This is another very descriptive note about wave probability:
Only in quantum mechanics does the amplitude of a wavefunction refer to probability.
It was discussed on the 18th of June that the space of picking a ball for N times should consist of all mental copies of that experiment (i.e. S_1, S_2, etc – https://alirastegar.net/index.php/2024/06/18/w48-18-june-2024-phys-bio/). It was then said that S_i is one micro-sate for that particular macro-state (p(A)=p(B)=p(C)=1/3).
The probability of a macro-state is based on the number of its micro-states. If each micro-state is expressed as a wave (in some space), then all micro-state interferences specify the amplitude of the overall macro-state’s wave. This is similar to quantum mechanics (the probability of that particular macro-state is expressed as the amplitude of a wave).
This is also like the Fourier transform. A wave is decomposed into inf many sine waves by changing the domain from time to frequency. Similarly, the probability of picking a ball for example can be decomposed into inf many waves (each wave in this context is one realization of that experiment, in this example picking a ball from the bag). So something similar to the Fourier transform occurs in the wave probability too.
UPDATE 1:
If each experiment (i.e. each time a ball is picked) is expressed as a wave, some sort of rotation should be attached to that experiment. Inspired by quantum mechanics, spin is the best option for developing the wave. It means each experiment should be, in some space, expressed as a type of rotation, where fuzziness occurs (i.e. values in the range [0,1] are produced). So each experiment should be defined in some space where probability is not binary (picked, not picked) instead it’s a value in the range [0,1]. then it’s possible to attach variable probabilities at different experiments (for example the probability of picking a particular ball after N experiment if that ball has never been picked is psychologically higher).
Things are still very ambiguous at this point (for example what do minus probabilities imply?) but it’s a bit clearer than the first explanation where wave probability was said to be about a rotating wave viewed from different perspectives.