Effect of catastrophe upon continuum statistics

In summary, the conversation discusses the concept of incorporating discontinuity into continuous probability, using examples such as the game of blackjack and retirement planning. The speakers also mention the role of discrete observables on phase space and the effects of encountering a physical singularity on past, present, and future statistics.
  • #1
Loren Booda
3,125
4
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?
 
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  • #2
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...
 
  • #3


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.
 

1. How does a catastrophe affect the continuity of statistics?

A catastrophe can disrupt the normal flow of events and can cause a sudden change in statistics. For example, a natural disaster such as a hurricane or earthquake can significantly impact the continuity of statistics by destroying data collection methods and altering the parameters being measured.

2. Can a catastrophe alter the overall trends and patterns in continuum statistics?

Yes, a catastrophe can greatly influence the overall trends and patterns in continuum statistics. This is because it can produce extreme and sudden changes in the data, which can significantly impact the statistical analysis and interpretation of the data.

3. How do scientists account for catastrophes in their continuum statistical models?

Scientists can account for catastrophes in their continuum statistical models by incorporating them as outliers or anomalies in the data. They can also adjust their models to include the impact of the catastrophe and make predictions based on these adjustments.

4. Can a catastrophe lead to a breakdown in the continuum statistical model?

In some cases, a catastrophe can lead to a breakdown in the continuum statistical model. This usually occurs when the catastrophe causes such a significant disruption in the data that it becomes impossible to accurately analyze and interpret the results. In these cases, scientists may need to adjust their model or develop new ones to account for the changes.

5. How can understanding the effect of catastrophes on continuum statistics help in disaster management?

Understanding the effect of catastrophes on continuum statistics can greatly aid in disaster management. By analyzing past data and predicting the potential impact of a catastrophe on statistical trends, scientists can help inform disaster management strategies and aid in preparedness efforts. Continuum statistics can also be used to track the progress and effectiveness of disaster management efforts after a catastrophe occurs.

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