If you’re a hard determinist, probabilities have no independent existence—they are merely a measurement of human ignorance.
In (a hard determinest) reality, what happened was always going to happen and could not have happened otherwise. Similarly, what will happen is the only thing that could have happened and even the phrase “could have” is incoherent as there is only one possibility—what actually happens.
In quantum chaos, people call th absolute value of the first Bessel function a probability. That's deeply problematic. If, interpreted as discrete (time) then likely the sum is not unity. If interpreted as continuous (time) the function isn't monotone non-descending. It looks like people call numbers between 0 and 1 a probability without noticing the Kolmogorov axioms.
The first time I noticed a confusion in terminology with respect to density and distribution was in a quantum physics introduction, and I’ve seen it elsewhere since. (I realize this isn’t exactly what your article is about.)
It isn’t hard to glean the meaning from context, but it is disconcerting.
Perhaps it’s because physicists eventually talk about Dirac’s delta function and they are thinking of the terms “generalized functions” and “distributions,” which are not about probability.
The older I get, the more I love math. Thx.
It's a probability density
If you’re a hard determinist, probabilities have no independent existence—they are merely a measurement of human ignorance.
In (a hard determinest) reality, what happened was always going to happen and could not have happened otherwise. Similarly, what will happen is the only thing that could have happened and even the phrase “could have” is incoherent as there is only one possibility—what actually happens.
In quantum chaos, people call th absolute value of the first Bessel function a probability. That's deeply problematic. If, interpreted as discrete (time) then likely the sum is not unity. If interpreted as continuous (time) the function isn't monotone non-descending. It looks like people call numbers between 0 and 1 a probability without noticing the Kolmogorov axioms.
The first time I noticed a confusion in terminology with respect to density and distribution was in a quantum physics introduction, and I’ve seen it elsewhere since. (I realize this isn’t exactly what your article is about.)
It isn’t hard to glean the meaning from context, but it is disconcerting.
Perhaps it’s because physicists eventually talk about Dirac’s delta function and they are thinking of the terms “generalized functions” and “distributions,” which are not about probability.