Thursday, November 19, 2009

God does not play dice

The title of this blog post is a famous quote by Einstein. This post is not on GOD or religion, but on the concept of probability. This post is also based on the concept of determinism and hidden variable theory.

First let's differentiate between an experiment and an event. An event simply occurs, whereas in experiment, we observe the event. Let's call this process of observing to note the outcome of the event as information retrieval process i.e we are trying to get information about the event when it occurs. Some of the information retrieval processes are seeing, hearing, or using any other sensory organs, taking a picture, video/audio recording, etc.

Note that information retrieval process may in someway disturb the event itself. See Heisenberg uncertainty principle. But for sake of this thought experiment, imagine we have some special information retrieval process that gets information about the event or experiment, without in any way disturbing the experiment. (Note, quantum mechanics says this is not possible. But I say this is not possible with currently available information retrieval mechanism. May be in future we may have sophisticated information retrieval mechanism where it might be possible).

Consider a experiment of rolling a dice. Do you think it is deterministic or probabilistic/stochastic ?

The deterministic point of view says that if we knew weight of dice, envirnomental factors (wind direction/strength, humidity), surface friction, density of dice, exact hand movements (angle of release, force during release), and many many other factors, then we can predict the exact outcome of the dice.

Since we don't know many of this factors (i.e hidden variables), we cannot predict the exact outcome of the dice. To model these variables, so that we can get very close to the outcome and in some way make the experiment useful, we use the concept of probability.

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