This is a question that I practically encountered while I was playing a game:
Is tossing a coin a deterministic experiment?
It might seem silly to ask but I had some thought over it.
By the definition of the term and apparent look, it is not. But I have a different notion.
Deterministic experiments have the same conditions (it may be physical or regarding apparatus) while conducting an experiment.
But while tossing a coin do we always apply the same force at the same point of the coin.
We toss with the same side of the coin upwards.
If we do so, then then the outcome would be same. A 10 kg block would move with 10 m/s² acceleration when a force of 10 N is applied. Similarly, if we toss a coin applying the same torque at the same point, then the number of rotations in the air would be the same and give a consistent result.
I was scolded by my teacher on asking this question.
Best Answer
I think a way to understand this is to compare to another deterministic transformation: the baker's map. If we always choose the same initial point in the square and apply 30 times the baker's map, the image of that point in the square will always be the same, in this sense, it is perfectly deterministic. But if we have the slightest inaccuracy in the initial position, the position after 30 iterations of the map becomes unpredictable, and has all the appearance of randomness.
Systems where small variations of the initial data implie large or unpredictable variations of the final outcome are common in mathematics. One often cites the butterfly effect in chaos theory to illustrate this. Many non linear hyperbolic systems of mathematical physics have the same behavior.