give a circumstance X you tend to behave differently in |Y| number of ways. For example Given a women issue a person comes up with the a stand favoring women or a stand that is not quite liked by women. So here

X -> circumstance -> A women issue.
Y -> number of stands you can take -> 2
(Well this is an assumption we make - we are only dealing with dichotomies ie. Y/N outcomes)

"Well we will answer who is more predictable given an circumstance on a scale of 0-1". That last sentence i made was quite an sentence if you get it. It says atleast more than what is clearly understood.

1. We are not answering who is a feminist and who is Mysogynist. To answer this the problem has to modeled in a different way :)
2. We are answering who is a more stable feminist or a Mysogynist.

That is, when posed with a feminist dichotomy (question) Virginia Wolf's (a well known feminist) stand can be more predictable than my answer. Now can we have a measure of this unpredictability ? (Its closely related to the corollary of probability i.e p-value. The chance that you are hit my misfortune). Below is a sample table.

Legend
Answer Y=Supporting feminist views N=No support feminist issues.
X=random women question

A staunch feminist
Answer Y Y Y Y N Y Y Y
QuestionX Q1 Q2 ..... Q8

A weak feminist.
Answer Y Y N Y N N Y Y
QuestionX Q1 Q2 ..... Q8

Entropy/Randomness Measure = Summation_over_outcomes ( -Probability(outcome) * log2(Probability(outcome)) )



Here we have only 2 outcome Y/N. (cleverly crafted na ? See iam smart). So we have to sum only over 2 outcomes.


Randomness in our case is just the summation of 2 terms =
-Probab(SupportFeminist) * log2(Probab(SupportFeminist))
-Probab(NotSupportFeminist)*log2(Probab(NotSupportFeminist))


K. Now the randomess/craziness/unpredictability of an staunch feminist is.
= - (7/8) log 2 (7/8) - (1/8) log 2 (1/8) .... (Because 7 out 8 she supported feminist)
= 0.168 + 0.375
= 0.543

K. Now the randomess/craziness/unpredictability of an weak feminist is.
= - (5/8) log 2 (5/8) - (3/8) log 2 (3/8) .... (Because 5 out 8 she supported feminist))
= 0.423 + 0.5306
= 0.9539

Well we calculated a measure of unpredictability. The measure of predictability is simply (1-unpredictability).

So people here we have the numbers on a scale of 0...1 (nice scale) as to who is more unpredictable than the other. A staunch feminist is unpredictable (0.543) and a weak feminist is (0.9533).

Well i will some food for thought.

When is unpredictability highest/lowest i.e 1 and 0. (in the dichotomy case)?
Why is the log to the base 2 ?
Many dollar Question. Is the weak feminist in our example a misogynist ?

Applications of the above include ?
- Qualitative analysis of 2 random number generators ?
- Manipulating sample spaces of an Exit polls in an election, thereby biasing the the most unpredictable voters towards a desired candidate.
- Understanding the other side of probability. i.e what are the chances that you will be hit by a result not obvious from an probability distribution.
- Appreciating unpredictability of a person. (nothing bad about the person he just has an higher index for randomness)

P.S None of the formulas are invented by me (it was Shannon), just to be clear about it. Example is mine and so are the applications.

The Raj Thackerey Paradox - The full story (full context is important)

Please watch the entire speech to make sense of it all.



RAJ adressing a sabha at borivali (east)....

Well my 2 cents:

The media is freaking biased against Raj and after listening to what he says I think he's got somewhat a point. Well i never changed my opinion in 180 degrees as I did after listening to what he says. (this is not because he is praising so particular community :D). I don't endorse any views but I don't like the media producing such a biased view about someone by taking his speech out of context. What to say - impressed by the oratory skills ?

And ... the reach of fair justice is universal. It includes everyone including Raj Thackerey. You for one matter cannot start dispensing justice by doing injustice to Raj's opinion as the first step. His rights for expressing concern cannot be overlooked. I think its a good problem to think about and get a fair solution may not always be possible. Plato's defination of justice fits in well over here.

--Snip--
"Plato described justice differently than most standard definitions. To Plato, justice meant carrying out one’s duty to one’s station, i.e. workers work, auxiliaries guard, and guardians rule. Under this premise, if lying is part of one’s job, it is only just if one lies. The reason the lie is noble is because it is for a noble cause: the good of the people.

Plato raised several questions that are still at the heart of many modern conflicts and heated debates. What is justice? What is goodness?"
.....
Irony is after all, a remarkably powerful teacher.
http://www.angelfire.com/md/byme/philosophysample.html
--Snip--

The Raj Thackerey Paradox: Well whats the point in Raj addressing in marathi? When only maharashtrians understand marathi. The audience is quite limited and people who need to understand Raj cannot understand marathi. Sigh !! Strange situation.

Well we are all Indians but I think we cannot dismiss Raj's opinion because it not that senseless

P.S Iam libra. They usually like to be on the other side of the discussion and probably more artistic about solving problems. And vanity is my favorite sin. As favorite as it was to Al pacino.