Impossible probability between theoretical possibility and reality

In summary, "Impossible probability between theoretical possibility and reality" explores the gap between what can theoretically happen and what actually occurs in practice. It discusses how certain events may be deemed possible in theory but are rendered improbable or impossible due to real-world constraints and variables. The tension between theoretical frameworks and empirical evidence highlights the complexities of understanding probability in various contexts.
  • #1
Kinker
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TL;DR Summary
Even if it is theoretically possible, does the physical probability of such an event in reality become 0 because there is a lower limit to the possibility of such an impossible event in reality?
Boltzmann's brain, entropy reduction, Poincaré's recursion theorem, the probability of oxygen molecules in a room gathering in one place, the probability of quantum tunneling of macroscopic objects, etc. are theoretically possible. But the probability of these events is very low. Additionally, physical interactions with the environment, emergent properties, and other factors make it even more difficult. Is there a difference between theoretical possibility and real possibility? Even if the time of the universe is infinite, are the above events only theoretically possible and will never happen in reality?
 
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  • #2
As best that is known, if the probability is theoretically tiny but non-zero, that it what should be expected from experiments. But it's always open to more precise verification.
 
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  • #3
As soon as we have observed for an infinite amount of time, we'll let you know. :smile:
 
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  • #4
phinds said:
As soon as we have observed for an infinite amount of time, we'll let you know. :smile:
You must do it. It's a promise😜
 
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  • #5
Kinker said:
Even if the time of the universe is infinite, are the above events only theoretically possible and will never happen in reality?
If the time is infinite, these things will not only happen, but happen infinitely many times.
 
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  • #6
Demystifier said:
If the time is infinite, these things will not only happen, but happen infinitely many times.
Isn't the probability of an event a measure of possibility, not certainty? Is the infinite monkey theorem valid in the reality of a universe with infinite time?
 
  • #7
Kinker said:
Isn't the probability of an event a measure of possibility, not certainty? Is the infinite monkey theorem valid in the reality of a universe with infinite time?
Yes. So?
 
  • #8
Demystifier said:
Yes. So?
Infinity cannot exist in reality, right? Therefore, I do not believe that the infinite monkey theorem is completely valid in reality. In reality and physics, I think an error occurs if you substitute infinity.
 
  • #9
Kinker said:
Infinity cannot exist in reality, right? Therefore, I do not believe that the infinite monkey theorem is completely valid in reality. In reality and physics, I think an error occurs if you substitute infinity.
You are making a category mistake. Infinity theorems, or any mathematical theorems for that matter, do not depend on physical reality.
 
  • #10
Demystifier said:
You are making a category mistake. Infinity theorems, or any mathematical theorems for that matter, do not depend on physical reality.
Probability does not indicate the certainty of an event, so wouldn't an event with an extremely low probability never occur even in a universe with infinite time?
 
  • #11
Kinker said:
Probability does not indicate the certainty of an event, so wouldn't an event with an extremely low probability never occur even in a universe with infinite time?
No, your reasoning is wrong.
 
  • #12
Demystifier said:
No, your reasoning is wrong.
Why? what is the reason?
 
  • #13
Kinker said:
Why? what is the reason?
Because for any arbitrary small ##{\cal P}>0## there is a sufficiently large ##T<\infty## such that ##{\cal P}T=1##.
 
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  • #14
Kinker said:
Infinity cannot exist in reality, right? Therefore, I do not believe that the infinite monkey theorem is completely valid in reality. In reality and physics, I think an error occurs if you substitute infinity.
Be patient, none of these events require an infinite amount of time.
For example, in the monkey experiment, it may only take a billion billion years for a billion monkeys to outdo Shakespeare.
You just need to keep them fed and their typewriters in good working order for that amount of time.
I'm not saying things could not go wrong. In that amount of time those monkeys could evolve - and perhaps decide to test your narrative skills.
 
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  • #15
Kinker said:
Isn't the probability of an event a measure of possibility, not certainty? Is the infinite monkey theorem valid in the reality of a universe with infinite time?
Methinks you miss the point. It is possible that the monkeys would produce Merchant of Venice overnight (with lotsa coffee)
I feel it necessary to reference a favorite comedy bit on the subject
 
  • #16
.Scott said:
Be patient, none of these events require an infinite amount of time.
For example, in the monkey experiment, it may only take a billion billion years for a billion monkeys to outdo Shakespeare.
You just need to keep them fed and their typewriters in good working order for that amount of time.
I'm not saying things could not go wrong. In that amount of time those monkeys could evolve - and perhaps decide to test your narrative skills.
They tried this with some real monkeys. The monkeys soon got bored and one defecated on its typewriter.
 
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  • #17
Demystifier said:
Because for any arbitrary small ##{\cal P}>0## there is a sufficiently large ##T<\infty## such that ##{\cal P}T=1##.
In reality, there is no infinity, right? Isn't that moment finite, no matter how old it is? I think it is a paradox to make predictions by substituting infinity in reality.
 
  • #18
Kinker said:
In reality, there is no infinity, right? Isn't that moment finite, no matter how old it is? I think it is a paradox to make predictions by substituting infinity in reality.
Take the longest moment of time that you care about. Multiply it by the largest number you can think of. An infinite universe will exist longer than that.
 
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  • #19
Kinker said:
Isn't that moment finite, no matter how old it is?
Didn't I write ##T<\infty##?
 
  • #21
Demystifier said:
Didn't I write ##T<\infty##?
So, are the events presented above inevitable?
 
  • #22
Kinker said:
So, are the events presented above inevitable?
Is the event with probability 99.999% inevitable?
 
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  • #23
Demystifier said:
Is the event with probability 99.999% inevitable?
Yes, I think so. But my head hurts.
 
  • #24
Kinker said:
Yes, I think so. But my head hurts.
That’s because you’re trying to make a distinction between “can’t happen” and “could happen but won’t”. You can avoid the pain by not using ill-defined terms like “inevitable” or “infinite” and instead thinking in terms of the probability of something happening as a function of time.
 
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FAQ: Impossible probability between theoretical possibility and reality

What is the concept of "impossible probability" in theoretical terms?

In theoretical terms, "impossible probability" refers to events that have a probability of zero. This means that, according to the theoretical framework or model being used, such events cannot occur. It is important to note that this is different from events that are merely highly improbable; impossible events are those that are deemed to have no chance of happening under any circumstances within the given model.

How does "impossible probability" differ from "improbable events" in real-world scenarios?

While "impossible probability" refers to events with a zero chance of occurring, "improbable events" are those that have a very low but non-zero probability. In real-world scenarios, improbable events can and do occur, albeit rarely. For example, winning a lottery is highly improbable but not impossible. On the other hand, an impossible event, like flipping a fair coin and getting a result other than heads or tails, cannot happen.

Can theoretical impossibilities ever become possible in reality?

In some cases, what is considered theoretically impossible might become possible with new knowledge or a better understanding of the underlying principles. For instance, certain scientific phenomena that were once deemed impossible have been observed and explained as our scientific models and technologies have advanced. However, some theoretical impossibilities, such as violating the fundamental laws of physics, are unlikely to ever become possible in reality.

How do scientists deal with "impossible probabilities" when developing models?

Scientists often use the concept of impossible probabilities to define the boundaries and limitations of their models. By identifying events that are theoretically impossible, they can better focus on the range of possible outcomes and refine their models to more accurately reflect reality. This helps in making predictions and understanding the behavior of complex systems within the constraints of the model.

Are there practical applications of understanding "impossible probability" in fields like engineering or computer science?

Yes, understanding impossible probabilities has practical applications in various fields. In engineering, it helps in designing systems that avoid failure modes deemed impossible by theoretical models, thus ensuring safety and reliability. In computer science, particularly in fields like cryptography and algorithm design, recognizing impossible events can optimize performance and security by focusing computational resources on feasible outcomes. This understanding also aids in risk assessment and decision-making processes across different industries.

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