Effect of catastrophe upon continuum statistics

3,073
3
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 existance.

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?
 
191
0
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...
 

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