Effect of catastrophe upon continuum statistics

[Loren Booda]

How does one incorporate discontinuity into otherwise continuous probability? The game of blackjack comes to mind - one may win by accumulating card values more than an opponent, but only up to the cutoff of 21 points, beyond which one most precipitously and surely loses. Optimum play may be calculated for the finite deck and discrete card values, though.

What if we are initially dealing with continuous values below that point which corresponds to the beginning of a zero-valued continuum? For instance, how do we know how much money to save and spend for retirement? We compensate for our impending, sudden and absolute zero of death by willing our estate, or elsewise relying on the security of family. We attempt to smooth out stochastic corners, the infinite uncertainties of our existence.

Is the time evolution of instantaneous quantum measurement probability (like that of radioactive decay) to any degree finite, because the "continuum" of measurements has a beginning and an end and because time is quantized (both like blackjack)? Does the local wavefunction actually rely on discrete observables, therefore discrete limits, on phase space?

If we encounter a (physical) singularity, what effect does that have on our past, present and future statistics?

 

[bogdan]

Tricky question...
I have just NO idea...as long as I try to think continuously...
Discontinuity appears only in the context of continuity...it's not possible viceversa...
A probable cause of the fact I have no idea is that I don't clearly understand what do you understand by "statistics"...or what do WE understand...

 

[tacman]

The effect of catastrophe upon continuum statistics can be significant and challenging to incorporate into traditional probability models. This is especially evident in scenarios such as the game of blackjack, where there is a clear discontinuity at the cutoff of 21 points. In order to incorporate this discontinuity into the otherwise continuous probability, one must consider the finite deck and discrete card values and calculate optimal play strategies accordingly.

Similarly, when dealing with continuous values that may eventually reach a point of sudden and absolute zero, such as in planning for retirement, we must find ways to smooth out the stochastic corners and uncertainties of our existence. This can be achieved through various means such as estate planning or relying on the security of family.

In terms of quantum mechanics, the time evolution of instantaneous quantum measurement probability may also have finite aspects due to the beginning and end of the continuum of measurements and the quantization of time, similar to the game of blackjack. This raises questions about the reliance of the local wavefunction on discrete observables and limits on phase space.

If we encounter a physical singularity, it can have a profound effect on our past, present, and future statistics. This is because a singularity represents a breakdown in our understanding and ability to predict events, making it difficult to incorporate into traditional probability models. In such cases, we may need to reassess our methods and consider alternative approaches to incorporate these singularities into our statistical analysis.