Isn't this just a simple matter of probability? Given an event, however unprobable it is, it can happen given infinite time? From a purely mathematical standpoint, this is correct.
Just because something has a nonzero probability doesn't mean it will ever occur.
Entropy is just dS = dQ/T. It's simply a thermodynamic property that measures where system energy is. All of these grand notions extrapolated from thermodynamics are crazy.
Thermodynamics is/was just a first approach at studying macroscale systems because we didn't yet grasp the underlying quantum behavior. It's incredibly useful when applied to chemical and physical problems, but you can't use it to make wild claims like this.
Its certainly possible that the universe will end in a crunch or a rip, and all this speculation will be for naught. But thermodynaics is still a perfectly valid way of looking at these things, and hasn't been changed much by the addition of quantum mechanics except that we now talk about probability distributions within phase space instead of points. Its basically the same stuff, with the same consequences.
Entropy is much more than just dS = dQ/T. I mean, that equation is mostly valid the same way that Newton's laws are mostly valid, but you won't be able to get any sort of feel for it approaching the subject that way. Imagine a mathmatical space with six dimensions for every particle, three for position and three for momentum. The state of the universe is a single point moving in this space according to pre-defined rules. Now, we don't know which point or microstate corresponds to our universe, because we can only make crude measurements of statistical aggregates of particles like temperature and pressure and so forth. So by making these measurements we can narrow which universe we're in to a set of these microstates, a 6N-k dimensional region of the 6N dimensional space that we'll call a macrostate. The entropy of an observed macrostate is proportional to the log of the number of microstates that a macrostate contains, S = k log W. In a sense, Entropy is a measure of our ignorance of which universe we're in, which is ultimately why Maxwell's demon doesn't work.
Please note, the above does contain simplifying assumptions which don't change the main point. For the full story, go get a physics minor at a good university or start reading Wikipedia[1] and asking your physics major friends questions until you can re-derive the laws of thermodynamics yourself.
If your assumption is infinite time and complete entropy, yes it's correct. It's also why some level of common sense (e.g. Occam's razor) should be applied before such silliness is seriously proposed. I don't think Boltzmann assumes infinite time and entropy, just enough for the completely random emergence of sentient life that thinks (perhaps falsely) that it lives in a universe populated by similar beings who created iPads from dirt and water.
Does it seem more reasonable that there is infinite time and every possible state of matter and history exists at some point, or that we simply haven't figured out the balancing forces of entropy and order?
Infinity is an interesting thought experiment, but it so thoroughly ridiculous that it should cause us to question our assumptions, not believe in absurdity conclusions based on faith in mathematics and unproven postulates that got us there.
We might as well believe the Bible is true. Not only is it less absurd, but given the infinite theory, there must exist a universe where it is true, and this could be it (unless it is truly contradictory and impossible even with infinite states of the universe, which we have no reason to believe.)
The absurdity heuristic is not a good way to decide what is true. People once thought that the idea of humans being descended from monkeys was absurd. Or that the earth going round the sun, rather than vice versa, was absurd.
Occam's razor is more sensible than the absurdity heuristic, but it applies to the fundamental building blocks of a theory, not to the outputs it predicts. So it would cut against a hypothetical unknown set of "balancing forces of entropy and order", since that's an entity not required by our current best known theories.
If a theory implies an absurd outcome, I think it is a reasonable heuristic to question the theory and it's assumptions. I am not saying absurd implications indicate the theory is flawed, only that they should cause one to suspect so and perhaps find a theory that explains reality with less broadly absurd implications.
The Bible as historical non-fiction is most certainly absurd, no implications about that. Not saying so out of sensitivity to those who believe otherwise does reason a disservice, just as not calling out Bolzmann because I don't want to offend him. If this makes anyone unwelcome, they should avoid places where their fragile ego might be challenged by rational conclusions. In a place like hacker news, I see no reason to let sensistivity toward faith restrict my speech any more than sensitivity toward programming language choice. Invite me for dinner and I will respect your religious and any other beliefs. Have a scientific debate in a web forum with me, and I will speak without concern for challenging you. It's not a personal attack to say the Bible is absurd - it's the truth.
By the same standard, "SOPA sucks. Just like PHP/Java." is appropriate. "PHP/Java sucks" may be appropriate when discussing programming languages, but dragging it into a thread about SOPA does not help.
I'm not sure I understand your point. "SOPA sucks. Just like PHP/Java" is a useless statement, since the only thing the two have in common is "sucking."
The Bible is an alternative theory of the origin and purpose of existence, and is directly analogous to the matter of this thread.
Occam's razor says that we should give more credence to the simpler theory, not the more commonsensical one, and I assure you that statistical mechanics is elegant in its simplicity. I hope you don't also go around telling biologists that its absurd that we're descended from Apes, or astronomers that its absurd that the Earth goes around the sun? How about atomic thoery (which Boltzman was an important proponent of)? Unlike the Bible Botzman was working from quantitative theories backed up by scientific experiments. You might say that being a famous scientist is almost the same as being someone who has said things that were regarded as utterly absurd, but which were true.
> Occam's razor says that we should give more credence to the simpler theory, not the more commonsensical one
Yes, and I find Occam's razor itself to be common sense, which is what my point was. If a theory seems to reflect more closely observable reality, I would bias my investigations toward that theory over one the projects something non-sensical.
> I hope you don't also go around telling biologists that its absurd that we're descended from Apes, or astronomers that its absurd that the Earth goes around the sun...
Evolution and Earth's orbit are explanations for observable reality. They do not lead us to conclude outlandish things that are conveniently not observable.
I am not saying Boltzmann was necessarily wrong, only that common sense should direct us to look for what we are missing, and for theories that direct us toward more sensible scenarios. Sure Boltzmann, could be right. I find the Bible more compelling, and Bolzmann's theory doesn't seem to preclude them both being correct.
> If a theory seems to reflect more closely observable reality, I would bias my investigations toward that theory over one the projects something non-sensical.
I don't understand your basis for saying one theory matches observable reality more closely than the other. I mean, have you observed the heat death of the universe? And how can you say that what is being projected is non-sensical, except to the extent that people reliably find arguments involving infinity hard to make sense out of?
It might be that theory of evolution and the heliocentric theory purport to explain the world we observe, but the much more sensible seeming theories that they replaced also purported to explain the world.
As for the Bible being more compelling, well, I'm not surprised since many other people who prize gut feelings over abstract reasoning feel the same way.
