Examples
The textbook examples for the application of the principle of indifference are coins, dice, and cards.
In a macroscopic system, at least, it must be assumed that the physical laws which govern the system are not known well enough to predict the outcome. As observed some centuries ago by John Arbuthnot (in the preface of Of the Laws of Chance, 1692),
- It is impossible for a Die, with such determin'd force and direction, not to fall on such determin'd side, only I don't know the force and direction which makes it fall on such determin'd side, and therefore I call it Chance, which is nothing but the want of art....
Given enough time and resources, there is no fundamental reason to suppose that suitably precise measurements could not be made, which would enable the prediction of the outcome of coins, dice, and cards with high accuracy: Persi Diaconis's work with coin-flipping machines is a practical example of this.
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