1. Interpretations of Probability
1.1. Bayesians and Frequentists
There are two possible ways to interpret the meaning of probability.
1.2. Maps and Territories
Here ‘territory’ refers to the world as it exists or the reality as it is.
The map refers to our model of the world or the way we see and interpret it.
We are constantly building ‘maps’ or models of the territory. The better our maps the closer we are to the ‘truth’.
1.3. PDFs – Existence in Maps or Territory
The main contention between frequentists and bayesians is the question: “Where do probability density functions exist – Do they exist in the map or in the territory?”
Frequentists hold that the probability density functions exist in the territory.
Bayesians believe that they exist only in our map of reality.
For example, suppose we toss a coin. Then the frequentists believe that there is a probability density function which is independent of our maps and interpretation of reality which forms the basis of randomness that is observed in the coin toss. Bayesians believe that if we know the force applied the fingers tossing the coin, the mass, shape and the orientation of the coin, the movement of molecules in the air at the time of tossing it, in summary if we have a very accurate model of reality than the probability density function changes and it might come to a point in this case where the entire question of coins landing heads or tails may become deterministic.
1.4. Many Worlds Interpretation of Quantum Mechanics
This states that there are multiple universe and each one corresponds to some combination of values which the various probability distributions of position and momentum happen to generate. If the many worlds interpretation is correct then our world is deterministic. Then the probability can only be in the map and not the territory.