Saturday, 5 March 2016

People do sin, no matter who they are!

If you check the meaning of the word "sin" in a dictionary it is something like "transgression of the law of God", I am going to rephrase it as "violation of the society accepted law" to talk about the nature of our decision making or the way our brain works. It is obvious why I'm using the rephrased version, isn't it?

Scenario
Consider a small city in which the wealthiest family of the city invites all the people to a party in their house. People know they always keep a vast amount of money and jewellery in one of the open rooms of the house. There are rumours that they do not even have any idea of the quantity of money or jewellery in that room, so if you take something from that room, they are not going to find it out. There is no CCTV or alarm system as well. Mr X is our subject who suddenly finds himself at the door of the mentioned room, and now we want to analyze the process of his decision making.

Look at the following simple network which shows the current state of Mr X and the options he has to do or thinks about them at the door.

Data Network of Mr X's status and the actions he can choose from.

The middle column contains nodes which define the current status of the state of our subject Mr X, and the side nodes are the actions he might choose. You can set any metrics or parameters might involve in his decision making or any options he may go for it. So you are free to increase the number of nodes in the middle column or sides. They just add more nodes and edges to the network and doesn't change the nature of our reasoning.

The process of decision-making
So thinking of Naive Bayesian, if we have access to the state of Mr X, we can find the probability of taking any of the available options as bellow:

P("action") = P("action" | "Curiosity") . P("action" | "Financial status") . P("action" | "Survival status")      [1]

Here "action" can be any of the side nodes. For example, if our Mr X is in the state we call it "worst state" like the following:

"worst state" :[ Curiosity = high, Financial Status = very bad, Survival Status = in danger ]

According to the values for each connection, the probabilities of actions are:

P("picking something" | "worst state") = p10 . p16 . p19

P("take a look" | "worst state") = p7 . p13 . p20

P("join the crowd" | "worst state") = p1 . p4 . p23

Or if the subject is in the state we call it "bast state" as bellow:

"best state" : [ Curiosity = low, Financial Status = good, Survival Status = safe ]

Then the actions probabilities is:

P("picking something" | "best state") = p3 . p6 . p24

P("take a look" | "best state") = p9 . p15 . p21

P("join the crowd" | "best state") = p12 . p18 . p22

The Same calculation can be done for any of 18 (= 2 x 3 x 3) states of Mr X, so for each of these 18 states, we can compare the probabilities and find out the which of these 3 actions is most likely to get done by him.

The probability values for edges of the graph are from what Mr X has experienced or learned in his  life and definitely for some people the calculated likelihood of "picking something" from the room in "best state" is more than the two others.

So basically, what I mean is that whomever this Mr X is, even in the best status of his moral, financial, ... life, we can calculate the probability of making a wrong decision. However, you may claim, the probability is not necessarily non-zero for anybody or it could even be a very small and Mr X would never do that wrong thing!

It is all about brain's wiring 
If there is something in your mind and you think about it, even if it somehow is forbidden; it doesn't mean you will never do it, it means the likelihood of doing that thing is tiny. 
In fact, when you think about it, it means the required connections exist in your mind. If you think about what in that room is? or what if I had just a single piece of those jewels? etc, it means the required connection exist in your mind. (We already have talked about how habits appear in our mind, get strong or weaken in our brain.)

Let me give you an example, you have some guests tonight, and your mum or spouse has bought some cookies and pastries. You come back from school or work; you are hungry, and you know these cookies or cakes are for guests, not you. You simply do the math and compare the cost or consequences of eating some of them and the satisfaction or the pleasure it gives you! That's it. You put both sides of the scenario on the scale.
The action you take is the result of your decision and it all depends on the wiring of your data network in your brain, which you may call it the mind. 

And putting on the scale is exactly like calculating the probabilities, but note that:
There is no classical boolean logic or "if ... then ... else ..." module in our brain, all is about a neural network or the wired data.

Now when it comes to decision-making the logic we use, comes from the data network we have in our brain, the mind. This logic is not the classical Boolean Logic, it is Fuzzy, and if you think (or study) about it, the Fuzzy Logic and Probability are very closely related concepts. It means what we have in classical Boolean Logic like:

if (it is good) then {
    do it
} else {
   do not do it
}

is more like:

1- Calculate the probabilities of P("it is good") and P("it is not good")
2- Toss a not fair coin with probability ratio of P("it is good") to P("it is not good")
3- Now based on the outcome decide to do it or do not do it

The above is what we talked about it in our previous post as the random walk on a graph and classical boolean logic is just a subset of this idea in which one of the probabilities is one, and the other one is zero.

What that means, is that for our cookie example even if you are not hungry at all, and know the consequences of eating the cookies are terrible, there is still a slight chance of doing that. When there is a chance, if you meet that situation enough (the law of large number) eventually, you'll eat some cookies even though your are not hungry and you know it costs you a lot. For our first scenario, Mr X, if he continues being in that situation more and more, finally someday he'll take something from the room regardless of his status or personality. 

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