Doing some basic math in my head, I figure the probability of another nuclear detonation is a function of time and the existence of nuclear weapons:
While nuclear weapons exist, the probability that another one is dropped approaches 1 with the passage of time
And so it's imperative that, in the future, nuclear weapons are wiped completely from the earth.
Is it as simple as this?
And you have a magic wand that can get rid of all nuclear weapons?
Nope, I'm only talking the probability of nuclear holocaust from a high level.
And it only took us 13 posts to conclude with 'despite being an
intelligent species we're going to blow ourselves up eventually'.
That's not the conclusion. You aren't calculating the probability correctly. It's perfectly possible for the total probability to be less than 1 even when the probability in any given period is always nonzero, as long as the instantaneous probability keeps decreasing. The probability that another nuclear weapon will be used is 1 - the probability that another will never be used. The probability that another will never be used is the probability that one won't be used in the 21st century, times the probability that one won't be used in the 22nd century, times the probability that one won't be used in the 23rd century, and so on forever. If we can get the non-use probability per century up to 99%, and then up to 99.9%, and then just forever keep on adding more nines, then the overall probability of non-use for the rest of eternity can asymptotically go to 93% or whatever, depending on exactly how fast we keep adding nines.
If that's hard to follow, here's a simplified calculation. (This formula isn't quite right, but it correctly conveys the flavor of the mathematics.) Suppose the total chance of a nuclear attack some time in the 21st century is 10%, and in the 22nd century it's 5%, and in the 23rd century it's 2.5%, and so on, forever. Then the overall probability that one will ever be used anywhere on earth, at any point from now to forever, is only 20%.
So no, we don't have to get rid of them. We just have to commit to a permanent lifestyle of better and better security practices, arms control treaties, verification measures, and international conflict de-escalation.