[PartiallyTyped]

Any point is infinitely improbable when sampling with infinite precision, only because this calculation is not computable.

Even if the point probability is 0 or approaching zero very fast, some event occurs with probability 1.

The probability that life would evolve on a blue planet that its anthropomorphic inhabitants will come to call Gaia or Earth, has as a star Sol, in this corner of the Milky Way, in this particular local group and so on is zero even if we limit ourselves to just the observable universe.

At the same time the probability that life will exist at some planet at some solar system at some galaxy at some local group and so on, is practically 1.

That is to say, depending on how you categorise and count said marbles, the reordering may occur.

While any individual marble will not be at its place with P=1. You can still end up in a situation where the marbles are ordered in layers.

The whole thing regarding entropy is concerned with a closed system. You can very much exchange energy to decrease entropy, but said exchange is a) leaky, and b) implies that the system is not isolated.

[a257]

A probability of zero does not mean that the event is impossible. When we refer to probabilities we are talking about probability densities. Infinite precision is a useful modeling tool in the same way that approximations of pi are useful.

[PartiallyTyped]

I think I was misunderstood. My comment regarding infinite precision was mostly aiming to argue that any single point has probability zero but an event still occurs.

This was then used again when mentioning earth to argue that depending on the definition of "order" here:

> And no practical amount of shaking the jar will ever return the marbles to a high order state again.

It is entirely possible to reach a state of higher order if you don't require that individual marbles don't hold the same arrangement relative to adjacent marbles, meaning that any permutation of marbles with identical color is acceptable.

This happens because the event you are asking for is a very large subset.

[lupire]

Define "large", at least in an estimate. Dividing two astronomically large numbers is not easily estimated. And define "entirely possible". Yes, could happen once, maybe, in the entire Universe is entirely possible. Anything is "entirely possible" because humans are not omniscient, so we have to start from Bayesian priors.

[dekhn]

In a well defined system, a probabiltiy of zero by definition means an event is impossible.

[lupire]

In physics, nothing can be measured exactly, so exact events are in fact impossible. Measurements are approximate, and thus have finite extent, and thus can have nonzero probability.

This whole thread is silly, The 2nd law is about probabilities which are asymptotically 0, so small in practice that we could never do experiments to frequentist probability empirically, using "jars of marbles" with more than 100 marbles", let alone trillions of trillions of particles.

[a257]

That is a great point. The laws of thermodynamics exist as a logical consequence to fundamental statistical principles. It is statistical mechanics that gives rise to entropy, not the other way around. (hence the beautifully elegant equation S = Kb*ln(Omega) where Omega is the number of microstates)

I realize that programmers are not always good scientists. Yet some claims are absurd in ways that I now believe this phenomenon necessitates rigorous study.

[a257]

> Zero probability does not mean an event cannot occur! It means the probability measure gives the event (a set of outcomes) a measure zero. [0]

[0] https://stats.stackexchange.com/a/273398