Is anything possible? If so, is it a paradox?

[I_Love_Me_Vol.I]

@Alan_Smithee

But even something with a zero percent chance can happen. The odds of hitting any particular point on an ideal dartboard are exactly zero (since there are an infinite number of points on a dartboard). That does not mean that you can never hit the dartboard.

I’ve heard this “dart/dartboard/zero percent chance” thing before and it has never struck me as very compelling.

Is there a better illustration of “something with a 0% chance” happening? Because every dart has a pointy end of measurable size. If one divides the area of the dartboard by the size of the dart’s tip that would lead to the probability of the dart hitting any given spot on the board. It would certainly be more than 0%.
ETA: looks like I’ve been beaten to the punch on this. But I still don’t see it.

I thought that if something is possible it is said to have a “non-zero % chance” of occurring. I’m not much of a mathematician so I’ll admit I have trouble seeing how a “zero % chance” of an event is the same as a “non-zero % chance”.

[Luk3112]

@Trinopus

This is a classic among sophomore philosophy students.

“It is possible…even though hugely unlikely…that a fair and honest roulette wheel will turn up hitting number 21 (red) five hundred times in a row.”

In some sort of pure abstract hypothetical theory, maybe it is possible. But it won’t happen. Mark this well: it will not happen. And that which will not happen isn’t “possible” in a pragmatic sense. It isn’t meaningfully possible.

In physics and thermodynamics, it is “possible” that all the molecules of air in the room will rush over to one corner, leaving a soft and very temporary vacuum. Again, this will not happen. The possibility is not only remote; it is (pardon the play on words) vacuous.

A solid gold meteorite might land in my back yard. A group of sunspots might form the Coca Cola logo. A cluster of minor earthquakes might signal “What Hath God Wrought” in Morse Code.

Rush Limbaugh might say something sensible.

Not gonna happen.

Hit the nail on the head.

[Trinopus]

@I_Love_Me_Vol.I

I’ve heard this “dart/dartboard/zero percent chance” thing before and it has never struck me as very compelling. . . .

Because every dart has a pointy end of measurable size. If one divides the area of the dartboard by the size of the dart’s tip that would lead to the probability of the dart hitting any given spot on the board. It would certainly be more than 0%.

Yep! I posted essentially the same thing. Darts aren’t mathematically abstract Euclidean points. They’re physical objects with non-zero width. Even if you had a dart-point only one atom across, the places it can go are limited. Quantized.

I thought that if something is possible it is said to have a “non-zero % chance” of occurring. I’m not much of a mathematician so I’ll admit I have trouble seeing how a “zero % chance” of an event is the same as a “non-zero % chance”.

I think I see three different kinds of “impossible” being talked about here.

Type I is “by definition impossible.” It is impossible for an odd number to be an even number.

Type II is perhaps possible in the abstract, but the probability is really zero.

Type III is where the odds are so close to zero that no one could ever meaningfully distinguish them.

The real juice of the debate is: are there any examples of a Type II impossibility? Or are all such examples actually Type III impossibilities? Is there any non-zero chance, at all, that an ordinary egg can survive, unbroken, if you shoot it dead-center with a 30.06 rifle? Or is there some ultra-microscopic chance that a lucky random distribution of the molecules of the eggshell could, without invoking miracles, bounce the bullet away? “Wow, did you see that? That wouldn’t happen one time in a trillion!”

The next question is: has a Type III impossibility ever actually happened? What, in all the universe’s history, is the single most “unlikely” event actually to have occurred? For instance, how far has an electron ever randomly tunnelled, by quantum laws? Since we know that there are quadrillions of electrons constantly subjected to electro-magnetic potentials…and since we know that many of them are, right now, tunnelling through such barriers…some very unlikely such tunnelling events must have occurred. There has to have been one event that stands out as the most unlikely.

What, then, are the highest odds that have ever actually been overcome?