@Mopman said in #30:
> Sorry friend there is a mathematical flaw in your argument. Flip a coin 10 times and have it land heads each time. What are the odds of the next flip showing heads. Answer: 50-50 ( look it up ) . You need to remember that a random chance does NOT have a memory of what happened before or it is no longer random.
>
> So the fact that a nuclear war is possible does not mean it MUST happen given enough time.
>
> That being said , the world would be a much safer place without nuclear weapons and if there was some reasonable method of policing and ensuring all nations actually disarmed without secretly stockpiling them , that would be a good thing.
>
> I do not think any of the major powers would trust each other enough to not have a stockpile stored away "just in case" .
Lol you don't understand probabilities much, do you?
Yes, after flipping the coin 10 times, the probability of getting heads the eleventh time does not depend on the past results.
That does not contradict the fact that if you keep flipping a coin again and again, then with probability one you will eventually get heads (though there is no way to predict for sure how long it will take).
That might appear counter-intuitive, but there is no contradiction between these two statements.
Edit: a small complement about probabilities, because I don't want to ask you to take my word for it. It's maths, after all.
Let's say every year there is a probability p that there is a nuclear war. So for a given year, the probability of there not being a nuclear war is 1-p. Then the probability that there is no nuclear war for n consecutive year is just (1-p)^n. Now let P be the probability that there will never be a nuclear war. If there never is a nuclear war then in particular there is no nuclear war for n consecutive years. Thus P is obviously smaller than the probability that there is no nuclear war for n consecutive years. But that holds for any arbitrary n. Which means P is smaller than (1-p)^n for all n. Now if p is non-zero, then 1-p is larger than 0 and strictly smaller than 1, from which follows that as n gets larger and larger, (1-p)^n becomes arbitrarily small. So P is a non-negative number which is also smaller than any arbitrarily small positive number. We see that the only possibility for P is P=0.
If that is too abstract for you, let's take a concrete example. Assume that the probability of a nuclear war occuring is 0.1% every year.
Then the probability of having at least a nuclear war occuring within 10 years is 1-0.999^10=0.9955%, still pretty small.
The probability of having a nuclear war within 100 years is 1-0.999^100=9.52%, already more scary.
Within 1000 years is 1-0.999^1000=63.23%, really scary.
And within 10000 years is 1-0.999^10000=99.995%, so almost sure.
But of course that doesn't change the fact that if after 10000 years no nuclear war happened, then on the 10001-st year the probability of having a nuclear war is still the same, namely 0.1%.
