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On "Fairness" of outcome of Flip of a Fair Coin.

posted Apr 6, 2012, 11:16 PM by Pratik Panchal   [ updated Apr 9, 2012, 11:05 PM ]
7th April, 2012, @stacks, Uris.

The arenas in which probabilities work 'too much' is something which I find difficult to comprehend. Say for example, the flip of a fair coin.



We say that the probability of an outcome - heads or tails - in case of a flip of a fair coin is 0.5. Well, isn't on larger scale, it is possible to know the outcome with certainty by referring to the kinetics of bodies? Taking this example of coin, isn't the outcome a function of following actions (variables):

1. The mass of the coin.
2. The state of coin just before flipping (which side is up and which side is down, and at what angles).
3. The vector force (which enables the coin to attain a height) given to it to move upwards.
4. The angular torque (which gives the coin its rotational speed) provided.
5. The air resistance that the coin is traversing through.
6. The gravitational field in which it is moving.
7. The instant at which it is caught.

Well, all these are real valued variables and if we precisely are aware of them and fit them into a beautiful equation describing the motion of the coin, we can say with certainty that if the coin is caught at a particular time instant t, the "heads" will be up.

Well, so, I asked Skye Nebulae,  a dear friend of mine, what do we mean by probability in such a case. What set of actions will make the outcome probable. Well the obvious reasoning was that "we don't know" with what (above mentioned) variables will we be flipping the coin and that is what will make the outcome probable. But, that is what my exact point of conveyance is: Isn't a "set of probable outcomes" is a set of all solutions which will be achieved on varying the input variables (the above mentioned points) from extremes? Isn't it that we are grouping the "likely" solutions and surrendering to the probabilities because of the ignorance involved in the process of determining the state; I mean the process of capturing variable values and constructing motion equations.

Consider another example of throwing a pack of cards up in air. The position of each of the card, well, is function of initial ordering of the cards, throw-related variables, effect of air resistance, effects of inter-collisions, topology of landing surface and some others.

Well, it seems doable and can be extended to systems comprising of larger variables with apparent increasing complexities.

But, well, we also have giant beautiful foundations like Quantum Mechanics which largely is based on deterministic probabilities - and I'm in no position to write a further word on that. :-|


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